College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 5 - Problems - Page 187: 40

Answer

The roller coaster should be moving at a minimum speed of $17.0~m/s$

Work Step by Step

To find the minimum required speed at the top of the loop, we can assume that the gravitational force provides the centripetal force at the top of the loop. That is we can set the radial acceleration equal to $g$: $\frac{v^2}{r} = g$ $v = \sqrt{g~r}$ $v = \sqrt{(9.80~m/s^2)(29.5~m)}$ $v = 17.0~m/s$ The roller coaster should be moving at a minimum speed of $17.0~m/s$
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