A rubber ball of mass m is dropped from a cliff. As the ball falls, it is
Question:
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 magnitude bv2, where b is a constant drag coefficient and v is the instantaneous speed of the ball. The drag coefficient b is 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.
c. Write a differential equation for the instantaneous speed v of the ball in terms of time t, the given quantities, and fundamental constants.
d. Determine the terminal speed vt in terms of the given quantities and fundamental constants.
e. Determine the energy dissipated by the drag force during the fall if the ball is released at height h and reaches its terminal speed before hitting the ground, in terms of the given quantities and fundamental constants.
College Mathematics For Business Economics, Life Sciences, And Social Sciences
ISBN: 978-0134674148
14th Edition
Authors: Raymond Barnett, Michael Ziegler, Karl Byleen, Christopher Stocker