Question

Two carts are positioned on a track. Cart A with mass M is at one end of the track moving with a velocity v. Cart B with a mass 2M is at the other end of the track and moves with a velocity of -v toward Cart A. There is velcro on the carts along the area where they collide so that they stick rather than bounce. Which answer is the best classification of the collision based on the elasticity of the collision and justification for this classification?

a. the collision is elastic because neither cart is at rest before or after the collision.

Answer 1

The collision is inelastic because the carts stick together, meaning kinetic energy is not conserved, though momentum is. The center of mass velocity remains unchanged if there is no external force, like friction, acting on the system.

Step-by-step explanation:

The collision described is inelastic because the two carts stick together after the collision, which indicates that kinetic energy is not conserved. In an elastic collision, both momentum and kinetic energy are conserved, while in an inelastic collision, only momentum is conserved. To calculate the velocity of the center of mass of the system before and after the collision on a frictionless surface, one would use the conservation of momentum:

• Before the collision: The center of mass velocity is calculated from the total momentum of the system divided by the total mass of the system.
• After the collision: Since the carts stick together, their combined mass is 3M, and the new velocity can be found using the conservation of momentum. Assuming no external forces, the center of mass velocity will remain the same.

If friction were present, it would be an external force that could affect the total momentum, potentially changing the velocity of the center of mass after the collision.