The downward force produced by the quadriceps muscles during the power stroke of bicycle-pedaling motion is shown in FIGURE 11-67 as a function of the crank angle ϕ (see Figure 11-39). The force from these muscles decreases linearly, but the torque depends on the crank angle according to t = r F sin (180° - ϕ). Use the information in the graph, together with a computer spreadsheet, to find the angle ϕ at which the pedaling torque produced by the quadriceps muscle is a maximum. (Note that the actual torque applied to the crank is a result of the action of many muscles in addition to the quadriceps.)

500 400 300 200 100 30 60 90 120 150 180 Crank angle, o (degrees) Force (N)