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 #4 kg # and speed of # 7 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-07-11T15:37:01

The spring will compress by #=5.3m#

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

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=4kg#

The speed is #u=7ms^-1#

#KE=1/2*4*(7)^2=98J#

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

#PE=98J#

So,

#1/2kx^2=98#

#x^2=(2*98)/(7)=28m^2#

#x=sqrt(28)=5.3m#