A spring with a constant of #8# #kgs^-2# is lying on the ground with one end attached to a wall. An object with a mass of #7# #kg# and speed of #6# #ms^-1# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2016-08-25T10:18:36

The initial kinetic energy is #E_k=1/2mv^2=1/2*7*6^2=126# #J#.

This will be converted to spring potential energy, which will have the same value, #126# #J#. The equation is #E_(sp)=1/2kx^2#.

Rearranging to make the compression distance, #x#, the subject: #x=sqrt((2E_(sp))/k)=sqrt((2*126)/8)=5.6# #m#.