A projectile is launched at an angle from a cliff. Velocity vectors are shown on the projectile. Determine the acceleration of the object.
In order to check your answer, click Show Graph. Graphs of vertical ..

A cannonball is launched from ground level. The angle of launch can be changed. For any target position, what values can the launch angle have in order for the ball to hit the target?

A cannonball is launched from ground level. The angle of launch can be changed. For any particular launch angle, how can you calculate the maximum height of the ball, the time to reach that height, ..

A cannonball is launched from a cannon on a cliff. What must the launch velocity be for the ball to hit the moving target? How does this depend on the launch angle?

A cannonball is launched from ground level at 55 degrees above the horizontal and strikes a target. At what different angle of launch (but with the same magnitude of launch velocity) will the ball have the ..

The view is looking down on an air hockey table. A puck initially moving at constant velocity receives a momentary push in the +y direction at x = -2 as shown in each of the animations (..

A satellite moves at constant velocity when, at x = -2, its thrusters are suddenly engaged, producing a constant force perpendicular to its original motion. Which animation correctly depicts the satellite's motion after the thrusters are ..

A red box slides along a blue wall. A perpendicular force holds the box in contact with the wall. What effects do the mass of the box, initial velocity, magnitude of the force, and coefficient ..

A red box slides along a blue wall. A perpendicular force holds the box in contact with the wall. What effects do the mass of the box, initial velocity, magnitude of the force, and coefficient ..

A sonic ranger sends ultrasonic pulses at the rate of 10 per second toward a wall and receives the reflected pulses. The output of the ranger goes to a computer which calculates the distance between the ..

A car and a wagon move away from a sonic ranger at constant but different velocities. Sketch the graphs of position vs. time and velocity vs. time for the two objects. Sketch both position graphs ..

A car moves away from a sonic ranger at constant velocity and bounces off a wall. The velocity after the bounce is also constant but in the opposite direction. Predict the position, velocity, and acceleration ..

Starting from rest, a car coasts frictionlessly down a hill with constantly-increasing velocity. Sketch position, velocity, and acceleration vs. time graphs of the motion. Take the +x axis to point parallel to the hill as ..

Now check your predictions by running the applet and clicking on Show Graph to display position, velocity, and acceleration vs. time graphs for the motion down the plane.

After being given a push, a wagon moves up a hill, comes to a stop, and then descends. Sketch position, velocity, and acceleration vs. time graphs of the motion. Assume that the positive x-axis points ..

Now check your predictions by running the applet and clicking on Show Graph to display position, velocity, and acceleration vs. time graphs for the motion.

A block resting on a piston compresses an ideal gas enclosed in a box. The gauge to lower right indicates the absolute pressure of the gas in atmospheres. A thermometer indicates the temperature of the ..

Play the animation to view an object moving horizontally across the screen. Its acceleration is uniform. Step through the animation and take measurements of x-position and time to use for finding the acceleration. The object ..

Monochromatic light is incident on an air wedge. Play the animation to advance the position of the incident ray by the given increment. The effective path length is given as an output in units of ..

Monochromatic light is incident on an air wedge composed of two glass slides. The angle of the wedge may be changed by changing the height of the triangular post. Playing the animation advances the position ..

Monochromatic light is incident on an air wedge. Play the animation to advance the position of the incident ray. The phase difference is given as an output in units of wavelengths. All distance units are ..

Monochromatic light is incident on an air wedge. Playing the animation advances the position of the incident ray by the given increment. The effective path length is given as an output in units of wavelengths. ..

Light of the given wavelength is incident on an air wedge. Determine the height of the post. Greatest accuracy is achieved by changing the angle of incidence to 0 deg and positioning the incident ray at ..

Monochromatic light is incident on an air wedge composed of two glass slides. The angle of the wedge may be changed by changing the height of the triangular post. Playing the animation advances the position ..

Monochromatic light is incident on an air wedge composed of two glass slides. The angle of the wedge may be changed by changing the height of the triangular post. Playing the animation advances the position ..

Monochromatic light is incident at Point a on an air wedge composed of two glass slides. The angle of the wedge may be changed by changing the height of the triangular post. Playing the animation ..

Monochromatic light is incident on an air wedge. The angle of the wedge may be changed by changing the height of the triangular post. Playing the animation advances the position of the incident ray in ..

An observer at upper right views a neutrally-buoyant object (orange) in the water. The angle subtended by the refracted rays at the observer's eye is shown in yellow. The apparent position of the object is ..

An alien on shore observes a neutrally-buoyant object (orange) in the water. The angle subtended by the refracted rays at the alien's eye is shown in yellow. The apparent position of the object is shown ..

An alien on shore observes a neutrally-buoyant object (orange) in the water. The angle subtended by the refracted rays at the alien's eye is shown in yellow. The apparent position of the object is shown ..

An observer at upper right views a neutrally-buoyant object (orange) in the water. The angle subtended by the refracted rays at the observer's eye is shown in yellow. The apparent position of the object is ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. The pulley is supported from above. When the blocks are released, the system of the two blocks accelerates. What ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. The pulley is supported from above. When the blocks are released, the system of the two blocks accelerates.
Caution: ..

A car and its unseatbelted crash test dummy accelerates uniformly from rest toward an immovable wall. The car bounces off the wall and then decelerates uniformly to a stop.
Click Show Graph to display a ..

A car and its unseatbelted crash test dummy accelerates uniformly from rest toward an immovable wall. The car bounces off the wall and then decelerates uniformly to a stop.
Click Show Graph to display a ..

Two cars of equal mass and initial velocity to the right collide with a wall. One car is stopped in the collision and the other bounces off the wall with a velocity of smaller magnitude ..

A ball is projected vertically from a moving cart. Select parameters such that the ball will land in the cart. Velocity vectors are shown on the cart and the ball.

Run the applet to view the waves. The blue and green waves are superimposed to produce the red wave. When the frequencies are nearly the same, beats are produced. The gray lines show the envelope ..

Run the applet to view the waves. The blue and green waves are superimposed to produce the red wave. When the frequencies are nearly the same, beats are produced. Determine the frequencies of the green ..

The animation shows an object falling in a fluid with acceleration a = (k/m)v-g.
The positive direction is up.
The object has an intial position of 0 and is released from rest.
The given inputs ..

The animation shows a spherical object falling through a fluid with acceleration
a = (k/m)v-g. The positive direction is up. The object has an intial position of 0 and is released from rest. The given ..

The animation shows a spherical object falling through a fluid with acceleration
a = (k/m)v-g. The positive direction is up. The object has an intial position of 0 and is released from rest. The given ..

The animation shows a spherical object falling through a fluid with
acceleration a = (k/m)v-g. The positive direction is up. The object has an intial position of 0 and is released from rest. The given ..

The animation shows a spherical object falling through a fluid with
acceleration a = (k/m)v-g. The positive direction is up. The object has an intial position of 0 and is released from rest. The given ..

A simple circuit contains a battery, resistor, capacitor, and switch in series. The switch is initially open and the capacitor is fully discharged. Run the applet to close the switch. The lines represent the potential ..

A simple circuit contains a resistor, capacitor, and switch in series. The switch is initially open and the capacitor is fully charged. Run the applet to close the switch. The lines represent the potential differences ..

A ball is launched horizontally off a cliff at the same time that a cart directly below the ball is pushed in the same direction. By adjusting the height of the cliff as well as ..

Two objects collide and rebound from each other. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The lengths of the vectors are drawn to the same ..

Two objects collide and stick together. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The lengths of the vectors are drawn to the same scale.
Unphysical ..

Two objects collide and stick together. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The lengths of the vectors are drawn to the same scale.
Unphysical ..

Two objects collide. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The lengths of the vectors are drawn relative to the magnitude of the momentum. The ..

A bullet is fired horizontally at high speed toward a block of wood resting on a very long table. The bullet embeds in the wood. Kinetic friction between the table and the block brings the ..

A bullet is fired horizontally at high speed toward a block of wood resting on a table. The bullet is slowed through the block and exits on the opposite side. Kinetic friction between the table ..

Two gliders collide in an elastic collision. The red glider is initially stationary. The x-coordinate of the center of mass of the system of gliders is shown as a black dot. Play the animation. Click ..

Two gliders collide in an elastic collision. The center of mass of the system of gliders is shown as a black dot. Play the animation. The animation will stop at the beginning of the collision. ..

Two gliders collide in an elastic collision. The center of mass of the system of gliders is shown as a black dot. Play the animation. The animation will stop at the beginning of the collision. ..

Two gliders collide in an elastic collision. The center of mass of the system of gliders is shown as a black dot. Play the animation. The animation will stop at the beginning of the collision. ..

A green ball makes a glancing elastic collision with an initially stationary red ball. The balls have equal mass. The paths of the balls after the collision are perpendicular. The vectors shown represent momenta.

A green ball makes a glancing elastic collision with an initially stationary red ball. The balls have equal mass. The momentum vectors of the ball are shown.

Two gliders collide in an elastic collision. The x-coordinate of the center of mass of the system of gliders is shown as a black dot. Play the animation. Click Show Graph. The velocities of the ..

What is the total momentum of this system? Why can't you use the law of conservation of momentum to calculate what the velocities of both objects after the collision are?
There is nevertheless a way ..

Determine the center of mass velocity for this elastic collision. Why is the center of mass velocity the same before and after the collision? Look at the velocity vs. time graphs. If you added a ..

Two objects collide elastically. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The total momentum of the system of the two blocks is conserved.

An explosion is an interaction where the objects are initially at rest but move apart after the collision. Total momentum is also conserved in this situation. Create an explosion.
Try different values for the Forcefulness ..

Answer these questions using the animation. The grid spacing in meters is given in the upper right, and the elapsed time and masses of the objects are given under Outputs.
1. What is the velocity before ..

Assume that momentum is conserved in the collision of these two blocks. Use the applet to measure the velocity of the blue block before collision and both blocks after collision. Then sketch velocity vs. time ..

Two objects collide and stick together. The animation stops as the collision starts. You are to predict the velocity after collision of the combined blocks. Use the fact that the total momentum is conserved. This ..

Two objects collide and stick together. The animation stops as the collision starts. Use conservation of momentum to predict the velocity after collision of the combined blocks.
Also sketch the velocity vs. time graph for ..

One object moving left collides with another moving right. They stick together in the collision. The animation stops as the collision starts. Use conservation of momentum to predict the velocity after collision of the combined ..

Create a collision where the combined blocks move to the left after the collision. You can change masses and initial velocities. After changing the inputs, click the Reset button before playing.

UNC and NCSU football players undergo a compeletely inelastic collision in 2 dimensions. The vectors represent the initial and final momenta. Verify by doing a conservation of momentum problem that the magnitude and direction of the ..

UNC and NCSU football players undergo a compeletely inelastic collision in 2 dimensions. The vectors represent the initial and final momenta. Determine the magnitude and direction of the velocity of the combined players. Of course, friction ..

Elastic collision in one dimension
Bug: If the initial velocities are equal, the objects will disappear. But then,
you wouldn't have a collision, would you?

Two gliders of equal mass collide in an elastic collision. Play the animation. Click Show Graph. The velocities of the two objects will be displayed as a function of time. Try collisions for different pairs ..

Two objects collide and rebound from each other. The momentum vector of each object as well as the sum of the momentum vectors is displayed. The lengths of the vectors are drawn relative to the ..

Elastic collision in one dimension
Bug: If the initial velocities are equal, the objects will disappear. But then,
you wouldn't have a collision, would you?

Elastic collision in one dimension
Bug: If the initial velocities are equal, the objects will disappear. But then,
you wouldn't have a collision, would you?

A photon initially moving to the right is scattered at 180 degrees by an electron initially at rest at the origin. The photon is repesented by an arrow.
Determine the wavelength of the scattered photon and ..

A photon initially moving to the right is scattered at by an electron initially at rest at the origin. The photon is repesented by an arrow.
Determine the wavelength of the scattered photon, the kinetic ..

A photon initially moving to the right is scattered by an electron initially at rest at the origin. The photon, which is represented by an arrow is scattered backward along its original path.

A light wave initially moving to the right is scattered by an electron initially at rest at the origin. While the electron appears to be moving very slowly after the collision, this must be considered ..

A light wave initially moving to the right is scattered by an electron initially at rest at the origin. The relative speeds of the light and the electron are physically accurate.

A blue block is lifted at constant velocity to a height and then returned to its starting point. In the same amount of time, a red block is pushed at constant velocity along a horizontal ..

Two balls of equal mass (see Input for value) are suspended from long strings of equal length. The balls are initially charged to the same value of charge Qo. You can add charge to each ..

The blue and red balls have the same size, shape, and composition. They have a coating of graphite paint, which makes their surfaces good conductors. The red ball, hanging from a long thread, is initially ..

A red ball is connected to a spring which is fixed at the left side of the screen. The ball is initially at the unstretched/uncompressed position of the spring, x = 0. A blue ball, soon ..

A charged particle moves under the influence of an electric field oriented along the y-axis. Note this sign convention: The direction of positive E is +y (toward top of screen) The red and blue vectors ..

A charged particle moves under the influence of an electric field oriented along the y-axis as shown by the vector at lower right. Note this sign convention: Direction of positive E is +y (toward top ..

A charged particle moves under the influence of an electric field oriented along the y-axis and a magnetic field oriented along the z-axis. Sign conventions:
positive E is +y (toward top of screen)
positive B ..

A charged particle moves under the influence of a magnetic field oriented along the z-axis (perpendicular to the screen). The direction of positive B is +z (outward from screen). The blue vector on the particle ..

A charged particle moves under the influence of a magnetic field oriented along the z-axis (perpendicular to the screen). The direction of positive B is +z (outward from screen). The blue vector on the particle ..

A charged particle moves under the influence of an electric field oriented
along the y-axis and a magnetic field oriented along the z-axis (perpendicular
to the screen). Note these sign conventions:
Direction of positive E ..

Three different charged particles of equal kinetic energy move under the influence of a uniform magnetic field oriented perpendicular to the screen. Graphs of vertical position vs. time can be displayed by clicking Show graph.
1. ..

Challenge 1. An electron is shot along the +y-axis from the origin. Enter the magnetic field that will make the electron move in a path of radius 0.050 m. Note that a positive value of B-field indicates ..

Challenge 1. An electron is shot along the +y-axis from the origin.
Enter the magnetic field that will make the electron move in a path of radius 0.050 m.
Note that a positive value of B-field indicates ..

Challenge 2. Orbiting alpha particle
An alpha particle is shot along the +y-axis from the origin. Enter the magnetic
field that will make the alpha move in a path of radius 0.050 m.
Notes:
A positive value ..

Challenge 3. Unknown X particle
Use magnetic fields to investigate the unknown X particle. Determine as
much as you can about the charge and mass.
Notes:
A positive value of B-field indicates that B points outward ..

Challenge 4. Explore Electric Field
Investigate the effect of an electric field on the motion of an electron.
Notes:
Positive E-fields are to the right and positive B-fields are out of the screen.
After making a ..

Challenge 5. A positron is shot along the +y-axis from the origin. Determine the charge-to-mass ratio of the particle.
A positive value of B-field indicates that B points outward from the screen.
The grid spacing is 0.01 ..

Challenge 7. Velocity Filter
Begin by finding the magnitude and direction of the electric field such that the electric force balances the magnetic force and the electron travels straight up.
Notes:
Positive E-fields are to the ..

Two singly-ionized isotopes of the same element are injected at the same velocity into a region of uniform magnetic field pointing out of the screen. (There is no field below the x-axis). Determine the ratio ..

A charged particle moves under the influence of an electric field oriented
along the y-axis and a magnetic field oriented along the z-axis (perpendicular
to the screen). Note these sign conventions:
Direction of positive E ..

This plots position (vertical) as a function of time (horizontal) for an object subject to a Hooke's Law restoring force.
Suppose that the object is also subject to a force that always acts opposite the ..

A string is oscillated by a rod on the left. The traveling wave created on the string damps to zero as it approaches the right end, which is initially fixed. In this mode the damping ..

In order to make this work, these variables must be entered in the wavebox properties. Note that this can not be done in the client application.
For Vx, enter vs.
For Frequency, enter f.
For ..

A source of point spherical waves moves along the x-axis at constant velocity. The current position of the source is indicated by a red dot. Note that the spacing of the dark, vertical grid lines ..

A source of point spherical waves moves along the x-axis at constant velocity. The current position of the source is indicated by a red dot. The grid spacing, both horizontal and vertical, is 100 m. Determine ..

Two sources of monochromatic waves are situated on either side of the origin. The sources oscillate in phase. The pattern of interference fringes is projected on a screen near the top of the display. Playing ..

Play the applet to show a position vs. time graph. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. time graphs. Then click on Show graph to check your ..

Play the applet to show a position vs. time graph. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. time graphs. Then click on Show graph to check your ..

Play the applet to show a position vs. time graph. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. time graphs. Then click on Show graph to check your ..

Play the applet to show a position vs. time graph. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. time graphs. Then click on Show graph to check your ..

Play the applet to show a position vs. time graph of an object having the given initial velocity and acceleration. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. ..

Play the applet to show a position vs. time graph of an object having the given initial velocity and acceleration. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. ..

Play the applet to show a position vs. time graph of an object having the given initial velocity and acceleration. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. ..

Play the applet to show a position vs. time graph of an object having the given initial velocity and acceleration. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. ..

Play the applet to show a position vs. time graph of an object having the given initial velocity and acceleration. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. ..

Play the applet to show a position vs. time graph of an object having the given initial velocity and acceleration. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. ..

Play the applet to show a position vs. time graph of the blue dot. In your notes, sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. time graphs. Then ..

Play the applet to show a position vs. time graph. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. time graphs. Then click on Show graph to check your ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge is represented by the green dot. Vectors representing the magnitude and ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge (green) is initially located on the y-axis. Lines (black) from the ..

A charge (red) is positioned at the origin. A positive test charge is represented by the black dot. A vector representing the magnitude and direction of the electric field of the red charge at the ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge is represented by the green dot. Vectors representing the magnitude and ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge is represented by the green dot. Vectors representing the magnitude and ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge is represented by the green dot. Vectors representing the magnitude and ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge is represented by the green dot. Vectors representing the magnitude and ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge is represented by the green dot. Vectors representing the magnitude and ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge is represented by the green dot. Vectors representing the magnitude and ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. Note the following:
The blue charge is always +1.0 C and is positioned at 3.0 m.

The four panels show four representations of the electric field vectors at the position of a positive test charge (green) due to blue and red charges. Only one panel shows the vectors correclty The signs ..

The Four panels show four representations on a charged particle. The Electric Field Vectors are shown, but only one panel is correct. The Charges of the point charges are given, and the charged particle has ..

The four panels show four representations of the electric fields at the indicated point due to the blue and red charged particles. The charges are given as inputs. The color of the vector indicates the ..

The four panels show four representations of the electric fields at the indicated point due to the blue and red charged particles. The charges are given as inputs. The color of the vector indicates the ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge is represented by the green dot. Vectors representing the magnitude and ..

Two charges (red and blue) are positioned on the x-axis and produce an electric field in the space surrounding them. A positive test charge is represented by the green dot. Vectors representing the magnitude and ..

Two charges (red and blue) are fixed in position on the x-axis. The green charge, which is positive, is moved by external means back and forth along the y-axis. The green vector represents the net ..

This is a multiple-choice problem. Enter each of the numbers 1 to 4 in the Choice box. Reset after entering a number. Each choice shows a different version of the electric forces on the positive green charge ..

If the green charge is +1.0 uc (microcoulomb), what are the magnitude and direction of the net electric force on the green charge? Note that all the charges are positive.

Two charges (red and blue) are fixed in position on the x-axis. The green vector represents the net electric force on the positive green charge due to the red and blue charges. At what position ..

Two charged objects (red and blue) are fixed in position on the x-axis. When the animation is started, a small green charged object is pushed back and forth between the red and blue objects. (If ..

Two charged objects (red and blue) are fixed in position on the x-axis. When the animation is started, a small green charged object is pushed back and forth between the red and blue objects. (If ..

Two gliders of collide in an elastic collision. The red glider is initially stationary. Play the animation. Click Show Graph. The velocities of the two objects will be displayed as a function of time. A 3..

A proton moves initially to the left in a uniform electric field. Assuming no forces are acting other than the electric force, what is the initial velocity of the proton? The position of the proton ..

A proton moves initially to the left under the influence of both a uniform electric field and an external force pointed to the left. What is the initial velocity of the proton? The position of ..

An electron is accelerated from rest under the influence of a potential V1. At the origin, the electron enters crossed electric and magnetic fields. The electric field is oriented in the -y direction and is ..

An electron is accelerated from rest under the influence of a potential V1 (not shown). At the origin, the electron enters a uniform electric field. The electric field is oriented in the -y direction and ..

An electron is accelerated from rest under the influence of a potential V1 (not shown). At the origin, the electron enters a uniform magnetic field produced by Helmholtz coils. Within the area encircled by the ..

An electron is accelerated from rest under the influence of a potential V1 (not shown). At the origin, the electron enters crossed electric and magnetic fields. The electric field is oriented in the -y direction ..

An electron is accelerated from rest under the influence of a potential V1. Near the origin, the electron enters a uniform magnetic field produced by Helmholtz coils. The magnetic field is oriented in the -z ..

An electron is accelerated from rest under the influence of a potential V1. At the origin, the electron enters crossed electric and magnetic fields. The electric field is oriented in the -y direction and is ..

An electron is accelerated from rest under the influence of a potential V. At the origin, the electron enters crossed electric and magnetic fields. The electric field is oriented in the -y direction and is ..

An electron is accelerated from rest under the influence of a potential V. At the origin, the electron enters crossed electric and magnetic fields. The electric field is oriented in the -y direction and is ..

An electron is accelerated from rest under the influence of a potential V1. At the origin, the electron enters crossed electric and magnetic fields. The electric field is oriented in the -y direction and is ..

A charged particle moves under the influence of an electric field oriented
along the y-axis and a magnetic field oriented along the z-axis (perpendicular
to the screen). Note these sign conventions:
Direction of positive E ..

A charged particle moves under the influence of an electric field oriented
along the y-axis and a magnetic field oriented along the z-axis (perpendicular
to the screen). Note these sign conventions:
Direction of positive E ..

A charged particle moves under the influence of an electric field oriented
along the y-axis and a magnetic field oriented along the z-axis (perpendicular
to the screen). Note these sign conventions:
Direction of positive E ..

An electron moves under the influence of an electric field oriented along the y-axis and a magnetic field oriented along the z-axis (perpendicular to the screen). Note these sign conventions:
Direction of positive E is +..

A charged particle moves under the influence of an electric field oriented
along the y-axis and a magnetic field oriented along the z-axis (perpendicular
to the screen). Note these sign conventions:
Direction of positive E ..

A charged particle moves under the influence of an electric field oriented
along the y-axis and a magnetic field oriented along the z-axis (perpendicular
to the screen). Note these sign conventions:
Direction of positive E ..

An electron is accelerated from rest under the influence of a difference of potential. At the origin, the electron enters crossed electric and magnetic fields. The electric field is oriented in the -y direction and ..

This is a template for a simulation that you are to complete. The simulation is that of electrons in an electron tube. Electron are accelerated horizontally from rest under the influence of a potential V1. ..

An electron is accelerated from rest under the influence of a difference of potential V. At the origin, the electron enters crossed electric and magnetic fields. The electric field is oriented in the -y direction ..

A ball is tossed upward in the absence of air friction. The situation depicted is for times after the upward push force is no longer acting on the ball. The vector shown represents the velocity ..

A ball is released from rest and falls freely. The system includes the ball and the Earth. The 0 level for gravitational potential energy is indicated. The values of kinetic energy, gravitational potential energy, and energy ..

A ball is released from rest and falls in the presence of air. The system includes the ball and the Earth. The 0 level for gravitational potential energy is indicated. The values of kinetic energy, gravitational ..

A ball is tossed upward in the absence of air friction. The situation depicted is for times after the upward push force is no longer acting on the ball. The vector shown represents the velocity ..

A block is given an initial velocity upward. The vector shown represents the velocity of the block. After t = 0, the forces acting on the block are gravity and the kinetic friction forces exerted by the ..

A block is given an initial velocity upward. The vector shown represents the velocity of the ball. After t = 0, the forces acting on the block are gravity and the kinetic friction forces exerted by the ..

A block is initially given a push to start it moving up a inclined plane. At t = 0, the push is removed. The 0 level for gravitational potential energy is taken to be the initial vertical position ..

A block is initially given a push to start it moving up a inclined plane. At t = 0, the push is removed. The 0 level for gravitational potential energy is taken to be the initial vertical position ..

A block is released from rest on a frictionless plane. The system is taken to be the block and the Earth. The external normal force of the plane on the block does no work, since ..

A block is initially given a push to start it moving up a inclined plane. At t = 0, the push is removed. The 0 level for gravitational potential energy is taken to be the initial vertical position ..

A block is initially given a push to start it moving up a inclined plane. At t = 0, the push is removed. This applet shows how the effect of changing the system selected for a conservation ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is friction between block 1 and the plane. When block 2 is released, the two blocks accelerate. What is the ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is friction between block 1 and the plane. When block 2 is released, the two blocks accelerate. What is the ..

When you play the animation, the block oscillates horizontally about the origin on a frictionless table. The origin is in the center, the direction of +x is to the right, and the grid spacing is 0.02 ..

When you play the animation, the block oscillates horizontally about the origin on a frictionless table. The origin is in the center and the direction of +x is to the right. The oscillation is the ..

A block oscillates horizontally about the origin on a frictionless table. The oscillation is the result of a Hooke's Law force applied by the spring to the block. The system is taken to be the ..

A block oscillates horizontally about the origin. There is kinetic friction between the block and the table. The origin is in the center, the direction of +x is to the right, and the grid spacing ..

A block oscillates horizontally about the origin. There is kinetic friction between the block and the table. The origin is in the center, the direction of +x is to the right, and the grid spacing ..

A block oscillates horizontally about the origin on a frictionless table. The block is already in motion at t = 0. Determine the magnitude of the initial velocity of the block,

At t = 0, a block attached to a spring is released from rest and oscillates horizontally about the origin on a table. There is friction between the block and the table. How much work does friction ..

At t = 0, a block attached to a spring is released from rest and oscillates horizontally about the origin on a table. There is friction between the block and the table. How much work does friction ..

A block is suspended from a fixed support by a rubber band. When held in place by the green stick, the rubber band is completely relaxed. When the green stick is pulled away, the block ..

A block is suspended from a fixed support by a rubber band. When held in place by the green stick, the rubber band is completely relaxed. When the green stick is pulled away, the block ..

A charged particle enters a uniform electric field at (-10 cm,0). The electric field is produced by 2 charged plates on opposite sides of the screen, 20 cm apart. The electric field is represented by the green ..

At t = 0 , a charged particle is released in a uniform electric field at the given position. The electric field is produced by 2 charged plates on opposite sides of the screen, 20 cm apart. The electric field ..

At t = 0 , a charged particle is released in a uniform electric field at the given position. The electric field is produced by 2 charged plates on opposite sides of the screen, 20 cm apart. The electric field ..

A charged particle moves in a uniform electric field produced by 2 charged plates on opposite sides of the screen, 20 cm apart. The electric field is represented by the green lines. The direction of the electric ..

A negative (blue) and a positive (red) particle are accelerated under the action of a uniform electric field. The masses and charges of the particles are given as outputs.
How do the magnitudes of the ..

An electron (blue) and a proton (red) are accelerated under the action of a uniform electric field. Why do the particles experience the same change in electric potential energy in moving through the same distance?

A charged particle is acted on by two forces: 1) the force of the electric field set up between the plates, and 2) an external force. The position and velocity of the charge are given as outputs. ..

A positively-charged particle is acted on by two forces: 1) the force of the electric field set up between the plates, and 2) an external force. The position and velocity of the charge are given as outputs.

A charged particle, initially moving, enters a uniform electric field at upper right. The only force acting on the particle when in the field is the electric force of the field. Determine each of the ..

A negative (blue) and a positive (red) particle are accelerated under the action of a uniform electric field produced by charged plates. The potentials and positions of the plates are shown. The charges and masses ..

A charged particle is acted on by two forces: 1) the force of the electric field set up between the plates, and 2) an external force. The position and velocity of the charge as well as the ..

A beam is held horizontal by a string attached to a wall and by an axle about which the beam is free to rotate. The red line is the moment arm of the tension force ..

A massless rod is held vertical by a string attached to the floor and an applied force acting to the right at the center of the rod. The bottom of the rod is fixed to ..

A ball is suspended by strong wires from two posts. The tension forces and weight are shown. Step through the animation using the >> button to see how the forces change for different vertical positions of ..

A ball is suspended by strong wires from two posts. The tension forces and weight are shown. Step through the animation using the >> button to see how the forces change for different horizontal positions of ..

A ball is suspended by strong wires from two posts. The tension forces and weight are shown. Step through the animation using the >> button to see how the forces change for different horizontal positions of ..

The green ball falls in a vacuum, while the red ball experiences a drag force from the fluid in which it falls. The acceleration of the red ball is a = -g + kvÂ², where g = 9.8 N/..

Simulation of two objects falling from rest in a gravitational field.
They experience air drag proportional to the square of the speed.
The vertical acceleration is given by: a = -g+kvÂ², where k is termed
..

Play the animation to see a ball falling freely in the gravitational field of an unknown planet. (Be patient for the ball to appear.) Take measurements from the graph to determine the acceleration and initial ..

1. Two dimunitive cars, initially at rest, are subjected at t =0 to an identical and constant force in the +x direction. How do the kinetic energies (see outputs) of the two cars compare after traveling the ..

Water drains from a tank through a spout near the bottom. Determine the maximum vertical height above the ground reached and the maximum horizontal distance from the right side of the tank to the ground ..

Water drains from a tank through a spout in the side. Enter a value of 0 to 100 for the Randomizer. Determine the height of the spout and the initial height of the water in the tank ..

Documentation for teacher: The initial velocity is fixed at 20 m/s in order that the vectors get all the way across the screen. This value is used in calculating the pressure difference. The climber variable ..

Water flows in a cylindrical pipe that changes diameter. What is the velocity of the fluid on the right side of the pipe and what is the pressure difference between the left and right sides?

Blood flows in an artery from left to right. The buildup of plaque reduces the diameter of the artery on the right. Determine the speed of blood flow in the constricted artery and the drop ..

Water travels through a pipe on the left and then rises to a higher elevation to flow through a pipe of different diameter on the right. What is the velocity of the water in the ..

A block is lowered by a string at constant velocity into a fluid. The force diagram shows the forces on the fluid as a function of time. (blue = weight; brown = tension; green = buoyancy)

A block is lowered by a string at constant velocity into a fluid. The force diagram shows the forces on the fluid as a function of time. (mg = weight; T = tension; B = buoyancy)

A block is lowered by a string at constant velocity into a fluid. The force diagram shows the forces on the fluid as a function of time. (mg = weight; T = tension; B = buoyancy) If the ..

A block is lowered by a string at constant velocity into a fluid. The force diagram shows the forces on the fluid as a function of time. (mg = weight; T = tension; B = buoyancy)
A digital ..

A block is lowered by a string at constant velocity into water. The force diagram shows the forces on the fluid as a function of time. (mg = weight; T = tension; B = buoyancy)
A digital scale ..

A block is lowered by a string at constant velocity into water. A digital scale provides a readout of the tension force. Determine the density of the block.

A beaker of fluid containing a floating object is accelerated by a piston. Unphysical results occur when the object sinks or when the piston accelerates downward with greater magnitude than acceleration due to gravity.

A block is lowered by a string at constant velocity into a fluid. The force diagram shows the forces on the block as a function of time. (mg = weight; T = tension; B = buoyancy)
A digital ..

A block is lowered by a string at constant velocity into a fluid. A digital scale attached to the string provides a readout of the tension force. A second digital scale supports the beaker and ..

A beaker of fluid containing a floating object is accelerated by a piston. The forces acting on the object are shown in the force diagram. Initially, the beaker is at rest and the forces are ..

A beaker of water containing a floating object is accelerated by a piston. Initially, the beaker is at rest and the forces are balanced. When the animation is run, the acceleration quickly increases from 0 to ..

A beaker of water containing a floating object is accelerated by a piston. The forces acting on the object are shown in the force diagram. Initially, the beaker is at rest and the forces are ..

A beaker of water containing a cubical floating object is accelerated by a piston. Initially, the beaker is at rest and the forces are balanced. When the animation is run, the acceleration quickly increases from 0 ..

A red box slides along a blue wall. A constant force (for example, from a hand) is applied on the box to the right. The directions of +x and +y are to the right and ..

A red box slides down a wall. The box is in motion at t = 0. A constant force (for example, from a hand) is applied on the box to the right. The grid spacing is 1 meter. ..

A red box slides down a wall. The forces on the box are shown. Try changing the parameters (mass of box, coefficient fo kinetic friction, applied force) to see how that affects the force vectors.

A red box slides along a blue wall. A constant force (for example, from a hand) is applied on the box to the right. The directions of +x and +y are to the right and ..

An object rests on a horizontal surface. A pulling force is applied on the block to the right. As the applet runs, the tension force is increased to the point at which the block begins ..

The pointer traces out a quadratic function of the form:
y = a + bx + cxÂ²
to do:
make strip trace out area
use Euler's method to get first and second integrals of acceleration

A balloon drifts through the air and expands as the temperature of the gas inside of it rises. The thin gray circle illustrates the original size of the balloon for comparison. The animation fails to ..

A balloon is released from the bottom of a deep lake where the temperature is always 4 degC and rises to the top, where the pressure is standard atmospheric pressure. Assume that the balloon rises slowly ..

A vertical piston compresses a gas in a rectangular container. Mode Zero represents an isothermal and isobaric process. Mode One is isobaric and adiabatic. Mode Negative One is isothermal and adiabatic.

A block resting on a piston compresses a gas. The blue scale to lower right indicates the pressure of the gas in atmospheres. A thermometer indicates the temperature of the gas in degrees Celsius. The ..

A block resting on a piston compresses a gas. The blue scale to lower right indicates the pressure of the gas in atmospheres. A thermometer indicates the temperature of the gas in degrees Celsius. The ..

A block resting on a piston compresses 0.30 moles of an ideal gas. A thermometer indicates the temperature of the gas in degrees Celsius. The dimensions of the cubical gas volume are initially 0.080 m x 0.080 m ..

A block resting on a piston compresses an ideal gas enclosed in a box. The gauge to lower right indicates the absolute pressure of the gas in atmospheres. A thermometer indicates the temperature of the ..

A block resting on a piston compresses 0.100 moles of an ideal gas enclosed in a box. The gauge to lower right indicates the absolute pressure of the gas in atmospheres. A thermometer indicates the temperature ..

A pump increases the pressure in a box enclosing 0.100 moles of an ideal gas. A pressure gauge indicates the absolute pressure of the gas in atmospheres. The dimensions of the gas volume are 0.0800 m x 0.0800 ..

A pump increases the pressure in a box enclosing 0.100 moles of an ideal gas. A pressure gauge indicates the absolute pressure of the gas in atmospheres. The dimensions of the gas volume are 0.0800 m x 0.0800 ..

A vertical piston compresses a blue gas. Mode Zero represents an isothermal and isobaric process. Mode One is isobaric and adiabatic. Mode Negative One is isothermal and adiabatic.

Global Crossing (TPT 9-04): Two cars X and Y approach an intersection of two perpendicular roads as shown. The velocities of the cars are vx and vy. At the moment when car X reaches the ..

Two satellites orbit the Earth in circular orbits. The ratio of each orbit to the radius of the Earth is given. The vectors represent the gravitational accelerations and orbital velocities of the satellites.

A satellite orbits the Earth in a circular orbit. The ratio of the radius of the satellite's orbit to the radius of the Earth is given. The red dot represents an apple falling near the ..

Two satellites orbit the Earth in circular orbits. The ratio of the radius of each satellite's orbit to the radius of the Earth is given. The vectors represent the accelerations of the satellites.

Earth and Mars orbit the Sun in approximately circular orbits. The ratio of the average orbital radii of the planets is given. Find the ratio of the accelerations.
(Note that in order for the Sun ..

Two satellites orbit Planet Q in circular orbits. The ratios of the orbital radii and of the masses of the satellites are given. The vectors represent the gravitational accelerations and orbital velocities of the satellites.

The space shuttle orbits the Earth in a circular orbit. The ratio of the shuttle's orbital radius to the Earth is given. The vectors represent the acceleration and velocity of the shuttle.
The view is ..

The space shuttle orbits the Earth. The ratio of the shuttle's orbital radius to the Earth is given.
The view is looking down on a pole. The white line represents a meridian. Hence, it rotates ..

The green satellite orbits the Earth in a geostationary orbit. This means that the satellite orbits in the Earth's equatorial plane and always remains above the same point on the Earth. The rotation of the ..

An object is dropped from rest into a tunnel drilled along the rotation axis of the Earth. A second object orbits the Earth in a path skimming along the Earth's surface. (Air friction, mountains, etc. ..

Run the animation to show the Earth (blue line) orbiting the Sun while the Moon (white line) orbits the Earth.
(Note that the amplitude of the Moon's motion had to be magnified by a factor ..

This is supposed to illustrate escape velocity. However, the Euler's method approximation is too crude except for very small time intervals that make the animation run too slow.

The red line at y = 0 represents a boundary between media of different indices of refraction. The path of a light ray is shown in blue. Playing the applet forward or backwards will increase or decrease ..

A pendulum is released from rest and oscillates in a vertical plane. The angle of release, mass of the bob, gravitational field, and length of the string can be adjusted. At large angles, the applet ..

A pendulum bob is released from rest. At the bottom of its path, the bob strikes a block and knocks it over. The bob rebounds. (String 2 needs some work. If bob2's position is selected, ..

The graph shows position vs. time of two objects which we will call a hare (red) and a tortoise (blue). The animals are in a race. The tortoise gets the advantage of a head start 100 ..

Now the tortoise has an acceleration to try to outrun the rabbit. (Note that the axis scales have been changed.) Play the animation to see how the hare won't be able to catch the tortoise. ..

Play the applet in order to plot the magnetic field along the axis of a pair of Helmholtz coils as a function of the distance from the axis midpoint. The red and blue lines are ..

Play the applet in order to plot the magnetic field along the axis of a pair of Helmholtz coils as a function of the distance from the axis midpoint. The red and blue lines are ..

This calculates the magnetic field of a Helmholtz coils configuration.
The blue and green lines are the fields of the individual coils.
The red line is the net field.
Position is measured relative to the ..

A platform (black) is suspended from a fixed support by a rubber band. Weight can be added to the platform. When the red stick is pulled away, the platform with its weight will oscillate vertically ..

A platform (black) is suspended from a fixed support by a rubber band. Weight can be added to the platform. When the red stick is pulled away, the platform with its weight will oscillate vertically ..

A platform (black) is suspended from a fixed support by a rubber band. Weight can be added to the platform. When the red stick is pulled away, the platform with its weight will oscillate vertically ..

A platform (black) is suspended from a fixed support by a rubber band. Weight can be added to the platform. When the red stick is pulled away, the platform with its weight will oscillate vertically ..

An object slides down a frictionless plane. The plane makes an angle theta with the horizontal. The forces acting on the object are the normal force acting perpendicular to the plane and the weight acting ..

An object slides down an inclined plane. The coefficient of kinetic friction, which is initially 0, can be changed. The inclination of the plane, the initial x-coordinate of the block, and the initial velocity can also ..

A charged ball hanging from a long thread is deflected to the left by a second charged ball connected to an insulating handle. As the second charge is moved to the left, the first charge ..

Play the applet to show a position vs. time graph of the blue dot. Sketch your predictions for the shapes of the corresponding velocity vs. time and acceleration vs. time graphs. Then click on Show ..

Play the animation to display a position vs. time graph of the red dot. The values of position and velocity are given as outputs. Graphs of velocity vs. time and acceleration vs. time may be ..

Play the animation to display a position vs. time graph of the red dot. The value of position is given as an output. What are the corresponding graphs of velocity vs. time and acceleration vs. ..

An object moves at constant velocity for 1.0 s. At that time, the object begins slowing down at a constant rate, reaching a velocity of 0, and then speeding up at a constant rate. Draw the velocity ..

A position vs. time graph is shown for an object. The object moves at constant velocity for 1.0 s followed by constant acceleration for the next 4.0 s.

A position vs. time graph is shown for an object. The object moves at constant velocity for 1.0 s followed by constant acceleration for the next 4.0 s.

The graph represents the position vs. time of a ball that rolls across a table at constant velocity for 2.0 s and then encounters a rough patch which cause the ball to decrease in velocity at ..

The graph represents the position vs. time of a ball that rolls across a table at constant velocity for 2.0 s and then encounters a rough patch which cause the ball to decrease in velocity at ..

The physical situation for this problem is like that of the falling leaf where the leaf experiences a lift force that is proportional to and perpendicular to its velocity. In this case, we treat the ..

The lower half of the screen is water, and the upper half is air. Running the animation plots paths of rays from an object in the lower left-hand corner of the screen to an observer ..

An object arrow is shown to the left of a converging lens and outside a focal point. (The lens is represented by a straight black line for simplicity.) Step through the applet frame-by-frame to see ..

An object arrow is shown to the left of a converging lens and inside the focal point. (The lens is represented by a straight blue line for simplicity.) Step through the applet frame-by-frame to see ..

An object arrow is shown to the left of a diverging lens. (The lens is represented by a straight black line for simplicity.) Step through the applet frame-by-frame to see the principal rays (red = C ..

A bar magnet is pushed into a loop of conducting wire. While the magnet is moving into the loop, what is the direction of the induced current in loop from the point of view of ..

A bar magnet is pulled out of a loop of conducting wire. While the magnet is moving out of the loop, what is the direction of the induced current in loop from the point of ..

A bar magnet is pulled out of a loop of conducting wire. While the magnet is moving out of the loop, what is the direction of the induced current in loop from the point of ..

Initially, there is a current in the large conducting loop. At the top of the loop, the direction of the current is out of the screen. (The direction of the current is counterclockwise from the ..

Change the pursuer's x- and y-velocity components to intercept
the target. When you are successful, you can make the circle fit
inside the square by stepping the animation. Note that there is
more than one ..

An object is subject to independent restoring forces along the x- and y-axes. It's like being pulled on by springs along both axes simultaneously. Do the following.
a. Change one input in order to make ..

An object is subject to independent restoring forces along the x- and y-axes. It's like being pulled on by springs along both axes simultaneously. Do the following.
a. Change one input in order to make ..

Three long wires arranged at the corners of a square and perpendicular to the screen carry equal currents into or out of the screen. The force that each current exerts on current 2 is shown. The ..

Six positively-charged particles (solid yellow circles numbered for easy reference) are near the equator of the Earth and are initially moving in the directions shown. The red dot indicates a velocity vertically out of the ..

Four positively-charged particles (solid yellow circles numbered for easy reference) are near the equator of the Earth and are initially moving in the directions shown. The directions of the Earth's Geographical North Pole and Magnetic ..

Four particles of equal mass and equal magnitudes of velocity have different charges. Run the applet to see how the particles move in a uniform magnetic field pointed perpendicularly out of the screen. Which particles ..

Three particles of equal mass and equal magnitudes of charge have different intial velocities. Run the animation to see how the particles move in a uniform magnetic field pointed perpendicularly out of the screen. Rank ..

Four positively-charged particles dust particles are near the equator of the Earth and are initially moving in the directions NW (1), SW (2), E (3), and up (4) with velocities of magnitude 15 m/s. The directions to the Earth's ..

Three particles of equal mass and magnitude of velocity move in a uniform magnetic field pointed perpendicularly out of the screen. Rank the particles in increasing order according to the magnitude of their charge.

The view is that of an observer in space looking down on one of the poles of the Earth. An electron orbits the Earth at the equator under the influence of the magnetic force due ..

The view is that of an observer in space looking down on one of the poles of the Earth. An electron orbits the Earth at the equator under the influence of the magnetic force due ..

An electron moves under the influence of a uniform magnetic field directed perpendicularly outward from the screen. What must the direction and magnitude of a uniform electric field be such that the net force on ..

The animation allows you to check your calculated results against your
measured results for a sphere falling through a fluid. Begin by entering your
measurements in Input boxes. For the mass of the ball, enter ..

Two singly-ionized isotopes of the same element are injected at the same velocity into a region of uniform magnetic field pointing out of the screen. (There is no field below the x-axis). Determine the ratio ..

The animation shows a spherical object falling through a fluid with acceleration
a = (k/m)v-g. The positive direction is up. The object has an intial position of 0 and is released from rest. The given ..

The animation allows you to check your calculated results against your
measured results for a sphere falling through a fluid. Begin by entering your
measurements in Input boxes. For the mass of the ball, enter ..

Start the applet. Blue moves in a circle at constant speed. At t=0, Blue releases a green ball. Note the path taken by the ball.
1. At t=0, suppose Blue throws the ball directly opposite his ..

An object arrow is shown to the left of a concave mirror and outside of the focal point. (The mirror is represented by a straight black line for simplicity.) Step through the applet frame-by-frame to ..

An object arrow is shown to the left of a concave mirror and inside the focal point. (The mirror is represented by a straight black line for simplicity.) Step through the applet frame-by-frame to see ..

An object arrow is shown to the left of a convex mirror. (The mirror is represented by a straight black line for simplicity.) Step through the applet frame-by-frame to see the principal rays and image ..

Step through the applet to see light rays traced to locate the position of the image. Two rays each are traced from the head and tail of the object arrow to the mirror. The rays ..

Step through the applet to see light rays traced to locate the position of the image. Two rays each are traced from the head and tail of the object arrow to the mirror. The rays ..

Select A and B and click Reset to perform the 4 functions listed under Outputs. The A Round B function rounds A to the precision of B. For example 2.15 Round 0.1 returns 2.2.

A DC motor requires for its operation a magnetic field, a loop of wire that can turn on an axis, and a source of current. With the correct orientation of the loop in the field, ..

This is a view of a DC motor looking down on the loop. (The line of sight is parallel to the plane of the loop.) The direction of current in the side of the loop ..

Two blocks initially rest next to each other on a frictionless surface. (The view is looking down on the surface.) At t = 0, an identical push is applied directly to each block. The push on each ..

Two blocks rest next to each other on a frictionless surface. At t = 0, a push (by a hand for example) is applied directly to the green block. The push remains constant as the two blocks ..

Two blocks rest next to each other on a frictionless surface. At t = 0, a push (by a hand for example) is applied directly to the red block. The push remains constant as the two blocks ..

Test of Ellipse should be 1 theoretically.
dA/dt is the rate at which the radius vector sweeps out area. This is r*v/2.
Area is the area swept out from t = 0. This is an integral ..

Test of Ellipse should be 1 theoretically. This applies only to the default values of the inputs.
dA/dt is the rate at which the radius vector sweeps out area. This is r*v/2.
Area is ..

Test of Ellipse should be 1 theoretically. This applies only to the default values of the inputs.
dA/dt is the rate at which the radius vector sweeps out area. This is r*v/2.
Area is ..

Test of Ellipse should be 1 theoretically. This applies only to the default values of the inputs.
dA/dt is the rate at which the radius vector sweeps out area. This is r*v/2.
Area is ..

A planet orbits a star. Investigate conditions for a stable orbit.
Note that the star would normally have motion, but that motion is
small compared to the motion of the planet when the mass
of ..

Run the applet to shine a source of light of the given frequency on the emitter. Photoelectrons are ejected from the emitter with varying kinetic energies up to a maximum value determined by the frequency ..

Run the applet to shine a source of light of the given frequency on the emitter. Photoelectrons are ejected from the emitter with varying kinetic energies up to a maximum value determined by the frequency ..

Run the applet to shine a source of light of the given frequency on the emitter. Photoelectrons are ejected from the emitter with varying kinetic energies up to a maximum value determined by the frequency ..

When an emitter is illuminated with light of the given frequency, the stopping potential for photoelectrons is found to be 0.448 V. What are a) the maximum kinetic energy of the photoelectrons, b) the work function ..

A pendulum is released from rest and oscillates in a vertical plane. The angle of release, mass of the bob, gravitational field, and length of the string can be adjusted. At large angles, the applet ..

A pendulum is released from rest and oscillates in a vertical plane. The angle of release, mass of the bob, gravitational field, and length of the string can be adjusted. At large angles, the applet ..

A pendulum is released from rest and oscillates in a vertical plane. The angle of release, mass of the bob, gravitational field, and length of the string can be adjusted. At large angles, the applet ..

A pendulum is released from rest and oscillates in a vertical plane. For which positions (A, B, C) is the tangential acceleration 0? maximum? centripetal acceleration 0? maximum?

A pendulum bob is released from rest and oscillates in a vertical plane. For the system of Earth and bob, match the energy bars with the energy terms that they represent.

A pendulum is set up on the surface of Planet X. The bob is released from rest and oscillates in a vertical plane. What is the acceleration due to gravity on the surface of Planet ..

A ball is launched horizontally off of a cliff at the same time as a cart is launched horizontally underneath. Input height between the objects, initial velocity of ball, and initial velocity of cart.

An electron is accelerated to the right in an electron gun under the influence of a uniform electric field. When the electron exits the gun, it enters a region of uniform magnetic field pointing from ..

An electron is accelerated to the right in an electron gun under the
influence of an accelerating potential V. When the electron exits
the gun, it enters a region of uniform magnetic field pointing per-
..

An electron is accelerated to the right in an electron gun under the
influence of an accelerating potential V. When the electron exits
the gun, it enters a region of uniform magnetic field pointing per-
..

An electron is accelerated to the right in an electron gun under the
influence of an accelerating potential V. When the electron exits
the gun, it enters a region of uniform magnetic field pointing per-
..

An electron is accelerated to the right in an electron gun under the influence of a uniform electric field. When the electron exits the gun, it enters a region of uniform magnetic field pointing from ..

An electron is accelerated to the right in an electron gun under the
influence of an accelerating potential V. When the electron exits
the gun, it enters a region of uniform magnetic field pointing per-
..

Four moons revolve around a planet in circular orbits. Determine the period and radius of each orbit. Use the buttons on the right to start/stop the animation and step it frame-by-frame. Readouts of time ..

This animation demonstrates the retrograde motion of an outer planet such as Mars as viewed from the Earth. In the animation, the Earth is the blue object and is stationary, since this is the frame ..

This animation demonstrates the retrograde motion of an inner planet such as Venus as viewed from the Earth. In the animation, the Earth is the blue circle and is stationary, since this is the frame ..

This animation shows the retrograde motion of two moons of a planet (blue) from the point of view of the middle moon. From the point of view of the planet, the orbits would be circular...

A proton initially moves to the right in a uniform electric field
directed upward. Alter the field strength or the initial speed
in order that the proton passes through the exit hole without
hitting the ..

A proton initially moves to the right in a uniform electric field directed
upward. Try changing values of charge, electric field, and initial speed
in order to make the proton pass through the gap in ..

A proton initially moves to the right in a uniform electric field directed
upward. Try changing values of charge, electric field, and initial speed
in order to make the proton pass through the gap in ..

A proton initially moves to the right in a uniform electric field directed
upward. Try changing values of charge, electric field, and initial speed
in order to make the proton pass through the gap in ..

This animation represents waves on a string plucked at its center. The yellow line is the actual waveform that would appear. This can be thought of as the superposition of two waves (blue and red) ..

Waves are incident from the left on a barrier. At t = 0, two apertures open in the barrier. Waves emerging from the two apertures interfere. At positions where the two waves reach the screen in phase, ..

Waves are incident from the left on a barrier. At t = 0, two apertures open in the barrier. Waves emerging from the two apertures interfere. At positions where the two waves reach the screen in phase, ..

Waves are incident from the left on a barrier. At t = 0, two apertures open in the barrier. Waves emerging from the two apertures interfere. The pattern of bright interference fringes is shown on the screen. ..

Waves are incident from the left on a barrier. At t = 0, two apertures open in the barrier. Waves emerging from the two apertures interfere. Determine the vertical position on the screen of the center of ..

Blue line: Jumps alternately between two polar functions of the form:
r = a + bcos(cit + d), where the coefficients a to d are selectable for each
function. The angle increment, i, is also selectable. The ..

Blue line: Jumps alternately between two polar functions of the form:
r = a + bcos(cit + d), where the coefficients a-d are selectable for each function. The angle increment, i, is also selectable. The value of ..

Blue line: Jumps alternately between two polar functions of the form:
r = a + bcos(cit + d), where the coefficients a-d are selectable for each function. The angle increment, i, is also selectable. The value of ..

A ray of light is incident from air on a prism with index of refraction 1.5. Playing the animation will decrease the angle of incidence in 1Â° increments. Normals to the sides of the prism are indicated ..

A ray of light is incident from air on a prism with index of refraction 1.5. Playing the animation will increase the angle of incidence in 1 degree increments. Normals to the sides of the prism are ..

A ray of light is incident horizontally from air on a prism with the given index of refraction. Normals to the sides of the prism are indicated by blue lines. (If the critical angle is ..

A ray of light is incident from air on a prism with the given index of refraction. Playing the animation will increase the vertex angle of the prism in 1 degree increments. Note that if the ..

A ray of light is incident from air on a prism with the given index of refraction. Normals to the sides of the prism are shown in red. Playing the animation will increase the vertex ..

A ray of light is incident from air on a prism with the given index of refraction. Normals to the sides of the prism are shown in red. Playing the animation will increase the vertex ..

A ray of white light is incident from air on a prism. The light is dispersed by the prism. The amount by which the index of refraction is incremented per color can be changed. Playing ..

A ray of white light is incident from air on a prism. The light is dispersed by the prism. The amount by which the index of refraction is incremented for each color can be changed. ..

The dispersion of white light by crown glass is modeled. The index of refraction ranges from 1.513 for red light to 1.532 for violet light. Playing the animation will decrease the angle of incidence in 1Â° increments.
The ..

The dispersion of white light by an equilateral prism made of crown glass is modeled. The index of refraction ranges from 1.513 for red light to 1.532 for violet light. Playing the animation will decrease the angle ..

A ray of white light is incident from air on a prism. The light is dispersed by the prism. Playing the animation will decrease the angle of incidence in 1Â° increments.
Determine to 4 digits the indices ..

A ray of light is incident from air on a glass prism. Playing the animation will increase the angle of incidence in 1Â° increments. Normals to the sides of the prism are indicated by blue lines.

A projectile is launched at an angle from a cliff on an unkown planet. Velocity vectors are shown on the projectile. Use the velocity vectors at two instants of time to determine the acceleration of ..

A projectile is launched at an angle from a cliff. Velocity vectors are shown on the projectile. Determine the acceleration of the object.
In order to check your answer, click Show Graph. Graphs of vertical ..

A projectile is launched at an angle from a cliff on Planet X. Velocity vectors are shown on the projectile. Determine the acceleration of the object.
In order to check your answer, click Show Graph. ..

A projectile is launched at an angle from a cliff on Planet X. Velocity vectors are shown on the projectile. Determine the acceleration of the object.
In order to check your answer, click Show Graph. ..

Three projectiles are launched with different initial velocities and reach the same maximum height. Denote the paths as follow:
A: red
B: green
C: blue
List the projectiles in order of a) increasing initial speed ..

The projectile is subject to a downward gravitational field, a drag force opposing the velocity and proportional to v-squared, and a lift force proportional to and perpendicular to the velocity.

A red ball slides off a table. Ignoring friction, which animation correctly represents the path of the ball? Enter 1, 2, 3, or 4 to change animations. The horizontal and vertical positions, velocities, and accelerations of the ball are ..

A bouncing ball is shown in the animation. What is the ratio of the vertical velocity of the ball just after it hits the ground to the vertical velocity of the ball just before it ..

A projectile is launched at an angle from a cliff. A target moves at 0, constant, or uniformly changing velocity. Hit the target with the projectile. Velocity vectors are shown on the projectile.

A projectile is launched at an angle from a cliff. A target moves at 0, constant, or uniformly changing velocity. Hit the target with the projectile. Velocity vectors are shown on the projectile.

The red and blue objects supposedly use the same equations. However,
the equation parsing is different for each. The red object has the correct
behavior. The physical situation is a projected object subject to a ..

Two blocks are connected by a massless, unstretchable string. The string passes over a frictionless, massless pulley. When the blue block is released, the system of the two blocks accelerates. The forces on the blocks ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

Two blocks are connected by a massless, unstretchable string which passes over a frictionless, massless pulley. There is no friction between the red block and the plane. When the blue block is released, the system ..

The upper pane shows a pulse moving to the right on a string while the lower pane shows a pulse moving to the left. If the two pulses move in strings of the same linear ..

The upper pane shows a pulse moving to the right on a string while the lower pane shows a pulse moving to the left. If the tension in the two strings is the same, how ..

The upper pane shows a pulse moving to the right on a string while the lower pane shows a pulse moving to the left. If the linear density of the upper string is twice that ..

Two pulses (green and blue) move in opposite directions on a string. The red line shows the superposition of the two pulses. This is the disturbance that one would actually see on the string.

Two pulses (green and red) move in opposite directions on a string. The red line shows the superposition of the two pulses. This is the disturbance that one would actually see on the string.

Change the pursuer's x- and y-velocity components to intercept the target. When you are successful, you can make the circle fit inside the square by stepping the animation. Note that there is more than one ..

Change the pursuer's x- and y-velocity components to intercept the target (blue). When you're successful, you can make the circle fit inside the square by stepping the animation. There's more than one solution. Try finding ..

Car A (red) and Car B (blue) move with zero or uniform acceleration in a
straight line starting from different positions. The graph plots position (y)
versus time (x).

A rainbow is formed when the direction of sunlight to raindrops is such that a ray internally reflected in a drop refracts out of the drop along a line of sight that reaches the observer. ..

The blue and gray areas represent media of different optical densities. n is the ratio of the optical density of the gray medium to that of the blue medium. The normal to the boundary is ..

The blue and gray areas represent media of different indices of refraction. n2/n1 is the ratio of the index of refraction of the gray medium to that of the blue medium. The normal to ..

The blue and gray areas represent media of different optical densities. n2/n1 is the ratio of the optical density of the gray medium to that of the blue medium. The normal to the boundary ..

The red line at y = 0 represents a boundary between media of different indices of refraction. The path of a light ray is shown in blue. Playing the applet forward or backwards will increase or decrease ..

The red line at y = 0 represents a boundary between different media. The path of a light ray is shown in blue. Playing the applet forward or backwards will change the angle of incidence.
Which ray ..

The blue and gray areas represent different media. Incident, reflected, and refracted light rays in the media are shown. In which medium is the speed of light greater? How do you know?
Run the applet ..

The red line at y = 0 represents a boundary between media of different indices of refraction. The path of a light ray is shown in blue. Note that both a reflected and a refracted ray are ..

A ray of light starting from lower left is refracted from Medium 1 to Medium 2 as well as reflected into Medium 1. Playing the applet forward or backwards will increase or decrease the angle of incidence. The ..

A ray of light travels through 3 successive media from 1 to 3.. The indices of refraction of media 1 and 3 are given as inputs. Normals are shown at the boundaries of adjacent media. The angle of incidence in ..

The blue, red, and gray areas represent media of different indices of refraction. (The media are indexed 1,2,3 from the bottom up.) The path of a light ray is shown in yellow. The ray is incident ..

The blue, red, and gray areas represent media of different indices of refraction. The path of a light ray incident from the blue medium is shown in yellow. The angle of incidence is given as ..

The blue, red, and gray areas represent media of different indices of refraction. They are indexed 1 to 3 from the bottom up. The path of a light ray incident from the blue medium is shown in ..

The blue, red, and gray areas represent different media. The path of a light ray incident from the blue medium is shown in yellow. Rank the media according to the speed of light in them.
..

The red and blue rectangles have equal length and height. The distance between adjacent black lines is 1.0 cm. Develop a method to measure the height of a rectangle to the nearest 0.01 cm.. Then carry out ..

Plane waves of constant frequency move up the screen, crossing from one medium (blue) into another (gray). The wave speed in each medium is different. Click Show graph to display a graph of vertical position ..

Plane waves of constant frequency move up the screen, crossing from one medium into another. The wave speed decreases in the upper medium. Since the frequency is constant and speed = frequency x wavelength, the wavelength ..

Plane waves cross a boundary at a non-zero angle of incidence. The angles of incidence and refraction are shown with respect to the normal to the boundary.

Plane waves cross a boundary between two media at a non-zero angle of incidence. The angles of incidence and refraction are shown with respect to the normal to the boundary.

A ray of light (red) is incident from air (blue) on a medium (yellow) with the given index of refraction. The ray enters from the bottom of the screen. The initial angle of incidence is ..

A ray of light (red) is incident from air on a transparent medium (blue box). The ray enters from the bottom of the screen. The initial angle of incidence is the smallest that it can ..

A ray of light (red) is incident from air on a box filled with water (blue). The ray enters from the bottom of the screen. The initial situation shows the least that the angle of ..

Run the applet with the default inputs. The observer (SO) is on a space station at rest with respect to the background of stars. The Interprize is moving at velocity v to the right. At ..

A boat travels across a river. Determine the heading of the boat so that it will reach point P on the opposite shore. The vectors represent the following:
blue--velocity of boat relative to shore
green--velocity ..

A ship moves at constant velocity to the right. (The view is that of an observer at rest relative to the water and looking down on the ship.) At t = 0.5 s, a passenger (blue dot) ..

A car moves at constant velocity to the right. (The view is looking down on the car.) At a particular time, a ball is thrown out the window at the angle given under Inputs. The ..

A car moves at constant velocity to the right. (The view is looking down on the car.) At a particular time, a ball is thrown out the window at the angle given under Inputs. The ..

A carship makes a journey from the Earth to Alpha Centauri. The journey can be viewed from the viewpoint of either the ship or the Earth by selecting 1 or 0 for the Frame. The notation (rf ..

Run the applet with the default inputs. The observer (SO) is on a space station at rest with respect to the background of stars. The Interprize is moving at velocity v to the right. At ..

This applet models a problem presented by Boris Korsunsky in The Physics Teacher magazine: Two objects approach each other initially with
accelerations in the opposite directions as their initial velocities. What is the time interval ..

The red arrow has a non-zero initial angular velocity. After t = 0, the arrow undergoes uniform angular deceleration. Determine the following for the arrow:
average angular speed from t = 0 to the time when v = 0
angular speed ..

The black dot undergoes constant angular acceleration. The vectors represent the following:
blue: tangential acceleration of the dot
red: radial (centripetal) acceleration of the dot
green: vector sum of tangential and radial accelerations

The green, blue, and red dots move at uniform angular acceleration. The vectors represent tangential and radial accelerations of the corresponding points. Run the applet to see how the vectors change with time.
(The scale ..

Four moons revolve around a planet in circular orbits. Determine the period
and radius of each orbit. Use the buttons on the right to start/stop the
animation and step it frame-by-frame. Readouts of time ..

Four moons revolve around a planet in circular orbits. Determine the period
and radius of each orbit. Use the buttons on the right to start/stop the
animation and step it frame-by-frame. Readouts of time ..

Four moons revolve around a planet in circular orbits. Determine the period
and radius of each orbit. Use the buttons on the right to start/stop the
animation and step it frame-by-frame. Readouts of time ..

Four moons revolve around a planet in circular orbits. Determine the period
and radius of each orbit. Use the buttons on the right to start/stop the
animation and step it frame-by-frame. Readouts of time ..

Two strings, one thick and one thin, are tied together. The thin string on the right is oscillated at constant frequency by a driver. The left end of the thick string is fixed in place. ..

A ball is attached to a horizontal spring (not shown) which causes the ball to oscillate about the origin. Run the animation. Note that values of time, position, velocity, and acceleration appear above the play ..

1. Two objects of equal mass oscillate independently in SHM about the origin. Find ratios of each of the following (blue/red):
a. amplitude
b. period
c. spring constant
d. total energy
2. The two objects are ..

Run the applet to display a position vs. time graph of an object in simple harmonic motion. By entering a value of phase other than 0, a second graph will appear shifted in phase by the ..

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Change the phase of the blue object so that ..

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Determine what the phase of the blue object must ..

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Click Show Graph to see position vs. time graphs ..

The red and blue objects have the same mass and oscillate in SHM with the same period and amplitude. The only thing different is the phase. Determine what the phase of the blue object must ..

Two objects of equal mass oscillate independently in SHM about the origin. The two objects are initially in phase.
Let b = the minimum number of cycles the blue object object must execute for the objects ..

Two objects of equal mass oscillate independently in SHM about the origin. The two objects are initially in phase.
Let b = the minimum number of cycles the blue object object must execute for the objects ..

For an object in 1-dimensional simple harmonic motion, he above is a graph of one of the following:
a. x-axis: position y-axis: velocity
b. x-axis: position y-axis: acceleration
c x-axis: velocity y-axis: acceleration

The black square shows an object in 1-dimensional simple harmonic motion along the x-axis. Each of the circular colored markers represents one of the following plots for the object's motion.
a. x-axis: position y-axis: velocity
..

A ball oscillates in simple harmonic motion about the origin, while a second ball moves at constant speed in a circular path. Both balls start at y = 0 and have the same initial velocity. The black ..

A ball oscillates in simple harmonic motion about the origin, while a second ball moves at constant speed in a circular path. Both balls start at y = 0 and have the same initial velocity. The black ..

A ball oscillates horizontally in simple harmonic motion on a frictionless surface. Write the equation of the ball's motion. The grid spacing is 0.01 m. Click Show Graph to see graphs of position and velocity vs. ..

A ball oscillates horizontally in simple harmonic motion on a frictionless surface. The ball is initially moving. Write the equation of the ball's motion. The grid spacing is 0.01 m. Click Show Graph to see graphs ..

A ball is attached to the end of a spring which is fixed at the top of the screen. The equilbrium position is fixed at the origin, so the amplitude is the ball's initial height.

A ball is attached to the end of a spring which is fixed at the top of the screen. The ball is released from some initial height and oscillates about its equilibrium position.

A ball is attached to the end of a spring which is fixed at the bottom of the screen. The ball is released from some initial height and oscillates about its equilibrium position.

A ball is attached to the end of a spring which is fixed at the top of the screen. The equilbrium position is fixed at the origin, so the amplitude is the ball's initial height.

A ball is fired out of a spring-loaded cannon. The spring is initially compressed 0.085 m before being released. Assume that the spring has lost all of its initial elastic potential energy as the ball is ..

A red ball is connected to a spring which is fixed at the left side of the screen. At t = 0, the ball is released and oscillates in simple harmonic motion.

A red ball is connected to a spring which is fixed at the left side of the screen. At t = 0, the ball is released and oscillates in simple harmonic motion. The surface on which the ..

When you play the animation, the block oscillates horizontally about the origin on a frictionless table. The origin is in the center, the direction of +x is to the right, and the grid spacing is 0.02 ..

A block slides frictionlessly toward a relaxed spring. As the block compresses the spring, the spring does work on the block, bringing it to a stop. Determine the spring constant of the spring.
The forces ..

At t = 0, a pin is released, allowing a compressed spring to push a block off a frictionless, horizontal table. The block leaves the table when the spring is in its fully-relaxed state.

A ball is held against a spring on a horizontal, frictionless table. At t = 0, the hand is quickly removed, allowing the spring to push the ball off the table. The ball leaves the table when ..

A red ball is connected to a spring which is fixed at the left side of the screen. At t = 0, the ball is released and oscillates in simple harmonic motion.

A red ball is connected to a spring which is fixed at the left side of the screen. At t = 0, the ball is released and oscillates in simple harmonic motion.

A block slides frictionlessly toward a relaxed spring. As the block compresses the spring, the spring does work on the block, bringing it to a stop. Determine the spring constant of the spring.
The forces ..

A block slides frictionlessly toward a relaxed spring. As the block compresses the spring, the spring does work on the block, bringing it to a stop. Determine the spring constant of the spring.
Caution: Unphysical ..

A block slides frictionlessly toward a relaxed spring. As the block compresses the spring, the spring does work on the block. A vector representing the spring force is shown as well as a graph of ..

1. Two objects of equal mass oscillate independently in SHM
about the origin. Find ratios of each of the following (blue/red):
a. amplitude
b. period
c. spring constant
d. total energy
2. The two objects are ..

An object oscillates in SHM in two dimensions.
1. Make the object move in a horizontal or vertical line.
2. Make the object move in a straight diagonal line.
3. Make the object move in a circle.
4. Make ..

A string is oscillated at the left side of the screen and is clamped in place at the right side. The horizontal distance between the ends of the string at equilibrium is 19.0 m. The linear ..

Four consecutive harmonics of a pipe open at one end and closed at the other are shown. The blue lines represent the displacement of the medium from equilibrium as a function of horizontal position along ..

The first four harmonics of a pipe open at both ends are shown. The blue lines represent the displacement of the medium from equilibrium as a function of the horizontal position along the pipe. The ..

The fundamental frequency is produced in closed and open pipes of equal lengths. How to the frequencies produced by the pipes compare? How long would the closed pipe have to be to have the same ..

The first four harmonics of a vibrating spring are shown. The points that do not move are the nodes, and the points having the greatest vertical motion are the antinodes. There is a node at ..

Standing waves are produced in a string that is oscillated at the left side of the screen and is clamped in place at the right side. As the string oscillates, change the value of n ..

For the standing wave shown, points a, c, e, g, and i are nodes. Points b, d, f, and h are antinodes. Note that the distance from c to g is one complete wavelength. This ..

The displacer type of stirling engine in action is shown. The displacer piston moves hot air between the upper and lower portions of the cylinder so that the heat is reused in successive cycles rather ..

The displacer type of stirling engine in action is shown. The displacer piston moves hot air between the upper and lower portions of the cylinder so that the heat is reused in successive cycles rather ..

An object moving horizontally is slowed by a force of kinetic friction. Adjust the initial velocity so that the right side of the block stops at the right-hand edge of the screen.

An object moving horizontally is slowed by a force of kinetic friction. Adjust the magnitude of the initial velocity so that the right side of the block stops at the right-hand edge of the screen.

An object moving horizontally is slowed by a force of kinetic friction. Adjust the magnitude of the initial velocity so that the left side of the block stops at the left-hand edge of the screen.

An object moving horizontally is slowed by a force of kinetic friction. Adjust the coefficient of friction so that the block moves at constant velocity. Next adjust the coefficient of friction so that the right ..

An object moving horizontally is slowed by a force of kinetic friction. Adjust the initial velocity so that the block stops at exactly t = 3 s. Click Show Graph to verify your prediction.

A ray of light is incident from air (blue) on a thin film (yellow). The film is deposited on a transparent medium (gray). Light is reflected from the upper and lower surfaces of the film. ..

A ray of light is incident from air (blue/1) on a thin film (yellow/2). The film is deposited on a transparent medium (gray/3). Light is reflected from the upper and lower surfaces of the film. ..

A ray of light is incident from air on a thin soap film (yellow). The medium below the film is also air. Light is reflected from the upper and lower surfaces of the film. The ..

A ray of light is incident from air on a thin soap film (yellow). The medium below the film is also air. Light is reflected from the upper and lower surfaces of the film. The ..

A light wave of the given frequency is incident from air on a thin film of the given thickness and index of refraction. The wavelength of the light decreases in the film due to the ..

This isn't working correctly. The 2nd reflected ray doesn't have the right angle or length. The corresponding refracted ray doesn't have the correct angle.
A ray of light is incident from air (blue) on a ..

The green disc is free to rotate about at axle located at its center. Three forces represented by the red vectors act on the disc at positions indicated by the blue vectors. If the net ..

The green disc is free to rotate about at axle located at its center. Three forces represented by the red vectors act on the disc at positions indicated by the blue vectors. If the net ..

The green disc is free to rotate about at axle located at its center. Two forces represented by the red vectors act on the disc at positions indicated by the blue vectors. If the net ..

The green disc is free to rotate about an axle located at its center. Three forces represented by the red vectors act on the disc at positions indicated by the blue vectors. If the net ..

A string represented by a chain of mass elements (assumed to be connected) is oscillated by a rod on the left. The right end of the string is initially free. The amount of damping can ..

The dots represent equally-spaced particles on a linear medium. Traveling waves of constant frequency and wavelength are generated on the medium. The motion of the wave is to the right while the motions of the ..

Consider the following model of a linear medium such as a string: a chain of point masses joined by light, strong threads. Traveling waves of constant frequency and wavelength are generated on the medium. The ..

A vertical rod is attached to one end of a string and oscillated at a constant frequency. This produces a transverse wave that travels to the right along the string. The red dots represent selected ..

A vertical rod is attached to one end of a string and oscillated at a constant frequency. This produces a wave that travels to the right along the string. The medium of the string itself ..

A vertical rod is attached to one end of a string and oscillated at a constant frequency. This produces a wave that travels to the right along the string. The medium of the string itself ..

A string represented by a chain of mass elements (assumed to be connected) is oscillated by a rod on the left. The right end of the string is initially free. The amount of damping can ..

A penny on a turntable slides off when the turntable reaches a certain frequency. What is the relationship between the radius of the coin's path and the frequency at which the coin slips? What is ..

A penny on a turntable slides off when the turntable reaches a certain frequency. What is the relationship between the radius of the coin's path and the frequency at which the coin slips? What is ..

A penny on a turntable slides off when the turntable reaches a certain frequency. What is the relationship between the radius of the coin's path and the frequency at which the coin slips? What is ..

Change the pursuer's x- and y-velocity components to intercept
the target. When you are successful, you can make the circle fit
inside the square by stepping the animation. Note that there is
more than one ..

At t = 0, a u-tube contains water (blue). Another fluid (orange) is separated from the water by a partition. When the animation starts, the partition self destructs, and the liquids move to their equilibrium heights. Determine ..

An object moves horizontally through a fluid that exerts a force on
the object that is proportional to the objects velocity. The acceleration
of the object is a = -(k/m)v, where k is ..

An object moves horizontally through a fluid that exerts a force on
the object that is proportional to the objects velocity. The acceleration
of the object is a = -kv, where k is a constant that ..

An object moves horizontally through a fluid that exerts a force on
the object that is proportional to the objects velocity. The acceleration
of the object is a = -(k/m)v, where k is ..

Each of the numbered diagrams shows three vectors. In each diagram, the blue vector is A, the red vector B, and the green vector C. For which diagrams do two of the vectors add to ..

The projectile is subject to a downward gravitational field, a drag force opposing the velocity and proportional the v-squared, and a lift force proportional to and perpendicular to the velocity.

The animation shows a spherical object falling through a fluid with
acceleration a = (k/m)v-g. The positive direction is up. The object has an intial position of 0 and is released from rest. The given ..

Elastic collision in one dimension
Bug: If the initial velocities are equal, the objects will disappear. But then,
you wouldn't have a collision, would you?

A charged particle moves under the influence of an electric field oriented
along the y-axis and a magnetic field oriented along the z-axis (perpendicular
to the screen). Note these sign conventions:
Direction of positive E ..

Play the animation to show a position vs. time graph of a uniformly-accelerating object (red dot). This animation shows how to determine the velocity of the object as a function of time. The two black ..

A charged particle moves under the influence of an electric field oriented along the y-axis and a magnetic field oriented along the z-axis. Sign conventions:
positive E is +y (toward top of screen)
positive B ..

A charged particle moves under the influence of an electric field oriented along the y-axis and a magnetic field oriented along the z-axis. Sign conventions:
positive E is +y (toward top of screen)
positive B ..

A charged particle moves under the influence of an electric field oriented along the y-axis and a magnetic field oriented along the z-axis. Sign conventions:
positive E is +y (toward top of screen)
positive B ..

Play the animation to show a position vs. time graph of a uniformly-accelerating object. The blue line remains tangent to the path of the object. Therefore, the slope of the blue line is the instantaneous ..

Play the animation to show a position vs. time graph of a uniformly-accelerating object. The blue line remains tangent to the path of the object. Therefore, the slope of the blue line is the instantaneous ..

The situation is similar to the last problem but with different initial values. Change the inputs in order to model the motion of an object thrown vertically from the ground at 30 m/s. (What should ..

The situation is similar to the last problem but with different initial values. Change the inputs in order to model the motion of an object thrown vertically from the ground (initial position of 0 m) at 25 ..

A ball is thrown vertically upward with an initial velocity of 5.5 m/s from the surface of a planet devoid of atmosphere. The path of the ball is shown in the right-hand pane.
A position ..

A position vs. time graph of a uniformly-accelerating object is shown. The blue line is always tangent to the path of the object. Determine the acceleration of the object by doing the following:
1. Visually read ..

A position vs. time graph of a uniformly-accelerating object is shown. The blue line is always tangent to the path of the object. Determine the acceleration of the object by first finding the velocities at ..

A position vs. time graph of a uniformly-accelerating object is shown. The blue line is always tangent to the path of the object. The instantaneous velocity is the slope of the tangent line, rise/run.

A position vs. time graph of a uniformly-accelerating object is shown. Collect data on position vs. time and use the finite-difference method to determine the acceleration of the object.

A position vs. time graph of a uniformly-accelerating object is shown. Collect data on position vs. time and use the finite-difference method to determine the acceleration of the object.

A position vs. time graph of a uniformly-accelerating object is shown. The blue line is always tangent to the path of the object. The instantaneous velocity is the slope of the tangent line, rise/run.

A position vs. time graph of a uniformly-accelerating object is shown. The blue line is always tangent to the path of the object. Determine the slopes of two points on the line and use those ..

A platform (black) is suspended from a fixed support by a rubber band. Weight can be added to the platform. When the red stick is pulled away, the platform with its weight will oscillate vertically ..

A platform (black) of mass 0.0500 kg is suspended from a fixed support by a rubber band that obeys Hooke's Law. Standard masses can be added to the platform in increments of 0.0500 kg. When the red ..

A platform of mass 0.050 kg hangs from a spring that obeys Hooke's Law. Mass can be added to the platform in 0.050 kg amounts. The platform is initially held above the equilibrium position by a stick. ..

A platform of mass 0.0500 kg hangs from a spring that obeys Hooke's Law. The platform is initially held above the equilibrium position by a stick. The stick is then pulled out quickly, and the mass ..

A ball is attached to the end of a spring which is fixed at the top of the screen. The equilbrium position is fixed at the origin, so the amplitude is the ball's initial height.

A ball is attached to the end of a spring which is fixed at the top of the screen. The equilbrium position is fixed at the origin, so the amplitude is the ball's initial height.

The physical situation for this problem is like that of a falling leaf where the leaf experiences a lift force that is proportional to and perpendicular to its velocity. We treat the leaf as if ..

The physical situation for this problem is like that of the falling leaf
where the leaf experiences a lift force that is proportional to and
perpendicular to its velocity. In this case, we treat the ..

The physical situation for this problem is like that of the falling leaf
where the leaf experiences a lift force that is proportional to and
perpendicular to its velocity. In this case, we treat the ..

red ball experiences lift proportional to velocity--parametric
blue ball experiences same--eulers
green ball experiences lift and drag proportional to velocity--parametric
black ball experiences lift and drag proportional to velocity--eulers (this
one doesn't calculate correctly)

These two objects fall from rest under the influence of gravity only. The red object is released at t = 0. The release of the green object is delayed by 1.0 s.
Change the height of the window ..

A blue and a red ball are dropped from the roof of Watts. The red ball is released time T after the blue ball. The balls are initially height h above the top of the ..

A blue and a red ball are dropped from the roof of Watts. The red ball is released time T after the blue ball. The balls are initially height h above the top of the ..