Question

A spring with a constant of `12 (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 `3 m/s` collides with and compresses the spring until it stops moving. How much will the spring compress?

Answer 1

`sqrt6m`

Explanation:

Consider the inital and final conditions of the two objects (namely, spring and mass):

• Initially:
  Spring is at lying at rest, potential energy = `0`
  Mass is moving, kinetic energy = `1/2mv^2`

• Finally:
  Spring is compressed, potential energy = `1/2kx^2`
  Mass is stopped, kinetic energy = 0

Using conservation of energy (if no energy is dissipated into the surroundings), we have:

`0+1/2mv^2 = 1/2kx^2+0`

`=>cancel(1/2)mv^2 = cancel(1/2)kx^2`

`=> x^2 = (m/k)v^2`

`:. x = sqrt(m/k)v = sqrt((8kg)/(12kgs^-2))xx3ms^-1 = sqrt(6)m`