Compressing the Ground A running track at Harvard University uses a surface with

Question

Compressing the Ground A running track at Harvard University uses a surface with a force constant of 2.5 times 10^5N/m This surface is compressed slightly every time a runner's foot lands on it. The force exerted by the foot, according to the Saucony shoe company, has a magnitude of 2700 N for a typical runner. Treating the track's surface as an ideal spring, find the amount of compression caused by a foot hitting the track. Express your answer using two significant figures. Treating the track's surface as an ideal spring, find the energy stored briefly in the track every time a foot lands. Express your answer using two significant figures.

Explanation / Answer

Assume the force constant has units of N/m.

1. Compression distance x = F / k = 2700N / 2.5*10^5 N/m = 0.0108m = 10.8mm

2. Energy E = 0.5*k*x^2 = 0.5 * 2.5*10^5 * (0.0108)^2 J = 14.6 J

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