College Physics (7th Edition)

Published by Pearson
ISBN 10: 0-32160-183-1
ISBN 13: 978-0-32160-183-4

Chapter 4 - Force and Motion - Learning Path Questions and Exercises - Exercises - Page 135: 19


(a) (4) one-fourth as great. (b) $4.0\,m/s^{2}$

Work Step by Step

(a) Newton's second law states that $F=ma$. If $F'=\frac{F}{2}$ and $m'=2m$, Then $a'=\frac{F'}{m'}=\frac{\frac{F}{2}}{2m}=\frac{1}{4}\times\frac{F}{m}=\frac{1}{4}a$. The acceleration will be one-fourth if the force is halved and the mass is doubled. (b) Given/Known: $F=ma,$ $F'=2F,$ $m'=\frac{1}{2}m,$ $a=1.0\,m/s^{2}$ We need to find $a'$ which is equal to $\frac{F'}{m'}$ $a'=\frac{2F}{\frac{m}{2}}=4\times\frac{F}{m}=4\times a=4\times1.0\,m/s^{2}=4.0\,m/s^{2}$
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