A spring with a constant of #3 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #3 kg# and speed of #9 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-09-06T05:41:10

The compression is #=9m#

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The spring constant is #k=1kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=3kg#

The speed is #u=9ms^-1#

#KE=1/2*3*(9)^2=243/2J#

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

#PE=243/2J#

The spring constant is #=3kgs^-2#

So,

#1/2kx^2=243/2#

#x^2=(243)/(3)=81m^2#

#x=sqrt(81)=9m#