Exercise \(\PageIndex{1}\): Determine momentum and its conservation
A \(1.5\text{-kg}\) box (position is given in meters and time is given in seconds) slides on ice for \(1.5\) seconds and then encounters a rough surface. Restart
- Find the momentum at the start of the animation.
- Is the momentum of the box constant during the first \(1.5\) seconds?
- Is the momentum of the box constant during the next three seconds?
- Is momentum conserved during the first \(1.5\) seconds?
- Is momentum conserved during the next three seconds?
Exercise \(\PageIndex{2}\): Determine \(\Delta p\) for two collisions
A flower pot and a basketball collide with a table (position is given in meters and time is given in seconds). Each has exactly the same mass. Restart.
- Which object undergoes the greater change in momentum after colliding with the floor?
- Which object undergoes the greater change in kinetic energy after colliding with the floor?
- Is the force of the floor on the flower pot greater or less than the force of the floor on the basketball?
Exercise \(\PageIndex{3}\): Determine \(\Delta p\) for two collisions
Two carts collide with a wall as shown in the animation (position is given in meters and time is given in seconds). Assume the two carts are identical. Restart.
- Is kinetic energy constant for either collision?
- Which cart, top or bottom, undergoes the greater change in kinetic energy due to colliding with the wall?
- Is this the same cart that undergoes the greater change in momentum?
- Explain how carts can change their momentum but not their kinetic energy.
Exercise \(\PageIndex{4}\): Determine mass of blue cart
Two carts on an air track collide as shown in the animation (position is given in meters and time is given in seconds). If the mass of the red cart is \(0.8\text{ kg}\), what is the mass of the blue cart? Restart.
Exercise \(\PageIndex{5}\): Determine mass of small car
A large \(2500\text{-kg}\) truck (blue) collides with a small car (brown) as shown in the animation (position is given in meters and time is given in seconds). After the collision, the vehicles move at constant velocity. What is the mass of the small car? Restart.
Exercise \(\PageIndex{6}\): Two carts: determine if momentum is conserved
Two identical carts are shown colliding on a frictionless air track (position is given in meters and time is given in seconds). Which animation(s), if any, correctly models the laws of classical physics? Restart.
Exercise \(\PageIndex{7}\): Three carts: determine if momentum is conserved
Three identical carts, two of which are attached, are shown colliding on a frictionless air track (position is given in meters and time is given in seconds). Which animation(s), if any, correctly models the laws of classical physics? Restart.
Exercise \(\PageIndex{8}\): An explosive collision
A spring that is attached to the end of a cart is compressed, and the cart is placed next to another cart on a low-friction track. The spring is released such that the two carts are "pushed" apart as shown in the animation (position is given in meters and time is given in seconds). The mass of the green cart is \(1.35\text{ kg}\), and the mass of the orange cart is \(0.9\text{ kg}\). Restart.
- What is the magnitude of the momentum of the green cart after the collision?
- What is the magnitude of the momentum of the orange cart after the collision?
- What is the change in momentum of the system due to the release of the spring?
- What is the change in kinetic energy of the system due to the release of the spring?
Exercise \(\PageIndex{9}\): Is the collision elastic or inelastic?
A collision occurs between two pucks on a frictionless surface (position is given in meters and time is given in seconds). Is the collision elastic or inelastic? Note that the masses of the pucks are not necessarily the same. Restart.
Exercise \(\PageIndex{10}\): Is the collision elastic, inelastic, or explosive?
The color-coded graphs show the velocities of the red and black balls, respectively (position is given in meters and time is given in seconds). Would you define the collision shown as elastic, inelastic, totally inelastic, or explosive? Assume both balls have the same mass. Restart.
Example \(\PageIndex{11}\): Determine \(\Delta p\)
Two carts undergo a perfectly inelastic collision (the carts stick together) as shown in the animation. Also shown is a velocity vs. time graph for each cart. You can see the acceleration vs. time graph by clicking the check box (position is given in meters and time is given in seconds). The two carts have equal speed before the collision. You may vary \(m_{1}\) from \(0.5\text{ kg}\) to \(2\text{ kg}\). Restart.
- For which values of \(m_{1}\) is the magnitude of the change in momentum, \(|\Delta\mathbf{p}|\), of the yellow cart greater than, less than, or equal to the magnitude of the change in momentum, \(|\Delta\mathbf{p}|\), of the bluish cart? Why?
- For which values of \(m_{1}\) is the magnitude of the change in acceleration, \(|\Delta\mathbf{a}_{\text{max}}|\), of the yellow cart greater than, less than, or equal to the magnitude of the change in acceleration, \(|\Delta\mathbf{a}_{\text{max}}|\), of the bluish cart? Why?
Example \(\PageIndex{12}\): Analyze several two-d collisions
Several two-dimensional collisions between two balls (the green ball is ball 1 and the blue ball is ball 2) are shown (position is given in meters and time is given in seconds). Also shown is a protractor, which you can drag around (by the little circles on its legs) to measure angles. Restart.
For each animation:
- Determine the initial momentum of each ball
- Determine the final momentum of each ball.
- Calculate and compare the initial momentum to the final momentum for the two-ball system.
Exercise \(\PageIndex{13}\): Determine the center of mass
Four spheres are shown in the animation. A blue sphere is half as massive as a red one and a purple sphere is twice as massive as a red one. Where should the purple one be placed in order for the center of gravity to be at the location of the black dot (position is given in meters)? Restart.
Problem authored by Aaron Titus.
Exercise \(\PageIndex{14}\): Using center of mass
A spring that is attached to the end of a cart is compressed, and the cart is placed next to another cart on a low-friction track. The spring is released such that the two carts are "pushed" apart as shown in the animation (position is given in meters and time is given in seconds). Restart.
- Find the ratio of the green mass to the red mass.
- Find the position of the center of mass.
- Find the distance from each mass to the center of mass at time \(t = 0\text{ s}\).
Physlets were developed at Davidson College and converted from Java to JavaScript using the SwingJS system developed at St. Olaf College.
