Question

A spring with a constant of `1 (kg)/s^2` is lying on the ground with one end attached to a wall. An object with a mass of `2/5 kg` and speed of `1/4 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

`0.16m`

Explanation:

According to the law of conservation of energy, the total energy before and after a reaction must be equal.

Kinetic energy before this reaction is `1/2mv^2`, where `m` is mass and `v` is velocity. Potential energy stored in the spring is `1/2kx^2`, where `k` is the spring constant and `x` is the distance it compresses.

Therefore, according to conservation,

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

`mv^2=kx^2`

Now we can put in what we know of the values and rearrange to find `x`,

`2/5*(1/4)^2=1*x^2`

`1/40=x^2`

`x=sqrt(1/40)approx0.16m`