How Far Does the Block Slide Before Coming to Rest?

[renaldocoetz]

Homework Statement

Consider a bullet of mass m fired at a speed of V₀ into a wooden block of mass M. The bullet instantaneously comes to rest in the block. The block with the embedded bullet slides along a horizontal surface with a coefficient of kinetic energy $$\mu$$.
How far does the block slide before it comes to rest? Express your answer in terms of m, M, $$\mu$$ and g.

Homework Equations

W = Fs

W = KE_f - KE₀

where s = displacement

The Attempt at a Solution

I started by saying W = Fs and thought the only net force working here is kinetic friction.
so W = F_N $$\mu$$ s and since F_N = mg i said...
W = (m +M)g $$\mu$$s

then i said since W = KE_f - KE₀ ...
(m + M)g$$\mu$$s = KE_f - KE₀

is this the right appoach?

I can't use conservation of momentum since the sum of external forces arent 0, I am assuming since they give the coefficient of kinetic friction.

 

[kuruman]

Yes, you can use conservation of momentum. The problem says that the bullet stops instantly. This means that the collision is completed before the block starts moving, i.e. before the external force of friction with the table starts acting on the block. You need to conserve momentum to find the initial velocity of the block+bullet system.

 

[renaldocoetz]

OK it seems i missread. It says "coefficient of kinetic energy", not "coefficient of kinetic friction".

Either way I am really clueless as to how to proceed :( Especially how to eventually get to distance. How do i know when to use conservation of momentum and when to use conserv of Kinetical Energy?

 

[kuruman]

It should be coefficient of kinetic friction. It is safe to say that you conserve momentum when you have a collision, when two objects come together or push each other apart. As far as energy conservation is concerned, one usually talks about conservation of mechanical energy, which the sum of kinetic and potential energy. You conserve that when there are no dissipative forces such as friction or air resistance. If there are such things present (there is usually wording in the problem to indicate one way or the other), you have to use the work-energy theorem that says that the change in kinetic energy is equal to the net work (work done by the net force).

In answer to your question, yes your approach is correct. All you need to do is find KE₀. You do that by conserving momentum for the part of the motion where the bullet embeds itself in the block.