A ball is held at rest at some height above a horizontal surface. Once the ball is released it falls under gravity, hits the surface at time T1 , and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fraction p (with 1>p>0) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc) that are left unspecified.How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer.How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time Tstop? Give your answer for Tstop as a single formula that contains only two independent variables, namely p and the time T1 . A ball is held at rest at some height above a horizontal surface. Once the ball is released it falls under gravity, hits thesurface at time T1, and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixedfraction p (with 1>p>0) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc) that are leftunspecified.1. How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, notsimply a one-line answer.2. How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time Tstop? Give your answer forTstop as a single formula that contains only two independent variables, namely p and the time T1.

Name: A ball is held at rest at some height above a horizontal surface. Onc
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Description: A ball is held at rest at some height above a horizontal surface. Once the ball is released it falls under gravity, hits the surface at time T1 , and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fracti

Given that: Time taken for first fall=T1Fraction of energy lost per each collision=p (0<p<1)

Answered: A ball is held at rest at some height…

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 9.19P

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A ball is held at rest at some height above a horizontal surface. Once the ball is released it falls under gravity, hits the surface at time T₁, and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed fraction p (with 1>p>0) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc) that are left unspecified.

How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not simply a one-line answer.
How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time T_stop? Give your answer for T_stopas a single formula that contains only two independent variables, namely p and the time T₁.

A ball is held at rest at some height above a horizontal surface. Once the ball is released it falls under gravity, hits the
surface at time T1, and starts bouncing vertically up and down. Suppose that with each bounce the ball loses a fixed
fraction p (with 1>p>0) of its energy. This loss could be due to a number of reasons (inelasticity, drag, etc) that are left
unspecified.
1. How many times will the ball bounce before coming to rest? Provide a detailed explanation of your reasoning, not
simply a one-line answer.
2. How long will it take for the ball to come to rest (if at all), i.e., what is the stopping time Tstop? Give your answer for
Tstop as a single formula that contains only two independent variables, namely p and the time T1.

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