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 `6 kg` and speed of `3 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

3.7m

Explanation:

Kinetic energy of the object just before hitting the spring:
`E_k=1/2mv^2`
`E_k=1/2*6kg*(3m*s^-1)^2`
`E_k=27J`

Spring potential energy:
`E_e=1/2kx^2`
Where k is the spring constant and x is the spring change in length.

`27J=1/2*4N*m^-1*x^2`
`27/2m^2=x^2`
`sqrt(27/2)m=x`
`3.67...=x`

So the spring will move 3.7m.