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 #7 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 · 2017-07-15T05:06:03

The spring will compress by #=6.61m#

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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=7kg#

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

#KE=1/2*7*(5)^2=145/2J#

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

#PE=175/2J#

So,

#1/2kx^2=175/2#

#x^2=(175)/(4)=43.75m^2#

#x=sqrt(43.75)=6.61m#