Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 7 - Newton's Third Law - Exercises and Problems - Page 186: 14

Answer

a) See the figures below. b) $T_1\gt T_2\gt F_{G,Trout }\gt F_{G,carp}$

Work Step by Step

a) We drew the force diagrams of the two fishes, as you see below. b) To rank the magnitude of the forces, we need to find the magnitude of each force of them. We assume that the wire is unstretchable, so both fishes are moving at the same speed. The net force exerted on the Carp fish is given by $$\sum F_{y,Carp}=T_1-m_{carp}g-T_2=m_{carp}a_{y,Carp}$$ Thus, $$a_{y,Carp}=\dfrac{T_1-m_{carp}g-T_2}{m_{carp}}\tag 1$$ And the net force exerted on the trout fish is given by $$\sum F_{y,Trout }=T_2-m_{Trout }g=m_{Trout }a_{y,Trout }$$ Thus, $$a_{y,Trout }=\dfrac{T_2-m_{Trout }g}{m_{Trout }}\tag 2$$ Since both of them are having the same acceleration, from (1) and (2), we got the following. $$\dfrac{T_1-m_{carp}g-T_2}{m_{carp}}=\dfrac{T_2-m_{Trout }g}{m_{Trout }}$$ Plugging the known; $$\dfrac{60-(1.5\cdot 9.8)-T_2}{1.5}=\dfrac{T_2-(3\cdot 9.8)}{3}$$ Solving for $T_2$; $$T_2=40\;\rm N$$ Now we know that $$T_1=\color{blue}{\bf 60}\;\rm N$$ $$T_2=\color{blue}{\bf 40}\;\rm N$$ $$F_{G,carp}=1.5\cdot 9.8=\color{blue}{\bf 14.7}\;\rm N$$ $$F_{G,Trout }=3\cdot 9.8=\color{blue}{\bf 29.4}\;\rm N$$ Therefore, $$\boxed{T_1\gt T_2\gt F_{G,Trout }\gt F_{G,carp}}$$
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.