University Physics with Modern Physics (14th Edition)

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

Chapter 5 - Applying Newton's Laws - Problems - Exercises - Page 163: 5.46

Answer

The normal force on the car when it is at the bottom of the track is 21.7 N.

Work Step by Step

At the top of the track: $\sum F = \frac{mv^2}{r}$ $F_N+mg = \frac{mv^2}{r}$ $F_N = \frac{mv^2}{r}-mg$ At the bottom of the track: $\sum F = \frac{mv^2}{r}$ $F_N-mg = \frac{mv^2}{r}$ $F_N = \frac{mv^2}{r}+mg$ The normal force at the bottom of the track is $2mg$ greater than the normal force at the top of the track. $F_N = 6.00~N + 2mg$ $F_N = 6.00~N+(2)(0.800~kg)(9.80~m/s^2)$ $F_N = 21.7~N$ The normal force on the car when it is at the bottom of the track is 21.7 N.
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