Engineering Mechanics: Statics & Dynamics (14th Edition)
Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780134117003
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 3.3, Problem 11P

Determine the maximum weight W of the block that can be suspended in the position shown if cords AB and CAD can each support a maximum tension of 80 lb. Also, what is the angle θ for equilibrium?

Chapter 3.3, Problem 11P, Determine the maximum weight W of the block that can be suspended in the position shown if cords AB

Expert Solution & Answer
Check Mark
To determine

The maximum weight of the block and the angle θ for equilibrium.

Answer to Problem 11P

The maximum weight of the block (W) is 42.6lb_ and the angle for equilibrium (θ) is 40°_.

Explanation of Solution

Given information:

  • The cords AB and CAD can each support a maximum tension of 80 lb.

Assumption:

  • For equilibrium, the tension along the length of cord CAD is constant.
  • The tension in cord AB (TAB) reaches the limit first.

Show the free body diagram of the block as in Figure 1.

Engineering Mechanics: Statics & Dynamics (14th Edition), Chapter 3.3, Problem 11P

Determine the maximum weight of the block and the angle θ by applying the equation of equilibrium.

Along the horizontal direction:

Fx=0WsinθTABsin20°=0Wsinθ=TABsin20°W=TABsin20°sinθ (I)

Along the vertical direction:

Fy=0TABcos20°WcosθW=0W(1+cosθ)=TABcos20°W=TABcos20°(1+cosθ) (II)

Formula used:

sinθcosϕcosθsinϕ=sin(θϕ)

Conclusion:

Substitute 80lb for TAB in Equation (I).

W=80sin20°sinθ (III)

Substitute 80lb for TAB in Equation (II).

W=80cos20°(1+cosθ) (IV)

Substitute 80sin20°sinθ for W in Equation (IV).

80sin20°sinθ=80cos20°(1+cosθ)sin20°(1+cosθ)=sinθcos20°sin20°+sin20°cosθ=sinθcos20°sinθcos20°sin20°cosθ=sin20° (V)

Substitute sin(θ20°) for (sinθcos20°cosθsin20°) in Equation (V).

sin(θ20°)=sin20°θ20°=20°θ=40°

Substitute 40° for θ in Equation (III).

W=80sin20°sin40°=42.6lb<80lb

Thus, the maximum weight of the block is 42.6lb_.

Thus, the angle (θ) for equilibrium is 40°_.

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Chapter 3 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

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