A spring with a constant of #5 (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 #12 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-06-21T12:09:21

The compression is #=9.3m#

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The spring constant is #k=5kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=3kg#

The speed is #u=12ms^-1#

#KE=1/2*3*(12)^2=216J#

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

#PE=216J#

So,

#1/2kx^2=216#

#x^2=(2*216)/(5)=86.4m^2#

#x=sqrt(86.4)=9.3m#