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09/09/09 - Air Resistance and Drag and Forces in Static Equilibrium
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 | Air resistance and drag at moderate velocities (1-100 m/s)
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| An object moving through air usually experiences resistance to its motion.
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 | This is called air drag. If you ever stuck your hand out of a car window when you were riding in a car at high speed, you may have felt the air pushing against your hand. You probably noticed that the amount of force on your hand depended on both the speed of the car and the angle at which you tipped your hand. This is summarized in the formula for air drag (for speeds from 1-100 m/s): F = 0.5ρAv2, where ρ is the density of air in kg/m3, A is the cross-sectional area in m2 of the object moving through the air, and v is the speed of the object relative to the air in m/s. If an object is falling through the air from rest, the drag force builds up as the object's speed increases. Eventually, the drag force is as large in the upward direction as the pull of gravity (mg) downward on the object. At this point, the two forces are in equilibrium and the falling object ceases to accelerate. Instead, it falls at a constant velocity called the "terminal velocity." Since 0.5ρAv2 = mg, the terminal velocity for a falling object is
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| Fluid resistance at low velocities (< 1 m/s)
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| The drag force for spherical objects moving slowly through a fluid is found to be described fairly well by the formula
where C is a constant that depends on the fluid (such as water), r is the radius of the spherical object, and v is the velocity of the object. From this equation we find that the magnitude of the terminal velocity of a spherical object moving slowly through a fluid is
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| Forces in static equilibrium
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| When the forces acting on an object are in balance (i.e., their vector sum is zero), the object is said to be in static equilibrium. It's acceleration is then zero, so it is either not moving, or it is moving at constant speed in a straight line.
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| Read the remainder of Chapter 3, pp. 75-84, and the first part of Chapter 4, pp. 91-99.
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