# Conservation of Momentum and/or Energy

1. Mar 30, 2009

### holmeskaei

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

You have been asked to design a “ballistic spring system” to measure the speed of bullets. A bullet of mass m is fired into a block of mass M. The block, with the embedded bullet, then slides across a frictionless table and collides with a horizontal spring whose spring constant is k. The opposite end of the spring is anchored to a wall. The spring’s maximum compression d is measured.

Find an expression for the bullet’s speed v_{\rm B} in terms of m, M, k, and d.

2. Relevant equations

Conservation of momentum m1v1f+m2m2F=m1v1i+m2v2i
Conservation of Energy Ki+Ugi(spring)=Kf+Ugf(spring)

3. The attempt at a solution

Conservation of Momentum rearrangement: (m1+m2)vf=m1v1i

Conservation of energy rearrangement:
1/2mvi^2+0=0+1/2k(delta s)^2
1/2mvi^2=1/2k(delta s)^2
However, I am stuck here. I tried to solve it for vf and got something that is not correct. I know they fit together somehow.

2. Mar 30, 2009

### LowlyPion

Looks like the Vf of your inelastic momentum conservation, becomes the Vi of your spring energy equation.