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?

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Answer 1 · 2016-05-13T13:04:21

#sqrt6m#

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#