A spring with a constant of #6 (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?

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Answer 1 · 2017-03-05T11:12:46

#5.77m#

Assuming no energy is lost, the energy stored by the spring will equal the kinetic energy beforehand.

Potential energy in a spring is

#E = 1/2kx^2#

where #k# is the spring constant and #x# is the extension.

Kinetic energy is given by

#E = 1/2mv^2#

where #m# is mass and #v# is velocity.

If all the energy is conserved between the two,

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

The question asks for the extension, #x#, so we rearrange to find #x#:

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

#kx^2 = mv^2#

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

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

We know from the question that #k = 6, m = 8# and #v = 5#, so

#x = sqrt((8xx5^2)/6) = sqrt(33.3) = 5.77m#