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 # 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 · 2017-08-23T09:28:48

The compression is #=1.15m#

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The spring constant is #k=4kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=4kg#

The speed is #u=2ms^-1#

#KE=1/2*4*(2)^2=8J#

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

#PE=8J#

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

So,

#1/2kx^2=8#

#x^2=(8*2)/(7)=2.29m^2#

#x=sqrt(2.29)=1.51m#