A spring with a constant of #6 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #7 kg# and speed of #4 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-10-04T05:14:19

The compression is #=4.32m#

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The spring constant is #k=6kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=7kg#

The speed is #u=4ms^-1#

#KE=1/2*7*(4)^2=56J#

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

#PE=56J#

The spring constant is #=6kgs^-2#

So,

#1/2kx^2=56#

#x^2=2*56/6=18.67m^2#

#x=sqrt(18.67)=4.32m#