Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Question: Forces ${\vec{F}}_{1}, {\vec{F}}_{2} and {\vec{F}}_{3}$ act on the structure of Fig. 12-33, shown in an overhead view. We wish to put the structure in equilibrium by applying a fourth force, at a point such as P. The fourth force has vector components ${\vec{F}}_{h} and {\vec{F}}_{v}$ . We are given that a = 2.0 m, b = 3.0m , c = 1 0 m , ${\vec{F}}_{1} = 20 N , {\vec{F}}_{2} = 10 N and {\vec{F}}_{3} = 5.0 N$ Find (a) F_h , (b) F_v , and (c) d.

Answer

$a . F_{h} = 5.0 N b . F_{v} = 30 N c . d = 1.3 m$

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Understanding the given information

$a = 2.0 m b = 3.0 m c = 1.0 m F_{1} = 20 N F_{2} = 10 N F_{3} = 5.0 N$

Step 2: Concept and formula used in the given question

By applying the equations of static equilibrium, you can get the equations in terms of unknown forces. By solving these equations, you can find the values of unknown forces and distance. The equations used are given below.

Static Equilibrium conditions:

$\sum F_{x} = 0 \sum F_{y} = 0 \sum τ = 0$

Step 3: (a) Calculation for the Fh

Using the given figure in the problem and applying static equilibrium conditions: $\sum F_{x} = 0 F_{h} - F_{3} = 0 \cdot \cdot \cdot \cdot \cdot \cdot (1) \sum F_{y} = 0 F_{v} - F_{1} - F_{2} = 0 \cdot \cdot \cdot \cdot \cdot \cdot (2) \sum = 0 (F_{v} \times d) - (F_{2} \times b) - (F_{3} \times a) = 0 \cdot \cdot \cdot \cdot \cdot \cdot (3)$

From equation (1):

$F_{h} - 5 = 0$

Hence, $F_{h} - 5 = 0$

Step 4: (b) Calculation for the Fv

From equation (2):

$F_{v} - 20 - 10 = 0$

Hence, $F_{v} = 30 N$

Step 5: (c) Calculation for the d

From equation (3):

$(30 \times d) - (10 \times 3) - (5 \times 2) = 0 d = 1.3 m$

Hence, d = 1.3 m

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Fundamentals Of Physics

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Short Answer

Step by Step Solution

Step 1: Understanding the given information

Step 2: Concept and formula used in the given question

Step 3: (a) Calculation for the Fh

Step 4: (b) Calculation for the Fv

Step 5: (c) Calculation for the d

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