Physics (10th Edition)

Published by Wiley
ISBN 10: 1118486897
ISBN 13: 978-1-11848-689-4

Chapter 5 - Dynamics of Uniform Circular Motion - Problems - Page 140: 41

Answer

(a) $F_c=1696N$ (b) $F_N=1656N$

Work Step by Step

(a) We have the mass of the motorcycle and driver $m=342kg$, their speed $v=25m/s$ and $r=126m$ The magnitude of the centripetal force is $$F_c=m\frac{v^2}{r}=1696N$$ (b) At the top of the hill, there are 2 vertical forces acting on the motorcycle: gravitational force pointing downward and normal force pointing upward. These two forces cancel each other out to make the centripetal force found in (a). In other words, $$mg-F_N=F_c$$ $$F_N=mg-F_c=342\times9.8-1696=1656N$$
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