Engineering Mechanics: Statics & Dynamics (14th Edition)
Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 3.3, Problem 10P

The block has a weight of 20 lb and is being hoisted at uniform velocity. Determine the angle θ for equilibrium and the force in cord AB.

Expert Solution & Answer
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To determine

The angle θ for equilibrium and the force in cord AB.

Answer to Problem 10P

The angle (θ) is 40°_ and the force in cord AB (TAB) is 37.6lb_.

Explanation of Solution

Given information:

  • The weight of block is 20 lb.

Assumption:

  • The tension along the length of cord CAD is constant.

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

Engineering Mechanics: Statics & Dynamics (14th Edition), Chapter 3.3, Problem 10P

Determine the angle and force in cord AB by applying the Equation of equilibrium.

Along horizontal direction:

Fx=020sinθTABsin20°=0TABsin20°=20sinθTAB=20sinθsin20° (I)

Along vertical direction:

Fy=0TABcos20°20cosθ20=0 (II)

Formula used:

sinθcosϕcosθsinϕ=sin(θϕ)

Substitute 20sinθsin20° for TAB in Equation (II).

TABcos20°20cosθ20=020sinθsin20°cos20°20cosθ20=020sinθcos20°20cosθsin20°=20sin20°20(sinθcos20°cosθsin20°)=20sin20° (III)

Conclusion:

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

20sin(θ20°)=20sin20°sin(θ20°)=sin20°θ20°=20°θ=40°

Substitute 40° for θ in Equation (I).

TAB=20sin40°sin20°=37.6lb

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

Thus, the force in cord AB is 37.6lb_.

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