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?

1 Answer
May 13, 2016

Answer:

#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#