Explanation Given info: 1. The drag force is F d r a g = − b v 2. The constant b is b = 6 π η R 3. At x = 0 , v 0 = 10 cm/s = 0.10 m/s (a) The acceleration is given by a x = d 2 x d t 2 = d d t ( d x d t ) = d d x ( d x d t ) d x d t (1.1) Now substitute d x d t = v x in the above equation to get a x = d v x d t v x (1.2) Rearrange the above equation a x = v x d v x d x (1.3) (b) The drag force on the ball is F d r a g = − b v x = − 6 π η R v x (1.4) Consider m is the mass of the ball, hence, the acceleration is a x = F d r a g m = − 6 π η R v x m (1.5) Substitute the value of a x from equation (1.3) to equation (1.5) v x d v x d x = − 6 π η R m v x d v x = − 6 π η R m d x [ v x ] v 0 v x = − [ 6 π η R m x ] 0 x v x − v 0 = − 6 π η R m x v x = v 0 − 6 π η R m x (1

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Chs 1-42) Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition)

4th Edition

ISBN: 9780133953145

Author: Randall D. Knight (Professor Emeritus)

Publisher: PEARSON

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Density of Solids

The density of a substance refers to how much matter is present in a given amount of space. It is expressed as the ratio of the mass of the substance to its volume.

Question

Chapter 6, Problem 77EAP

To determine

(a)Using calculus prove that ax=vxdvdx.

(b)The expression for speed vx as a function of x.

(c)For the given parameter, calculate the distance ball will travel before stopping.

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Chapter 6, Problem 76EAP

Chapter 6, Problem 78EAP

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Chapter 6 Solutions

Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (Chs 1-42) Plus Mastering Physics with Pearson eText -- Access Card Package (4th Edition)

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(a)Using calculus prove that a x = v x d v d x . (b)The expression for speed v x as a function of x . (c)For the given parameter, calculate the distance ball will travel before stopping.

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(a)Using calculus prove that ax=vxdvdx. (b)The expression for speed vx as a function of x. (c)For the given parameter, calculate the distance ball will travel before stopping.

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Chapter 6 Solutions

(a)Using calculus prove that ax=vxdvdx.

(b)The expression for speed vx as a function of x.

(c)For the given parameter, calculate the distance ball will travel before stopping.