A spring with a constant of #6# #kgs^-2# is lying on the ground with one end attached to a wall. An object with a mass of #3# #kg# and speed of #9# #ms^-1# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2018-03-12T14:01:45

This is a case where kinetic energy #E_k=1/2mv^2# is converted to spring potential energy #E_(sp)=1/2kx^2#.

#E_k=1/2mv^2=1/2xx3xx9^2=121.5# #J#

Rearranging: #x=sqrt((2E)/k)=sqrt((2xx121.5)/6)=6.36# #m#

Here is the rearranging of the spring potential energy equation. I have left off the subscript for simplicity:

#E=1/2kx^2#

Multiply both sides by 2:

#2E=kx^2#

Divide both sides by #k#:

#(2e)/k=x^2#

Swap the sides:

#x^2=(2E)/k#

Take the square root of both sides:

#x=sqrt((2E)/k)#