PEARSON ETEXT ENGINEERING MECH & STATS
PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 3, Problem 1FP

The crate has a weight of 550 lb. Determine the force in each supporting cable.

Chapter 3, Problem 1FP, The crate has a weight of 550 lb. Determine the force in each supporting cable.

Expert Solution & Answer
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To determine

The force in each supporting cable.

Answer to Problem 1FP

The force in cable AB (FAB) is 478lb_.

The force in cable AC (FAC) is 518lb_.

Explanation of Solution

Given information:

The weight of a crate is (W) is 550 lb.

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

PEARSON ETEXT ENGINEERING MECH & STATS, Chapter 3, Problem 1FP

Determine the force of the members AB and AC by applying the Equation of equilibrium.

Along horizontal direction:

Fx=0FACcosθACFABcosθAB=0 (I)

Here, the angle of force AC is θAC and the angle of force AB is θAB.

Along the vertical direction:

Fy=0FACsinθAC+FABsinθABW=0 (II)

Conclusion:

Substitute (45) for cosθAC and 30° for θAB in Equation (I).

FAC(45)FABcos30°=0FAC(45)=0.866FABFAC=(0.866×54)FABFAC=1.0825FAB (III)

Substitute 1.0825FAB for FAC, (35) for sinθAC and 30° for θAB, 550 lb for W in Equation (II).

(1.0825FAB)(35)+FABsin30°550=00.649FAB+0.5FAB=5501.149FAB=550FAB=5501.149

FAB=478lb

Thus, the force in cable AB (FAB) is 478lb_.

Substitute 478 lb for FAB in Equation (III).

FAC=1.0825×478=518lb

Thus, the force in cable AC (FAC) is 518lb_.

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PEARSON ETEXT ENGINEERING MECH & STATS

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