Question

A spring with a constant of `2/5 (kg)/s^2` is lying on the ground with one end attached to a wall. An object with a mass of `7/5 kg` and speed of `2 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

I got `3.7m`

Explanation:

At the start there will be the Kinetic Energy `K` of the object that will be converted into Elastic Potential Energy `U_(el)` by compressing the spring.
So we have:
`K=U_(el)`
or:
`cancel(1/2)mv^2=cancel(1/2)kx^2`
the compression `x` will then be given by:
`x=vsqrt(m/k)=2sqrt((7/5)/(2/5))=2sqrt(7/2)=3.7m`