A running track at a university uses a surface with a forceconstant of 2.5 *10 5

Question

A running track at a university uses a surface with a forceconstant of 2.5 *105 N/m. This surface is compressed slightlyevery time a runner's foot lands on it. The force exerted by thefoot, according to a popular shoe company, has a magnitude of2700 N for a typical runner. Treat thetrack's surface as an ideal spring. (a) Find the amount of compression caused by afoot hitting the track.
cm
(b) Find the energy stored briefly in the trackevery time a foot lands.
J (a) Find the amount of compression caused by afoot hitting the track.
cm
(b) Find the energy stored briefly in the trackevery time a foot lands.
J

Explanation / Answer

    Force constant, K = 2.5 * 105 N/m     Force, F = 2700 N     (a)     Compression, X = F / K                              = 2700 / 2.5 * 105                              = 1080 X 10 -5 m                              = 0.0108 m                              = 1.08 cm (b)     Energy stored, E = ( 1/ 2) K X 2                                        = 0.5 * 2.5 * 105 *0.0108 2                              = 14.58 J

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