# Homework Help: Ballistic Spring System help!

1. Oct 26, 2008

### jemstone

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 spring whose spring constant is k is suspended from the ceiling. A block of mass M hangs from the spring. A bullet of mass m is fired vertically upward into the bottom of the block. The spring's maximum compression d is measured.

Find an expression for the bullet's speed vB.
Express your answer in terms of the variables m, M, k, d, and constant g.

2. Relevant equations
KE = (1/2)mv2
Ug = mgy
Us = (1/2)kx2

KEi + Ugi + Usi = KEf + Ugf + Usf

3. The attempt at a solution

This problem is going to end up getting really messy, but I am not sure how to incorporate the mass of the box (M) This is what I started with:

(1/2)mvi2 + mgyi + (1/2)kxi2 = (1/2)mvf2 + mgyf + (1/2)kxf2

now I'm assuming that mgy values are 0 because we are not given any value for the height the box is above the ground. so that would give:

(1/2)mvi2 + (1/2)kxi2 = (1/2)mvf2 + (1/2)kxf2

Incorporating the variables we are given:

(1/2)mvi2 = (1/2)kd2

however this does not include gravity (which I am sure needs to be included somewhere) or the mass of the box (M)

2. Oct 27, 2008

### loferbri

i don't know if this help but maybe if you put the spring at rest at y=0 and then when it's compress the y=d you could incorporate then the mgy equitation therefore putting g and M in the equation