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?

Question

1221 views around the world

You can reuse this answer
Creative Commons License

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)#