# How many meters does the spring compress?

1. Dec 3, 2007

### linnus

1. The problem statement, all variables and given/known data
A 10.5 kg block, attached to the left end of a horizontal massless spring, sits on a frictionless table. The right end of the spring is attached to a vertical piece of wood that is firmly nailed to the table. A 0.0500 kg projectile is fired, from left to right, into the block at 85.5 m/s and stops inside it (this is a completely inelastic collision). The spring constant is k = 105 N/m. How many meters does the spring compress? The potential energy due to the compression of the spring can be calculated with the following formula: PE = (1/2)kx^2.

2. Relevant equations
1/2mv^2
1/2kx^2
momentum before=momentum after

3. The attempt at a solution
uh...
Why can't you do...
1/2mv^2=1/2kx^2?
x=1.866...which isn't right

2. Dec 4, 2007

### dwintz02

Break down the problem into 2 steps. The bullet is going to become embedded in the block. For inelastic collisions, energy conservation is generally not useful because some of the kinetic energy of the bullet is dissipated by friction or turned into heat, and neither of these are easy to calculate. Therefore, use conservation of momentum to calculate the velocity of the block with the bullet embedded in it IMMEDIATELY after the bullet is embedded (ignore the spring for now). Then, when you have that velocity, you can calculate the kinetic energy of the block/bullet (sum the masses also, do you see why?) combo and then use energy conservation to solve for the compression of the spring.