Physics Technology Update (4th Edition)

Published by Pearson
ISBN 10: 0-32190-308-0
ISBN 13: 978-0-32190-308-2

Chapter 12 - Gravity - Problems and Conceptual Exercises - Page 412: 60

Answer

a) $v=2.07\times 10^{-7}m/s$ b) the speed in part(a) will increase by a factor of $\sqrt 2$

Work Step by Step

(a) We can find the required speed as follows: $K.E_i+U_i=K.E_f+U_f$ $0-G\frac{m^2}{r_i}=2(\frac{1}{2}mv^2)-G\frac{m^2}{r_f}$ $\implies mv^2=GM^2(\frac{1}{r_f}-\frac{1}{r_i})$ This simplifies to: $v=\sqrt{GM(\frac{1}{r_f}-\frac{1}{r_i})}$ We plug in the known values to obtain: $v=\sqrt{(6.67\times 10^{-11})(0.148)(\frac{1}{145}-\frac{1}{395})}$ $v=2.07\times 10^{-7}m/s$ (b) Since speed is directly proportional to the square root of the mass (that is $v\propto \sqrt m$), then if the mass is doubled the speed in part(a) will increase by a factor of $\sqrt 2.$
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