A spring with a constant of #9 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #5 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

1 Answer
Mar 9, 2017

Answer:

#(5sqrt3)/3m#

Explanation:

The object has kinetic energy, and assuming that the motion takes place horizontally, all this is given to the spring which stores it as Elastic Potential Energy

so

#KE=EPE#

#1/2mv^2=1/2kx^2#

#cancel(1/2)xx3xx5xx5=cancel(1/2)xx9xxx^2#

#x^2=75/9#

#x=sqrt(75/9)=sqrt(75)/3#

#x=(5sqrt3)/3m#

of course we assuming that the natural length of the spring
#>(5sqrt3)/3m#