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 #7# # kg# and speed of #2# #ms^-1# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2016-04-28T10:12:57

When the initial kinetic energy, #14# #J# is converted to spring potential energy, the spring will be compressed by #2.16# #m#.

The kinetic energy of the moving mass will be converted to spring potential energy.

Initial kinetic energy:

#E_k=1/2mv^2=1/2*7*2^2=14# #J#.

Final spring potential energy:

#E_p=1/2kx^2#.

Rearranging: #x=sqrt((2E_p)/k)=sqrt((2*14)/6)~~2.16# #m#