Question

A physic student sets out to experiment on the effect of drag forces on a ball of mass m by giving the ball an initial velocity nu_0 upwards and then downwards as describe below. In both cases, the ball experiences a force of air resistance whose magnitude is given by F = -k nu Where k is a positive constant. The positive direction for all vector quantities is taken to be upwards. Express all algebraic answers in terms of m. k, nu_0, and fundamental constants. Case A: Standing on the ground, he throws the ball of mass m vertically upward with an initial speed of v_0. Case B: Standing on top of a very tall building, he throws the ball of mass m vertically downwards with an initial speed of v_0. The round dots below represents the ball in both cases, draw free-body diagrams indicating all of the forces acting on the ball. Indicate the direction of acceleration on the side in each case. Using Newton's Second Law of Motion, write, but do NOT solve, a differential equation for the instantaneous speed v of the ball in both cases as a function of time t. Determine the terminal speed of the ball in both cases. How similar and different are they? Does the magnitude of the acceleration of the ball in Case A increase, decrease, or remain the same as the ball moves upward? Increases decreases remains the same Justify your answer. Does the magnitude of the acceleration of the ball in Case B increase, decrease, or remain the same as the ball moves downward? Increases decreases remains the same Justify your answer. Does the magnitude of the acceleration of the ball in Case A greater, less than, or the same as the magnitude of the acceleration of the ball in Case B? Greater Less than the same Justify your answer. Solve the differential equation in part (b) to determine the velocity of the ball as a function of time. Show all appropriate steps. Case A, ball thrown upwards Case B, ball thrown downwards Determine the time for the ball to reach maximum height in case A. On the space provided below, sketch a graph of velocity versus time for the upward and downward parts of the ball's flight (case A), where t, is the time at which the ball returns to the height from which it was thrown. Does it take longer for the ball to rise to its maximum height or to fall from its maximum height back to the height from which it was thrown? longer to rise longer to fall Justify your answer.

Answer 1

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