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

1 Answer
Apr 19, 2016

Answer:

#10m#

Explanation:

Energy is conserved in this reaction.

Kinetic energy of the object is given by #1/2mv^2#, where #m# is mass and #v# is velocity, and potential energy stored in the spring is given by #1/2kx^2#, where #k# is the spring constant and #x# is the distance it compresses. If there is always the same amount of energy, then

#1/2mv^2 = 1/2kx^2#

#therefore mv^2=kx^2#

Rearranging this to make #x#, the distance of compression, the subject (because the question asks for #x#),

#mv^2 = kx^2#

#(mv^2)/k = x^2#

#sqrt((mv^2)/k) = x#.

Putting in values the question gives us, #k=2(kg)/s^2#, #m=8kg#, #v=5m/s#, then

#x = sqrt((8*5^2)/2)#

#x=sqrt(200/2)#

#x=10m#