(adsbygoogle = window.adsbygoogle || []).push({}); 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 v_{B}.

Express your answer in terms of the variables m, M, k, d, and constant g.

2. Relevant equations

KE = (1/2)mv^{2}

U_{g}= mgy

U_{s}= (1/2)kx^{2}

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)mvi^{2}+ mgyi + (1/2)kxi^{2}= (1/2)mvf^{2}+ mgyf + (1/2)kxf^{2}

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)mvi^{2}+ (1/2)kxi^{2}= (1/2)mvf^{2}+ (1/2)kxf^{2}

Incorporating the variables we are given:

(1/2)mvi^{2}= (1/2)kd^{2}

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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Ballistic Spring System help!

**Physics Forums | Science Articles, Homework Help, Discussion**