Question

A spring with a constant of `4 (kg)/s^2` is lying on the ground with one end attached to a wall. An object with a mass of `2 kg` and speed of `1 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

I got `0.7m`

Explanation:

In theory all the Kinetic Energy of the object will be converted into Elastic Potential Energy so we can write:
`1/2mv^2=1/2kx^2`
`cancel(1/2)mv^2=cancel(1/2)kx^2`
rearranging and solving for the compression of the spring `x`:
`x=vsqrt(m/k)=1*sqrt(2/4)=sqrt(1/2)=0.7m`