Force and equilibrium: Comparing stress exerted by different running shoes

A team of scientists is attempting to develop a new type of running shoe that reduces the stress exerted on a runner’s body during high-intensity running. One important measurement that determines the amount of stress experienced by the body is vertical force exerted on the body during running---both the magnitude and the duration for which the body experiences this force influences the tissue fatigue experienced by runners.

As part of their efforts, they devise an experiment in which they ask subjects to run across a specialized scale that measures the vertical force acting on their body as a function of time. They ask four subjects to run for 7 steps across the scale while wearing each of three different types of shoes, resulting in a total of 12 time series consisting of four participants each testing three shoes. To simplify their data, for each time series they then average the 7 steps into a single “average” step. Then, for each of the three shoes tested, they average together the results of the four participants, resulting in a final experimental data set consisting of three curves showing the force versus time for a typical running step in each of the shoes. These curves are shown in Figure 1.