A spring with a constant of #1# #kgs^-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# #ms^-1# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2016-02-04T06:10:29

In this instance kinetic energy is converted into spring potential energy. The spring compresses by #8.5# #m#.

The initial kinetic energy of the moving mass is given by:

#E_k=1/2mv^2=1/2*8*3^2=36# #J#

All of this energy (we are assuming no friction) will be converted to spring potential energy in the spring, according to the equation:

#E_p=1/2kx^2# where #k# is the spring constant and #x# is the distance compressed (or expanded).

We can rearrange this to make #x# the subject:

#x=sqrt((2E_p)/k) = sqrt((2*36)/1) = sqrt 72 =8.5# #m#