A spring with a constant of #7 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #8 kg# and speed of #2 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-05-17T06:02:36

The compression is #=2.14m#

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The spring constant is #k=7kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

#KE=1/2*8*(2)^2=16J#

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

#PE=16J#

So,

#1/2kx^2=16#

#x^2=16*2/(7)=4.57m^2#

#x=sqrt(4.57)=2.14m#