Book edition 10th Edition

Author(s) David Halliday

Pages 1328 pages

ISBN 9781118230718

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Short Answer

Question: The system in Fig. 12-28 is in equilibrium, with the string in the center exactly horizontal. Block A weighs 40 N , block B weighs 50 N , and angle $ϕ$ is 35⁰ . Find (a) tension T₁ , (b) tension T₂ , (c) tension T₃ , and (d) angle $θ$ .

Answer:

The tension T₁ in the string is 49 N
The tension T₂ in the string is 28 N
The tension T₃ in the string is 57 N
The angle $θ$ made by T₃ with vertical is 29⁰ .

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Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Understanding the given information

The weight of the block A, W_A = 40 N

The weight of the block B, W_B =50 N

The angle made by T₁ with vertical is, $ϕ = 35^{0}$

Step 2: Concept and formula used in the given question

Using the free body diagram and the condition for equilibrium, you can find the tensions in the string and the angle theta. The formulas used are given below.

Newton’s second law:

F_net= ma

At equilibrium,

F_net= 0

Step 3: (a) Calculation for the tension T1

The free body diagram:

At equilibrium,

F_ynet= 0

From the figure we can write,

$\ begingathered W_{A} = T_{1} cos ϕ T_{1} = \frac{W_{A}}{cos ϕ} = \frac{40}{cos 35 °} = 49 N \ endgathered$

Hence, the tension T₁ in the string is 49 N

Step 3: (b) Calculation for the tension T2

At equilibrium,

$F_{x n e t} = 0 T_{2} = T_{1} sin ϕ = 49 sin 35 ° = 28 N$

Hence, the tension T₂ in the string is 28 N

Step 3: (c) Calculation for the tension T3

From the free body diagram, you can write that: $T_{3 x} = T_{3} sin θ = T_{2} = 28 N$

Also, $T_{3 y} = T_{3} cos θ = W_{B} = 50 N$

So, the tension T₃ is,

$T_{3} = \sqrt{{T_{3 x}}^{2} + {T_{3 y}}^{2}} = \sqrt{28^{2} + 50^{2}} = 57.3 ~ 57 N$

Hence, the tension T₃ in the string is 57 N

Step 3: (d) Calculation for the angle θ

$T_{3} sin θ = T_{2} 57 sin θ = 28 θ = \sin^{- 1} (\frac{28}{57}) θ = 29$

Hence, the angle( $θ$ ) made by T₃ with vertical is 29⁰ .

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Fundamentals Of Physics

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Short Answer

Question: The system in Fig. 12-28 is in equilibrium, with the string in the center exactly horizontal. Block A weighs 40 N , block B weighs 50 N , and angle $ϕ$ is 35⁰ . Find (a) tension T₁ , (b) tension T₂ , (c) tension T₃ , and (d) angle $θ$ .

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 tension T1

Step 3: (b) Calculation for the tension T2

Step 3: (c) Calculation for the tension T3

Step 3: (d) Calculation for the angle θ

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Question: The system in Fig. 12-28 is in equilibrium, with the string in the center exactly horizontal. Block A weighs 40 N , block B weighs 50 N , and angle ϕ is 350 . Find (a) tension T1 , (b) tension T2 , (c) tension T3 , and (d) angle θ .

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 tension T1

Step 3: (b) Calculation for the tension T2

Step 3: (c) Calculation for the tension T3

Step 3: (d) Calculation for the angle θ

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Question: The system in Fig. 12-28 is in equilibrium, with the string in the center exactly horizontal. Block A weighs 40 N , block B weighs 50 N , and angle $ϕ$ is 35⁰ . Find (a) tension T₁ , (b) tension T₂ , (c) tension T₃ , and (d) angle $θ$ .