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 `8 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

`10m`

Explanation:

Energy is conserved in this reaction.

Kinetic energy of the object is given by `1/2mv^2`, where `m` is mass and `v` is velocity, and potential energy stored in the spring is given by `1/2kx^2`, where `k` is the spring constant and `x` is the distance it compresses. If there is always the same amount of energy, then

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

`therefore mv^2=kx^2`

Rearranging this to make `x`, the distance of compression, the subject (because the question asks for `x`),

`mv^2 = kx^2`

`(mv^2)/k = x^2`

`sqrt((mv^2)/k) = x`.

Putting in values the question gives us, `k=2(kg)/s^2`, `m=8kg`, `v=5m/s`, then

`x = sqrt((8*5^2)/2)`

`x=sqrt(200/2)`

`x=10m`