A spring with a constant of #8 (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 #3 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-07-19T09:18:23

The compression is #=2.12m#

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The spring constant is #k=8kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=4kg#

The speed is #u=3ms^-1#

#KE=1/2*4*(3)^2=18J#

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

#PE=18J#

So,

#1/2kx^2=18#

#x^2=(36)/(8)=4.5m^2#

#x=sqrt(4.5)=2.12m#