A spring with a constant of #9# #kgs^-2# is lying on the ground with one end attached to a wall. An object with a mass of #2# #kg# and speed of #12# #ms^-1# collides with and compresses the spring until it stops moving. How much will the spring compress?

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Answer 1 · 2017-06-11T07:54:32

The compression is #=5.66m#

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The spring constant is #k=9kgs^-2#

The kinetic energy of the object is

#KE=1/2m u^2#

#KE=1/2*2*(12)^2=144J#

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

#PE=144J#

So,

#1/2kx^2=144#

#x^2=2*(144)/(9)=32m^2#

#x=sqrt(32)=5.66m#

Answer 2 · 2017-06-11T07:56:44

The displacement of the spring, #x#, will be #4# #m#.

The kinetic energy of the moving object will be #E_k=1/2mv^2=1/2xx2xx12^2=144# #J#.

This will be converted to spring potential energy: #E_"sp"=1/2kx^2#.

Rearranging: #x=sqrt((E_"sp")/k)#

We can substitute in the calculated value of #E_k# for #E_"sp"#:

#x=sqrt((E_"sp")/k)=sqrt((E_k)/k)=sqrt((144)/9) = 12/3 = 4# #m#