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?

Question

2007 views around the world

You can reuse this answer
Creative Commons License

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#