University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 6 - Work and Kinetic Energy - Problems - Exercises - Page 195: 6.18

Answer

(a) $KE = 2.184\times 10^{-18}~J$ (b) KE = 9.80 J (c) The speed would be $v = 2.58~m/s$, which seems perfectly reasonable for a young person.

Work Step by Step

(a) $KE = \frac{1}{2}mv^2$ $KE = \frac{1}{2}(9.109\times 10^{-31}~kg)(2.190\times 10^6~m/s)^2$ $KE = 2.184\times 10^{-18}~J$ (b) We can find the speed $v$ after the object falls 1.0 meter. $v^2 = v_0^2+2ay = 0+2ay$ $v = \sqrt{2ay} = \sqrt{(2)(9.80~m/s^2)(1.0~m)}$ $v = \sqrt{19.6}~m/s$ $KE = \frac{1}{2}mv^2$ $KE = \frac{1}{2}(1.0~kg)(\sqrt{19.6}~m/s)^2$ $KE = 9.80~J$ (c) $KE = \frac{1}{2}mv^2$ $v^2 = \frac{2\times 100~J}{30~kg}$ $v = \sqrt{\frac{200~J}{30~kg}}$ $v = 2.58~m/s$ The time to run 100 meters would be $\frac{100~m}{2.58~m/s}$, which is 38.8 seconds, and this seems perfectly reasonable for a young person.
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