Question

You have two carts (like the iOLabs from Studio) with different masses (m1 and m2) that you are doing an experiment with. You give cart 1 an initial speed v1i and send it toward cart 2, which is initially at rest. There is Velcro on each cart such that they will stick together when they collide. The wheels on the cart can be treated as ideal, so you don't need to worry about including the effects of friction. For the following questions, you can assume you know the values of m1, m2, and v1i, in addition to g. a) If your system is cart 1 and cart 2, which of the following is constant during the collision between the carts? [ ] The linear momentum of the system is constant during the collision [ ] The kinetic energy of the system is constant during the collision [ ] Both the linear momentum and the kinetic energy of the system are constant during the collision [ ] Neither is constant during the collision b) Explain your answer to the previous part (addressing both linear momentum and kinetic energy). c) Derive an expression for the final speed vf of the carts right after the collision. d) Now the carts (which are still stuck together) move up a curved part of the track as shown. If your system is cart 1 and cart 2, which of the following is constant during the time when the carts move up the track? [ ] The linear momentum of the system is constant during the time when the carts move up the track [ ] The kinetic energy of the system is constant during the time when the carts move up the track [ ] Both the linear momentum and the kinetic energy of the time when the carts move up the track [ ] Neither is constant during the time when the carts move up the track e) Derive an expression for the maximum height h the carts reach in terms of m1, m2, and v1i, in addition to g.

          You have two carts (like the iOLabs from Studio) with different masses (m1 and m2) that you are doing an experiment with. You give cart 1 an initial speed v1i and send it toward cart 2, which is initially at rest. There is Velcro on each cart such that they will stick together when they collide. The wheels on the cart can be treated as ideal, so you don't need to worry about including the effects of friction. For the following questions, you can assume you know the values of m1, m2, and v1i, in addition to g.

a) If your system is cart 1 and cart 2, which of the following is constant during the collision between the carts?
[ ] The linear momentum of the system is constant during the collision
[ ] The kinetic energy of the system is constant during the collision
[ ] Both the linear momentum and the kinetic energy of the system are constant during the collision
[ ] Neither is constant during the collision

b) Explain your answer to the previous part (addressing both linear momentum and kinetic energy).

c) Derive an expression for the final speed vf of the carts right after the collision.

d) Now the carts (which are still stuck together) move up a curved part of the track as shown. If your system is cart 1 and cart 2, which of the following is constant during the time when the carts move up the track?
[ ] The linear momentum of the system is constant during the time when the carts move up the track
[ ] The kinetic energy of the system is constant during the time when the carts move up the track
[ ] Both the linear momentum and the kinetic energy of the time when the carts move up the track
[ ] Neither is constant during the time when the carts move up the track

e) Derive an expression for the maximum height h the carts reach in terms of m1, m2, and v1i, in addition to g.

Added by Heather R.

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