A spring with a constant of #4 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #5 kg# and speed of #5 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-06-20T18:08:59

The compression is #=5.59m#

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The spring constant is #k=4kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=5kg#

The speed is #u=5ms^-1#

#KE=1/2*5*(5)^2=62.5J#

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

#PE=62.5J#

So,

#1/2kx^2=62.5#

#x^2=(2*62.5)/(4)=31.25m^2#

#x=sqrt(31.25)=5.59m#