A spring with a constant of #3 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #4 kg# and speed of #1 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-05-18T11:53:38

The compression is #=1.15m#

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The spring constant is #k=3kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

#KE=1/2*4*(1)^2=2J#

This kinetic energy will be stored in the spring as potential energy.

#PE=2J#

So,

#1/2kx^2=2#

#x^2=2*2/(3)=1.33m^2#

#x=sqrt(1.33)=1.15m#