Book edition 9th Edition

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

Pages 1624 pages

ISBN 9781133947271

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Short Answer

The helicopter view in Fig. P3.29 (page 74) shows two W people pulling on a stubborn mule. The person on the right pulls with a force ${\vec{F}}_{1}$ of magnitude $120 N$ and direction of $θ_{1} = 60.0 °$ .
The person on the left pulls with a force $80.0 N$ of magnitude $θ_{2} = 75.0 °$ and direction of . Find (a) the single force that is equivalent to the two forces shown and (b) the force that a third person would have to exert on the mule to make the resultant force equal to zero. The forces are measured in units of newtons (symbolized N).

$a) | \vec{F} | = 185 N a t θ = 77.8 ° b) (- 39.3 \hat{i} - 181 \hat{j})$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Define magnitude

In simple terms, magnitude means' distance or number.' It describes the absolute or relative size or direction in which an object moves in the feeling of motion.
It's a term for describing the size or scope of something. In general, magnitude in physics refers to distance or amount.

Step 2 (a): Determine the magnitude and angle of the single force.

We must first find the resultant force in the x and y directions before we can find the single force.

$F_{x} = F_{1} c o s θ_{1} - F_{2} c o s θ_{2} = 120 \times c o s 60 ° - 80 \times c o s 75 ° = 39.3 N F_{y} = F_{1} s i n θ_{1} + F_{2} s i n θ_{2} = 120 \times s i n 60 ° + 80 \times s i n 75 ° = 181 N$

As a result, the magnitude is determined by:

$| \vec{F} | = \sqrt{F_{x}^{2} + F_{y}^{2}} | \vec{F} | = \sqrt{39 . 3^{2} + 181^{2}} | \vec{F} | = 185 N$

In addition, the angle is determined by:

$θ = t a n^{- 1} \frac{y}{x} = t a n^{- 1} \frac{181}{39.3} = 77.8 °$

Hence, the single force is $| \vec{F} | = 185 N a t θ = 77.8 °$

Step 3 (b): Determine the magnitude and angle in the opposite direction.

$F_{x} = 39.3 N F_{y} = 181 N$

Hence, the magnitude and angle in the opposite direction is $(- 39.3 \hat{i} - 181 \hat{j}) N$ .

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Short Answer

Step by Step Solution

Step 1: Define magnitude

Step 2 (a): Determine the magnitude and angle of the single force.

Step 3 (b): Determine the magnitude and angle in the opposite direction.

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Physics For Scientists & Engineers

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Short Answer

Step by Step Solution

Step 1: Define magnitude

Step 2 (a): Determine the magnitude and angle of the single force.

Step 3 (b): Determine the magnitude and angle in the opposite direction.

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