Exploration 1: Compare Momentum in Different Frames
How does the momentum of a particle change when viewed from a different reference frame? The momentum of each ball in the animation is shown in the table (position is given in meters and time is given in seconds). The graph displays color-coded plots of the velocities of the two particles. Restart.
You can view the collision in another inertial reference frame by entering a new value into the frame velocity text box, \(-10\text{ m/s} < v < 10\text{ m/s}\), before you start the animation. Consider the two particles to be an isolated system and answer the following questions using at least two different inertial reference frames for each animation.
- Does the total momentum depend on your choice of reference frame?
- Does the change in momentum depend on the reference frame?
- Is the total momentum conserved in different reference frames?
- Find the mass and the ratio of the masses of the two balls. Does this result depend on the reference frame?
- Is there a reference frame in which the total momentum is zero? If so, observe the change in velocity in this reference frame and explain why analysis of the collision is particularly simple in this reference frame.
Exploration 2: Compare Energy in Different Frames
How does the energy of a particle change when viewed from a different reference frame? The energy of the two balls in the animation is shown in the table and on the bar graphs to the right. The graph displays the velocity (position is given in meters and time is given in seconds). Restart.
You can view the collision in another inertial reference frame by entering a new value into the frame velocity text box, \(-10\text{ m/s} < v < 10\text{ m/s}\), before you start the animation. Consider the two particles to be an isolated system and answer the following questions using at least two different inertial reference frames for each animation.
- Do the kinetic energies of the individual particles depend on your choice of reference frame?
- Does the change in total kinetic energy due to the collision depend on the reference frame?
- Is the total kinetic energy constant in different reference frames? (Be sure to answer for both animations.)
- Find the mass and the ratio of masses of the two balls. Does this result depend on the reference frame?
- What is special about the reference frame in which the total momentum is zero? Is the kinetic energy zero in this frame?
Exploration 3: Compare Relative Motion in Different Frames
An object may appear to have one motion to one observer and a different motion to a second observer, depending on how the two observers are moving relative to one another. This Exploration lets you view objects from different frames of reference.
There is a river (shown in green) in the center of the screen (the yellow dots are stationary with respect to the water) and two red boats are moving with respect to the river. There is a rectangular barge that is stationary with respect to the river and changes color based on your reference frame. There is also a person (shown in blue) walking on the ground (shown in gray with black dots stationary relative to the ground) near the river.
You can easily change your frame of reference by moving the mouse to different regions and to different objects. For example, if you move the mouse within the river, YOU will become an observer moving with the water. The long thin rectangle (the barge) in the water moves with the water and changes color to represent the reference frame you are in. In addition,
- If you the "Show Information" check box, velocity vectors for your frame of reference will be shown with numbers (position is given in meters and speed is given in \(\mathbf{m/s}\)). Each vector's color corresponds to the color of the object whose reference frame you are in.
- If you click the "show ball" check box, a blue ball is thrown upward from the barge on the river. When you change reference frames you can see how the projectile motion of the ball looks different in different reference frames. Deselect the "show ball" check box to clear the ball's trajectory.
- You can press the mouse button to suspend the animation. If you press with left mouse button, the animation will resume when you release it. If you press with right mouse button, you need to click it again to resume the animation.
- To change the velocity vectors, it is easier to first suspend the animation. Then click anywhere in the animation to bring up the vectors. Now click near the tip of the arrow and drag it to the left or right.
- There are two numbers near the person. Those are the vertical and horizontal speeds of that person in your frame of reference.
- While the animation is suspended, click near the left leg of the person and drag the mouse up and down. You are changing her vertical speed. Click with the right mouse button to resume the animation. The person will now move toward the river, and then swim across it. (The horizontal speed with respect to the ground will increase due to river current).
- Suspend the animation and then turn on "show information." Change the horizontal and vertical speeds of the person so that she swims straight across the river (as seen from the ground). Once you are satisfied with your choice of velocity, deselect the "show information" check box, click in the animation (things are easier to see this way), and resume the animation.
- What ground velocity do you have to give her to accomplish this task?
- Now move the mouse around to change reference frames. Does the person still swim straight across the river in other reference frames? If not, what velocity must you give her (relative to the ground) to accomplish this as seen from the boats? What velocity must you give her (relative to the ground) to accomplish this as seen from the river?
Exploration authored by Fu-Kwun Hwang and Mario Belloni.
Applet authored by Fu-Kwun Hwang, National Taiwan Normal University.
Exploration 4: Compare Motion in Accelerating Frames
Is physics different when viewed in different reference frames? The momentum of each ball is shown in the table, and the kinetic energy of each cart is shown in the bar graph in joules (position is given in meters and time is given in seconds). You can change your reference frame using the text box, \(-2\text{ m/s}^{2} < a < 2\text{ m/s}^{2}\). Answer the following questions. Restart.
- Does the total momentum depend on the reference frame?
- Does the change in momentum depend on the reference frame?
- Is the total momentum conserved in all reference frames?
- Find the ratio of the two masses. Is this result the same in all reference frames?
- Is there a reference frame in which the total momentum is zero?
Exploration 5: Two Airplanes with Different Land Speeds
Two airplanes (not shown to scale) travel the same round-trip distance between two cities (position is given in kilometers and time is given in hours). Both airplanes have the same air speed (\(200\text{ km/hr}\)), but one airplane (the top airplane with the blue wingtip) travels faster or slower relative to the ground because it is subject to a headwind and tailwind. A positive wind velocity means a tailwind on the outbound part of the trip and a headwind on the inbound part of the trip. The wind velocity can be changed by entering a value (\(-199 < v_{\text{wind}} < 199\)) in the text box and registering the value. Restart.
- Before entering a nonzero value in the text box, predict which airplane will reach its destination first if the top (blue) airplane is subject to a head/tail wind.
- Once you have made your prediction, play the animation to see if you were right.
- If you were incorrect, can you now see why you were incorrect? Explain.
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.
