Momentum and Kinetic Energy after an Inelastic Collision

[Manh]

Homework Statement

A small bullet is fired into a large piece of wood. After the bullet penetrates the wood, the assembly moves as one unit along a low-friction track in the direction of travel of the bullet.

A. After the bullet is stuck in the piece of wood, is the momentum of the wood (not including the bullet; assuming the piece of wood was initially at rest) greater than, equal to, or less than the initial momentum of the bullet?
a) The momentum of the wood is equal to the initial momentum of the bullet.
b) The momentum of the wood is less than the initial momentum of the bullet.
c) The momentum of the wood is greater than the initial momentum of the bullet.

B. Is the combined kinetic energy of the bullet and the wood after the bullet is stuck in the wood greater than, equal to, or less than the initial kinetic energy of the bullet?
a) The combined energy is greater than the initial kinetic energy of the bullet.
b) The combined energy is equal to the initial kinetic energy of the bullet.
c) The combined energy is less than the initial kinetic energy of the bullet.

2. Homework Equations

The Attempt at a Solution

A.
a) The momentum of the wood is equal to the initial momentum of the bullet.

B.
c) The combined energy is less than the initial kinetic energy of the bullet.

*I'm not sure with my answers if they are correct or incorrect.

 

[Chestermiller]

Please tell us your rationale for each of these answers.

 

[Manh]

For part A, According to the conservation of momentum, I picked a) The momentum of the wood is equal to the initial momentum of the bullet. Also, I see the wood does not move and remains at rest and therefore it may have a zero of momentum. The answer could be b) The momentum of the wood is less than the initial momentum of the bullet.

For part B, The bullet is stuck in the wood and the wood does not make a motion. So, their combined kinetic energy could be zero and that is less than initial kinetic energy of the bullet.

 

[Chestermiller]

For part A, According to the conservation of momentum, I picked a) The momentum of the wood is equal to the initial momentum of the bullet. Also, I see the wood does not move and remains at rest and therefore it may have a zero of momentum. The answer could be b) The momentum of the wood is less than the initial momentum of the bullet.

If the bullet is stuck in the wood, and the wood is moving in the final state, is the bullet also moving? If momentum is conserved, is the combined momentum of the wood and the bullet the same as the original momentum of the bullet? If, in the final state, the bullet still has momentum, what does this imply about how the final momentum of the wood compares with the initial momentum of the bullet?

For part B, The bullet is stuck in the wood and the wood does not make a motion. So, their combined kinetic energy could be zero and that is less than initial kinetic energy of the bullet.

If m_W is the mass of the wood, m_B is the mass of the bullet, and V₀ is the initial velocity of the bullet, write the conservation of momentum equation you can use to determine the final velocity V of the combination of wood and bullet. In terms of these parameters, what is the starting kinetic energy. In terms of these parameters, what is the final kinetic energy. What is the change in kinetic energy?

Chet