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 #2 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 · 2016-12-18T15:17:07

Use conservation of energy to show that the compression of the spring will be 3.54 m.

Initially, the mass has kinetic energy equal to #1/2 mv^2# = #1/2 (2)(5)^2# = 25 J

During the collision, this kinetic energy is converted completely into potential energy in the compressed spring, given by #1/2kx^2#

So, Once the mass is stopped, all the initial KE is now PE:

25 J = #1/2 kx^2#

Since k = #4(kg)/s^2# we can solve for #x#

25 = 2 #x^2#

#x^2# = 12.5 #m^2#

#x# = 3.54 #m#