Question

A bullet with a mass of 4.1g and a speed of 650m/s is fired at a block of wood with a mass of 9.6*10^2kg . The block rests on a frictionless surface, and is thin enough that the bullet passes completely through it. Immediately after the bullet exits the block, the speed of the block is 22m/s .

Part A

What is the speed of the bullet when it exits the block? (m/s)

Part B

Is the final kinetic energy of this system equal to, less than, or greater than the initial kinetic energy?

Part C

Explain Part B.

Part D

Verify your answer to part B by calculating the initial kinetic energies of the system. (J)

Part E

Verify your answer to part B by calculating the final kinetic energies of the system. (J)

Answer 1

Use conservation of momentum and conservation of energy concepts to solve this problem.
Start by listing your knowns:

Bullet (let's designate lower case 'a' for the bullet)
m=.0041kg
vi=650m/s
vf= ?

Block (let's designate lower case 'b' for the block)
m=.096kg
vi=0m/s
vf=22m/s

Use conservation of momentum (which is always conserved regardless of the type of collision) to solve for the final velocity of the bullet:

mvai + mvbi = mvaf + mvbf
(.0041kg)(650m/s) + 0 = (.0041kg)vfa + (.096kg)(22m/s)
vaf= 134.88m/s
This is the velocity of the bullet immediately after it exits the block.

Now that you've solved for the velocity, you can compare the initial and final kinetic energies to see if kinetic energy was conserved.

KEai + KEbi
1/2*mvai^2 + 1/2*mbi^2
1/2(.0041kg)(650m/s)^2 + 0
KEi = 866 J

KEaf + KEbf
1/2*mvaf^2 + 1/2*mvbf^2
1/2(.0041kg)(134m/s)^2 + 1/2(.096kg)(22m/s)^2
KEf = 60.522 J

Clearly, Kinetic energy is not conserved. So, the relevent question is, if the energy was not lost to friction, what accounts for the discrepancy between the initial and final kinetic energies?
You are told in the question stem that the block is very thin, which means that during the collision it probably undergoes some extent of deformation. A large amount of the initial kinetic energy is lost to heating up and deforming the block.