Question

A spring with a constant of `4` `kgs^-2` is lying on the ground with one end attached to a wall. An object with a mass of `1` `kg` and speed of `3` `ms^-2` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

The kinetic energy, `E_k=1/2mv^2`, of the moving mass will be converted to spring potential energy in the spring, `E_p=1/2kx^2`. The compression in the spring will be `1.5` `m`.

Explanation:

The kinetic energy of the moving mass is:

`E_k=1/2mv^2=1/2*1*3^2=4.5` `J`

As it collides with the spring, this kinetic energy will be converted into spring potential energy:

`E_p=1/2kx^2`

Rearranging:

`x=sqrt((2E_p)/k)=sqrt((2*4.5)/4) = sqrt(9/4) = 3/2 = 1.5` `m`