Question

A spring with a constant of `9 (kg)/s^2` is lying on the ground with one end attached to a wall. An object with a mass of `3 kg` and speed of `5 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

`(5sqrt3)/3m`

Explanation:

The object has kinetic energy, and assuming that the motion takes place horizontally, all this is given to the spring which stores it as Elastic Potential Energy

so

`KE=EPE`

`1/2mv^2=1/2kx^2`

`cancel(1/2)xx3xx5xx5=cancel(1/2)xx9xxx^2`

`x^2=75/9`

`x=sqrt(75/9)=sqrt(75)/3`

`x=(5sqrt3)/3m`

of course we assuming that the natural length of the spring
`>(5sqrt3)/3m`