Running on a treadmill is slightly easier than running outside because there is no drag force to work against. Suppose a \(60 \mathrm{~kg}\) runner completes a \(5.0 \mathrm{~km}\) race in 18 minutes. Use the cross-section area estimate of Example 5.14 to determine the drag force on the runner during the race. What is this force as a fraction of the runner's weight?

Example 5.14

A skydiver and his pet mouse jump from a plane. Estimate their terminal speeds, assuming that they both fall in a prone position with limbs extended. PREPARE There is no net force on a man or a mouse that has reached terminal speed. This is the situation shown in Fig- ure 5.23b, where the drag force D and the weight w are equal in magnitude. Equating expressions for these two forces, we find that PAv = mg To solve this for the terminal speed v for both the man and the mouse, we need to estimate the mass m and cross-section area A of each. FIGURE 5.24 shows how. A typical skydiver might be 1.8 m long and 0.4 m wide (A = 0.72 m) with a mass of 75 kg, while a mouse has a mass of perhaps 20 g (0.020 kg) and is 7 cm long and 3 cm wide (A = 0.07 mx 0.03 m = 0.0021 m). FIGURE 5.24 The cross-section areas of a skydiver and a mouse. 7 cm 0.4 m 1.8 m 3 cm