A ball of mass m moves in a resisting medium that produces a friction force of magnitude kv2, where v is the ball's speed. If the ball is projected vertically upwards with initial speed u, show by dimensional analysis that when the ball returns to its point of projection, its speed w can be written in the form w = uf(\lambda), where \lambda ku2/mg. Integrate the equations of motion to show that f(\lambda) = (1 + \ lambda)-1/2. Discuss what happens in the two extremes \lambda >> 1, and \lambda << 1. Skip question Exit

A ball of mass m moves in a resisting medium that produces a friction force of magnitude kv2, where v is the ball's speed. If the ball is projected vertically upwards with initial speed u, show by dimensional analysis that when the ball returns to its point of projection, its speed w can be written in the form w = uf(\lambda), where \lambda ku2/mg. Integrate the equations of motion to show that f(\lambda) = (1 + \ lambda)-1/2. Discuss what happens in the two extremes \lambda >> 1, and \lambda << 1. Skip question Exit

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.17P

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