A spring with a constant of #1/5 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #1 kg# and speed of #2 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-06-17T12:06:46

The compression is #=4.47m#

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The spring constant is #k=1/5kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

The mass is #m=1kg#

The speed is #u=2ms^-1#

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

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

#PE=2J#

So,

#1/2kx^2=2#

#x^2=(4)/(1/5)=20m^2#

#x=sqrt(20)=4.47m#