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

Given that

Length of the rod =5m

Forces applied

$F_{1} = 8 N$

$F_{2} = 12 N$

Formulas used

The magnitude of torque $t = F l$ where

F is force and l is distance

$l = r \sin θ$ where

r is distance and $θ$ is angle between r and F

Find Torque due to two forces

Find torques due to two forces $F_{1}$ and $F_{2}$ and add them

Let counterclockwise be positive.

$τ_{1} = - F_{1} l_{1}$

Force $F_{1} = 8$ N

Distance $r = 5$ m

Angle $θ = 90 °$

$l = r \sin θ = (5 m) \sin 90 ° = 5 m$

Hence Torque $τ_{1} = - (8 N) (5 m) = - 40 Nm$

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

$τ_{2} = + F_{2} l_{2}$

Force $F_{2} = 12$ N

Distance $r = 2$ m

Angle $θ = 30 °$

$l = r \sin θ = (2 m) \sin 30 ° = 1 m$

Hence Torque $τ_{1} = (12 N) (1 m) = 12 Nm$

Find net Torque

Net torque $τ = τ_{1} + τ_{2}$

$τ = - 40 Nm + 12 Nm = - 28 Nm$

Hence, net torque is 28 Nm in clockwise direction.

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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

Step by step solution

Given that

Formulas used

Find Torque due to two forces

Find net Torque

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