A spring with a constant of #4 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #6 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
Apr 9, 2018

Answer:

3.7m

Explanation:

Kinetic energy of the object just before hitting the spring:
#E_k=1/2mv^2#
#E_k=1/2*6kg*(3m*s^-1)^2#
#E_k=27J#

Spring potential energy:
#E_e=1/2kx^2#
Where k is the spring constant and x is the spring change in length.

#27J=1/2*4N*m^-1*x^2#
#27/2m^2=x^2#
#sqrt(27/2)m=x#
#3.67...=x#

So the spring will move 3.7m.