A spring with a constant of #2/5 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #7/5 kg# and speed of #5/4 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-05-02T21:02:14

The spring will compress by #=2.34m#

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

The kinetic energy of the object is

#KE=1/2m u^2#

#KE=1/2*7/5*(5/4)^2=1.09375J#

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

#PE=1.03975J#

So,

#1/2kx^2=1.03975#

#x^2=1.03975*2/(2/5)=5.46875m^2#

#x=sqrt(5.46875)=2.34m#