## Essential University Physics: Volume 1 (3rd Edition)

Published by Pearson

# Chapter 5 - Exercises and Problems - Page 87: 41

#### Answer

a) 307.5 Newtons b) $F_{seat}=\frac{-m_{seat}v^2}{r}$ c) Nothing would happen

#### Work Step by Step

a) We know that the centripetal forces are the force of gravity and the force of the seat. Thus, we find the centripetal force first: $F_c = \frac{mv^2}{r}=\frac{(60)(9.7)^2}{6.3}=896.10N$ We subtract the force of gravity to find the force of the seat: $F_{seat}=896.10-mg=896.10-(60)(9.81)=\fbox{307.5 Newtons}$ b) We know that the force of the seat belt is equal to the centripetal force on the seat belt. This is opposite the other force, so we see that it is: $F_{seat}=\frac{-m_{seat}v^2}{r}$ c) Nothing would happen, for the centripetal force keeps the person in circular motion instead of letting them fall out of circular motion.

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