Momentum problem driving me crazy.

[Demondo]

I asked this on IRC but with only 7 people there, including myself, I'm not too confident I'll get an answer anyway...

A 7g bulet, when fired from a gun into a 1kg block of wood held in a vise, penetrates the block to a depth of 8cm. What If? This block of wood is placed on a frictionless horizontal surface, and a second 7g bullet is fired from the gun into the block. To what depth will the bullet penetrate the block in this case?

It seems like such an odd question because you aren't given the bullet's speed. Anyone have any idea what would happen? It is possible that the bullet would push the block, but that just doesn't seem likely at all because of it's speed. Or it could puncture just as deeply, but this time the block moves. But I'm really uncertain about what happens. Any help would be appraicted.

 

[Ebolamonk3y]

Impulse... I think the bullet still goes in regardless... Probably not as deep or will not penetrate it... It will be a perfect inelastic collision where the 2 masses become one...

Say... If someone where to shoot you with a paintball gun in the face and you had your mask on... You would get paint all over your face. If you were to stand on ice or some frictionless surface and the same situation occured... You still get paint over your face and a fun slide in the direction of the paintball...

Thats what I think at least...

 

[Doc Al]

If you make a few simplifying assumptions, the problem is straightforward.

With the wood in the vise, all the kinetic energy of the bullet goes into penetrating the wood and thus is transformed into thermal energy. We'll make the simplifying assumption that the force between the bullet and wood is uniform: thus the given KE of the bullet leads to the given penetration, FxD = ΔKE.

With the wood free to move, assume that the bullet will again penetrate the wood making the collision perfectly inelastic. (Not unreasonable.) Apply conservation of momentum to get the speed of the block plus bullet post collision, then use that speed to calculate its KE. Now find the ΔKE during the collision--that's the energy used to penetrate the wood. In this case the penetration is less because some of the bullet's energy is used to accelerate the wood.