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 #2 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 · 2018-05-22T06:17:11

The compression is #=4.28m#

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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=2kg#

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

#KE=1/2*2*(8)^2=64J#

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

#PE=64J#

So,

#1/2kx^2=64#

#x^2=(128)/(7)=18.29m^2#

#x=sqrt(18.29)=4.28m#