Question

A spring with a constant of `2 (kg)/s^2` is lying on the ground with one end attached to a wall. An object with a mass of `4 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

The spring will compress by `=1.4m`

Explanation:

Mass of the object is `m=4kg`

Speed of the object is `v=1ms^-1`

The kinetic energy of the object is

`KE=1/2mv^2=1/2*4*1^2=2J`

This energy will be stored in the spring

`E=1/2kx^2`

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

Let the compression of the spring be `=xm`

Therefore,

`2=1/2*2*x^2`

`x^2=(2*2)/2=2m^2`

The compression is

`x=sqrt2=1.4m`