A spring with a constant of #6 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 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 · 2017-05-16T11:18:18

The spring will compress by #=0.71m#

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The spring constant is #k=6kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

#KE=1/2*3*(1)^2=1.5J#

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

#PE=1.5J#

So,

#1/2kx^2=1.5#

#x^2=1.5*2/(6)=0.5m^2#

#x=sqrt(0.5)=0.71m#