6 - Circular Motion and Other Applications of Newton's Laws

# Of gravity is balanced by the resistive force the net

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Unformatted text preview: everal objects falling through air. The high cost of fuel has prompted many truck owners to install wind deﬂectors on their cabs to reduce drag. 6.4 Motion in the Presence of Resistive Forces 167 TABLE 6.1 Terminal Speed for Various Objects Falling Through Air Object Sky diver Baseball (radius 3.7 cm) Golf ball (radius 2.1 cm) Hailstone (radius 0.50 cm) Raindrop (radius 0.20 cm) Mass (kg) 75 0.145 0.046 4.8 10 3.4 10 Cross-Sectional Area (m2) vt (m/s) 0.70 10 10 10 10 60 43 44 14 9.0 4 5 4.2 1.4 7.9 1.3 3 3 5 5 CONCEPTUAL EXAMPLE 6.12 Consider a sky surfer who jumps from a plane with her feet attached ﬁrmly to her surfboard, does some tricks, and then opens her parachute. Describe the forces acting on her during these maneuvers. Solution When the surfer ﬁrst steps out of the plane, she has no vertical velocity. The downward force of gravity causes her to accelerate toward the ground. As her downward speed increases, so does the upward resistive force exerted by the air on her body and the board. This upward force reduces their acceleration, and so their speed increases more slowly. Eventually, they are going so fast that the upward resistive force matches the downward force of gravity. Now the net force is zero and they no longer accelerate, but reach their terminal speed. At some point after reaching terminal speed, she opens her parachute, resulting in a drastic increase in the upward resistive force. The net force (and thus the acceleration) is now upward, in the direction opposite the direction of the velocity. This causes the downward velocity to decrease rapidly; this means the resistive force on the chute also decreases. Eventually the upward resistive force and the downward force of gravity balance each other and a much smaller terminal speed is reached, permitting a safe landing. (Contrary to popular belief, the velocity vector of a sky diver never points upward. You may have seen a videotape in which a sky diver appeared to “rocket” upward once the chute opened. In fact, what happened is that the diver slowed down while the person holding the camera continued falling at high speed.) EXAMPLE 6.13 A sky surfer takes advantage of the upward force of the air on her board. ( Falling Coffee Filters The dependence of resistive force on speed is an empirical relationship. In other words, it is based on observation rather than on a theoretical model. A series of stacked ﬁlters is dropped, and the terminal speeds are measured. Table 6.2 presents data for these coffee ﬁlters as they fall through the air. The time constant is small, so that a dropped ﬁlter quickly reaches terminal speed. Each ﬁlter has a mass of 1.64 g. When the ﬁlters are nested together, they stack in 168 CHAPTER 6 Circular Motion and Other Applications of Newton’s Laws such a way that the front-facing surface area does not increase. Determine the relationship between the resistive force exerted by the air and the speed of the falling ﬁlters. Solution At term...
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## This document was uploaded on 09/19/2013.

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