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A rubber ball of mass m is dropped from a cliff. As the ball falls, it is subject to air drag (a resistive force caused by the air). The drag force on the ball has a magnitude bv2, where bis a constant drag coefficient and v is the instantaneous speed of the ball. The drag coefficient bis directly proportional to the cross-sectional area of the ball and the density of the air and does not depend on the mass of the ball. As the ball falls, its speed approaches a constant value called the terminal speed.

Draw and label all the forces on the ball at some instant before it reaches terminal speed.

State whether the magnitude of the acceleration of the ball of mass m increases, decreases, or remains the same as the ball approaches terminal speed. Explain.

Write, but do NOT solve, a differential equation for the instantaneous speed vof the ball in terms of time t, the given quantities, and fundamental constants.

Determine the terminal speed vtin terms of the given quantities and fundamental constants.

Determine the energy dissipated by the drag force during the fall if the ball is released at height hand reaches its terminal speed before hitting the ground, in terms of the given quantities and fundamental constants. (this question requires knowledge of potential and kinetic energy, often not introduced until later in a physics course)

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Posted by Fiona Cunningham 8 months ago

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