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Chapter 1: Q2E (page 329)

Calculate the net torque about point O for the two forces applied as in Fig. The rod and both forces are in the plane of the page.

Short Answer

Expert verified

The net torque is 28 Nm, clockwise.

Step by step solution

01

Given that

Length of the rod =5m

Forces applied

F1=8N

F2=12N

02

Formulas used

The magnitude of torquet=Fl where

F is force and l is distance

l=rsinθwhere

r is distance andθ is angle between r and F

03

Find Torque due to two forces

Find torques due to two forcesF1 andF2 and add them

Let counterclockwise be positive.

τ1=-F1l1

ForceF1=8 N

Distancer=5 m

Angleθ=90°

So

l=rsinθ=5msin90°=5m

Hence Torqueτ1=-(8N)(5m)=-40Nm

This force is producing counterclockwise rotation, so by right-hand thumb rule, the torque is directed out of the plane of the figure.

τ2=+F2l2

ForceF2=12 N

Distancer=2 m

Angleθ=30°

So

l=rsinθ=2msin30°=1m

Hence Torqueτ1=(12N)(1m)=12Nm

04

Find net Torque

Net torqueτ=τ1+τ2

τ=-40Nm+12Nm=-28Nm

Hence, net torque is 28 Nm in clockwise direction.

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