A spring with a constant of #7 (kg)/s^2# is lying on the ground with one end attached to a wall. An object with a mass of #2 kg# and speed of #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 · 2017-06-13T13:00:33

I got #214cm#

During this process the initial kinetic energy #K# of the object will be converted into elastic potential energy #U_(el)#; so we have:

#K=U_(el)#

Or:

#cancel(1/2)mv^2=cancel(1/2)kx^2#

Where #x# represents the compression of the spring. Rearranging:

#x=vsqrt(m/k)=4sqrt(2/7)=2.14m=214cm#