# Conservation of momentum with a spring

• magnifik

## Homework Statement

A spring with spring constant K is compressed by x and used to shoot a ball of mass m into an initially stationary block also of mass m. The ball sticks to the block after the collision. Calculate the final velocity of the ball + block.

## The Attempt at a Solution

F=kx
m1v1 + m2v2 = (m1+m2)v2
1/2mv^2 + 1/2kx^2 = (m1+m2)v2
v2 = 1/4v1^2 + kx^2/4m

i think my value for the spring's energy is wrong and that messed everything up??

F=kx
m1v1 + m2v2 = (m1+m2)v2

So far so good. 1/2mv^2 + 1/2kx^2 = (m1+m2)v2
v2 = 1/4v1^2 + kx^2/4m

That's not quite right. The spring's potential energy is completely converted into the ball's kinetic energy (ignoring friction and the mass of the spring itself).

You can use conservation of energy to find the speed of the ball before it hits the block, but you need to stop there.

When the ball hits the block, kinetic energy is not conserved, because some of the energy is lost to heat.

On the other hand, momentum is conserved before and after the collision between the ball and the block. So use conservation of momentum to find the velocity of the ball+block.