A spring with a constant of #5 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #6 kg# and speed of #8 m/s# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-12-13T07:14:15

The compression is #=8.76m#

Mass of the object is #m=6kg#

Speed of the object is #v=8ms^-1#

The kinetic energy of the object is

#KE=1/2mv^2=1/2*6*8^2=192J#

This energy will be stored in the spring

#E=1/2kx^2#

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

Let the compression of the spring be #=xm#

Therefore,

#192=1/2*5*x^2#

#x^2=(2*192)/5=76.8m^2#

The compression is

#x=sqrt76.8=8.76m#