A spring with a constant of #5 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #5 kg# and speed of #8 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-10-16T06:28:34

The spring will compress by #=8m#

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The spring constant is #k=5kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=5kg#

The speed is #u=8ms^-1#

#KE=1/2*5*(8)^2=160J#

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

#PE=160J#

The spring constant is #=5kgs^-2#

So,

#1/2kx^2=160#

#x^2=2*(160)/(5)=64m^2#

#x=sqrt(64)=8m#