Running indoors on a treadmill is slightly easier than running outside because you aren't moving through the air and there is no drag force to oppose your motion. A \(60 \mathrm{~kg}\) man is running at \(4.5 \mathrm{~m} / \mathrm{s}\) on an indoor treadmill. To experience the same intensity workout as he'd get outdoors, he tilts the treadmill at a slight angle, choosing the angle so that the component of his weight force down the ramp is the same as the missing drag force. What is the necessary angle? Use the cross-section area estimate of Example 5.14 to compute the drag force.

Example 5.14

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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