A spring with a constant of #1 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #2/3 kg# and speed of #1/4 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-08-31T06:45:59

THe compression is #=0.289m#

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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=4kg#

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

#KE=1/2*2/3*(1/4)^2=1/48J#

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

#PE=8J#

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

So,

#1/2kx^2=1/48#

#x^2=(2)/(28)=0.0833m^2#

#x=sqrt(0.0833)=0.289m#