# Bullet hitting block of wood

## 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 = KEf - 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 = FN $$\mu$$ s and since FN = mg i said...
W = (m +M)g $$\mu$$s

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

is this the right appoach?

I cant use conservation of momentum since the sum of external forces arent 0, im assuming since they give the coefficient of kinetic friction.

kuruman
Homework Helper
Gold Member
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.

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

Either way im 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