Question

In recent years, the Nike vaporfly running shoes have caused a stir in the world of high-performance marathon running. The shoes, as can be seen in the picture at right, are significantly thicker than conventional running shoes. They have a special midsole that is exceptionally squishy. Imagine a 70-kg runner is wearing the vaporfly shoes. At the top of his stride (when his center of mass is at its farthest point above the ground), his speed is 10 m/s.

b. After the runner achieves the speed you calculated in part a, his center of mass drops by another 2.0 cm as the midsole of his shoe compresses, slowing the runner back down to 10 m/s. How much work does the shoe do on the runner? Show your work.

Answer 1

Part A

The speed at the bottom of the stride can be calculated by adding the gained potential energy to his inital kinetic energy to find his final kinetic energy

We know that

Equating the two, we get

Part B

Here, the sole dissipates both kinetic energy and potential energy to do work.

Therefore, the work done will be the sum of the kinetic energy dissipated, as well as the potential energy.

Since we are going back to the original speed, the kinetic energy dissipated will be the difference between the final and initial kinetic energy is Part A

The potential energy gained will also be dissipated, as the body is at the original speed, and has not increased its speed.

Therefore, the total work done by the sole is