Question

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

Answer 1

`x = 2sqrt(5/2)`[m]

Explanation:

The moving object has a kinetic energy given by `E_c =1/2 m v^2`
All this energy is absorbed by the spring as potential energy as `E_p = 1/2K x^2`. Equating the energies
`1/2 m v^2 = 1/2K x^2`
and solving regarding `x` gives
`x = v sqrt(m/K) = 2sqrt(5/2)`[m]