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 198: 6.67

Answer

(a) The maximum speed is 1.8 m/s. The maximum speed is 4.0 mi/h. (b) The acceleration is $180~m/s^2$, which is 18.4 g. The force exerted on the head is 900 N.

Work Step by Step

(a) $E = \frac{1}{2}mv^2 = 8.0~J$ $v^2 = \frac{16.0~J}{m}$ $v = \sqrt{\frac{16.0~J}{5.0~kg}}$ $v = 1.8~m/s$ The maximum speed is 1.8 m/s. We can convert this speed to mi/h. $v = (1.8~m/s)(\frac{3600~s}{1~h})(\frac{1~mi}{1609~m})$ $v = 4.0~mi/h$ The maximum speed is 4.0 mi/h. (b) $a = \frac{v}{t} = \frac{1.8~m/s}{0.010~s}$ $a = 180~m/s^2$ $a = \frac{180~m/s^2}{9.80~m/s^2} = 18.4~g$ The acceleration is $180~m/s^2$, which is 18.4 g. We can find the force exerted on the head. $F = ma = (5.00~kg)(180~m/s^2)$ $F = 900~N$ The force exerted on the head is 900 N.
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