A spring with a constant of #2/3 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #1/5 kg# and speed of #1/4 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-04-13T05:45:57

The spring will compress by #=0.14m#

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

The kinetic energy of the object is

#KE=1/2m u^2#

#KE=1/2*1/5*(1/4)^2=1/160J#

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

#PE=1/160J#

So,

#1/2kx^2=1/160#

#x^2=1/(80k)=1/(2/3*80)=3/160#

#x=sqrt(3/160)=0.14m#