Question

A spring with a constant of `7 (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 `8 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

The compression is `=4.28m`

Explanation:

The spring constant is `k=7kgs^-2`

The kinetic energy of the object is

`KE=1/2m u^2`

The mass is `m=2kg`

The speed is `u=8ms^-1`

`KE=1/2*2*(8)^2=64J`

This kinetic energy will be stored in the spring as potential energy.

`PE=64J`

So,

`1/2kx^2=64`

`x^2=(128)/(7)=18.29m^2`

`x=sqrt(18.29)=4.28m`