Book edition 9th Edition

Author(s) Raymond A. Serway, John W. Jewett

Pages 1624 pages

ISBN 9781133947271

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Short Answer

Calculate the net torque (magnitude and direction) on the beam in Figure P11.5 about
(a) an axis through O perpendicular to the page and
(b) an axis through C perpendicular to the page.

a) Therefore, the net torque about the point O perpendicular is $30.0 N . m$

The direction of the net torque is in counter clockwise direction

b) Therefore, the net torque about perpendicular is $36.0 N . m$

The direction of the net torque is in counter clockwise direction

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Formula to calculate the Torque

$τ = r F$

Here is the Torque, is the perpendicular force and is the applied force.

The force that acts on the beam is shown in figure

From this figure $O O$ is the perpendicular distance for the force $F_{1}$ , $O D$ is the perpendicular distance for the force $F_{2}$ , $O O$ is the perpendicular distance for the force $F_{3}$ , $F_{1} c o s θ_{1}$ is the horizontal component of the force $F_{1}$ , $F_{2} s i n θ_{2}$ is the vertical component of $F_{2}$ , $F_{3} s i n θ_{3}$ is the vertical component of the force $F_{3}$

Step 2: To find the net torque about perpendicular point

The net torque about the point O perpendicular is

$τ_{O} = O C F_{1} c o s θ_{1} + O D (- F_{2} s i n θ_{2}) + O O (- F_{3} s i n θ_{3})$

$τ_{O}$ is the net torque about the point O,OO is the perpendicular distance for the force $F_{1}$ ,OD is the perpendicular distance for the force $F_{2}$ ,OO is the perpendicular distance from the $F_{3}$ , $F_{1} c o s θ_{1}$ is the horizontal component for $F_{1}$ , $F_{2} s i n θ_{2}$ is the horizontal component for $F_{2}$ , $F_{3} s i n θ_{3}$ is the horizontal component for $F_{3}$

$\begin{array}{l} S u b s t i t u t e 2.0 m f o r O C, 25 N f o r F_{1}, 30^{o} f o r θ_{1}, 4.0 m f o r O D, 10 N f o r F_{2}, 20^{o} f o r θ_{2}, 0 \\ m f o r O O, 30 N f o r F_{3}, a n d 45^{o} f o r θ_{, i n t h e e q u a t i o n} \end{array}$

$τ_{O} = O C F_{1} c o s θ_{1} + O D (- F_{2} s i n θ_{2}) + O O (- F_{3} s i n θ_{3}) a n d s o l v e f o r τ_{O}$

$τ_{O} = (2.0 m) (25 N) c o s 30^{o} - (4.0 m) (10 N) s i n 20^{o} - (0 m) (30 N) s i n 45^{o}$

$τ_{O} = 30.0 N \times m$

Therefore, the net torque about the point O perpendicular is $30.0 N \times m$

The direction of the net torque is in counter clockwise direction

The net torque about the point C perpendicular is

$τ_{C} = (C C) F_{1} s i n θ_{1} + (O C) (- F_{2} s i n θ_{2}) + (- O C) (- F_{3} s i n θ_{3})$

$τ_{C}$ is the net torque about the point C,CC is the perpendicular distance for the force $F_{1}$

$S u b s t i t u t e 0 m f o r C C, 25 N f o r F_{1}, 30^{o} f o r θ_{1}, 2.0 m f o r O C, 10 N f o r F_{2}, 20^{o} f o r θ_{2}$

$30 N f o r F, a n d 45^{o} f o r θ, i n t h e e q u a t i o n$

$τ_{C} = (C C) F_{1} s i n θ_{1} + (O C) (- F_{2} s i n θ_{2}) + (- O C) (- F_{3} s i n θ_{3}) a n d s o l v e f o r τ_{C}$

$τ_{C} = (0 m) (25 N) c o s 30^{o} - (2.0 m) (10 N) s i n 20^{o} + (2.0 m) (30 N) s i n 45^{o}$

$τ_{C} = 36.0 N \times m$

Therefore, the net torque about perpendicular is $36.0 N \times m$

The direction of the net torque is in counter clockwise direction

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Short Answer

Calculate the net torque (magnitude and direction) on the beam in Figure P11.5 about
(a) an axis through O perpendicular to the page and
(b) an axis through C perpendicular to the page.

Step by Step Solution

Step 1: Formula to calculate the Torque

Step 2: To find the net torque about perpendicular point

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Physics For Scientists & Engineers

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Short Answer

Calculate the net torque (magnitude and direction) on the beam in Figure P11.5 about (a) an axis through O perpendicular to the page and (b) an axis through C perpendicular to the page.

Step by Step Solution

Step 1: Formula to calculate the Torque

Step 2: To find the net torque about perpendicular point

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Calculate the net torque (magnitude and direction) on the beam in Figure P11.5 about
(a) an axis through O perpendicular to the page and
(b) an axis through C perpendicular to the page.