firing a bullet at a block

[Oerg]

1. The problem statement, all variables and given/known data

A 7.00g bullet, when fired from a gun into a 1:00-kg block of wood held
in a vise, penetrates the block to a depth of 8.00 cm. This block of wood
is placed on a frictionless horizontal surface, and a second 7.00g bullet is
fired from the gun into the block. To what depth will the bullet penetrate
the block in this case?

2. Relevant equations



3. The attempt at a solution
It looks deceptively simple, but I thought the answer was the same at 8 cm. I think it is wrong? Am I?

[LowlyPion]

1. The problem statement, all variables and given/known data

A 7.00g bullet, when fired from a gun into a 1:00-kg block of wood held
in a vise, penetrates the block to a depth of 8.00 cm. This block of wood
is placed on a frictionless horizontal surface, and a second 7.00g bullet is
fired from the gun into the block. To what depth will the bullet penetrate
the block in this case?

2. Relevant equations

3. The attempt at a solution
It looks deceptively simple, but I thought the answer was the same at 8 cm. I think it is wrong? Am I?

Yes, you are wrong.

In the first case all of the Kinetic Energy is absorbed in the block decelerating the bullet.

In the second case since there is no friction your kinetic energy will go into moving the block AND being stopped within the wooden block.

You know from the first case that the stopping power of the wood in terms of the velocity of the bullet.

If you construct your equations to conserve Kinetic Energy - including the deceleration times mass times the unknown distance - and Momentum conservation, you should expect to be able to solve for the depth in the free moving block.