Engineering Mechanics: Statics
Engineering Mechanics: Statics
13th Edition
ISBN: 9780132915540
Author: Russell C. Hibbeler
Publisher: Prentice Hall
Question
Book Icon
Chapter 7.4, Problem 94P
To determine

The tension in each segment of the cable and the cable’s total length.

Expert Solution & Answer
Check Mark

Answer to Problem 94P

  • The tension in the cable BD is TBD=78.19lb_.
  • The tension in the cable AC is TAC=74.75lb_.
  • The tension in the cable CD is TCD=43.72lb_.
  • The total length of the chain is l=15.75ft_.

Explanation of Solution

Given information:

  • Set P=80lb.

Assumption:

  • The self-weight of the cable is ignored.
  • The cable is perfectly flexible and inextensible.
  • The tensile force acting in the cable is always tangent to the cable at points along its length.
  • Being inextensible, the cable has a constant length both before and after the load is applied.
  • The cable or a segment of the cable can be treated as a rigid body.
  • Method of joints is used to determine the force in the cable.
  • Consider the state of the member as tension where the force is pulling the member as compression where the force is pushing the member.
  • Consider the force indicating the right side as positive and left side as negative in horizontal components of forces.
  • Consider the force indicating upward is taken as positive and downward as negative in vertical components of forces.
  • Consider clockwise moment as negative and anti-clock wise moment as positive wherever applicable.
  • Apply Equation of equilibrium wherever applicable.

Segment ACD:

Show the free-b0dy diagram of the segment ACD as in Figure (1).

Engineering Mechanics: Statics, Chapter 7.4, Problem 94P , additional homework tip  1

Using Figure (1),

Determine the value of θ using the relation:

tanθ=OppositesideAdjacentside (I)

Moment about point A:

Determine the tension in the BD by taking moment about point A.

MA=0TBDcosθ1(3)+TBDsinθ1(7)50(7)P(3)=0 (II)

Along the vertical direction:

Determine the vertical reaction at point A by resolving the vertical component of forces.

Fy=0TBDsinθ150P+Ay=0 (III)

Along the horizontal direction:

Determine the horizontal reaction at point A by resolving the horizontal component of forces.

Fx=0TBDcosθ1Ax=0 (IV)

Conclusion:

Substitute 5 ft for opposite side and 3 ft for adjacent side in Equation (I).

tanθ1=53θ1=59.04°

Substitute 59.04° for θ1 and 80 lb for P in Equation (II).

TBDcos59.04°(3)+TBDsin59.04°(7)35080(3)=01.543TBD+6.003TBD350240=07.546TBD=590TBD=78.19lb

Substitute 78.10 lb for TBD, 59.04° for θ1, and 80 lb for P in Equation (III).

78.10sin59.04°5080+Ay=0Ay=63.03lb

Substitute 78.10 lb for TBD and 59.04° for θ1 in Equation (IV).

78.10cos59.04°Ax=0Ax=40.18lb

Thus, the tension in the cable BD is TBD=78.19lb_.

Joint A:

Show the free-body diagram of the joint A as in Figure (2).

Engineering Mechanics: Statics, Chapter 7.4, Problem 94P , additional homework tip  2

Using Figure (2),

Along the vertical direction:

Determine the tension in the cable AC and the angle θ2 by resolving the vertical component of forces.

Fy=0AyTACsinθ2=0 (V)

Along the horizontal direction:

Determine the tension in the cable AC and the angle θ2 by resolving the horizontal component of forces.

Fx=0TACcosθ2Ax=0 (VI)

Conclusion:

Substitute 63.03 lb for Ay in Equation (V).

63.03TACsinθ2=0TACsinθ2=63.03 (VII)

Substitute 40.18 lb for Ax in Equation (VI).

TACcosθ240.18=0TACcosθ2=40.18 (VIII)

Divide Equation (VII) by Equation (VIII).

TACsinθ2TACcosθ2=63.0340.18tanθ2=63.0340.18θ2=57.48°

Substitute 57.48° for θ2 in Equation (VII).

TACsin57.48°=63.03TAC=74.75lb

Thus, the tension in the cable AC is TAC=74.75lb_.

Joint D:

Show the free-body diagram of the joint D as in Figure (3).

Engineering Mechanics: Statics, Chapter 7.4, Problem 94P , additional homework tip  3

Using Figure (3),

Along the vertical direction:

Determine the tension in the cable CD and the angle θ3 by resolving the vertical component of forces.

Fy=0TBDsinθ1TCDsinθ350=0 (IX)

Along the horizontal direction:

Determine the tension in the cable CD and the angle θ3 by resolving the horizontal component of forces.

Fx=0TBDcosθ1TCDcosθ3=0 (X)

Conclusion:

Substitute 78.19 lb for TBD and 59.04° for θ1 in Equation (IX).

78.19sin59.04°TCDsinθ350=0TCDsinθ3=17.05 (XI)

Substitute 78.19 lb for TBD and 59.04° for θ1 in Equation (X).

78.19cos59.04TCDcosθ3=0TCDcosθ3=40.22 (XII)

Divide Equation (XI) by Equation (XII).

TCDsinθ3TCDcosθ3=17.0540.22tanθ3=17.0540.22θ3=22.97°

Substitute 22.97° for θ3 in Equation (XI).

TCDsin22.97°=17.05TCD=43.72lb

Thus, the tension in the cable CD is TCD=43.72lb_.

Entire segment:

Show the free-body diagram of the entire segment with the length of each cable as in Figure (4).

Engineering Mechanics: Statics, Chapter 7.4, Problem 94P , additional homework tip  4

Using Figure (4),

Determine the entire length of the cable:

l=5sin59.04°+4cos22.97°+3cos57.48°=5.83+4.34+5.58=15.75ft

Thus, the total length of the chain is l=15.75ft_.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 7 Solutions

Engineering Mechanics: Statics

Ch. 7.1 - Prob. 5PCh. 7.1 - Determine the distance a as a fraction of the...Ch. 7.1 - Prob. 7PCh. 7.1 - Prob. 8PCh. 7.1 - Take P = 8 kN. Prob. 7-9Ch. 7.1 - Determine the largest vertical load P the frame...Ch. 7.1 - The shaft is supported by a journal bearing at A...Ch. 7.1 - Determine the internal normal force, shear force,...Ch. 7.1 - Prob. 13PCh. 7.1 - Prob. 14PCh. 7.1 - Prob. 15PCh. 7.1 - Prob. 16PCh. 7.1 - Prob. 17PCh. 7.1 - Point E is just to the right of the 3-kip load....Ch. 7.1 - Prob. 19PCh. 7.1 - Determine the internal normal force, shear force,...Ch. 7.1 - Prob. 21PCh. 7.1 - Prob. 22PCh. 7.1 - Prob. 23PCh. 7.1 - Determine the internal normal force, shear force,...Ch. 7.1 - Prob. 25PCh. 7.1 - Determine the ratio of a/b for which the shear...Ch. 7.1 - Prob. 27PCh. 7.1 - Prob. 28PCh. 7.1 - Determine the normal force, shear force, and...Ch. 7.1 - Determine the normal force, shear force, and...Ch. 7.1 - Prob. 31PCh. 7.1 - Prob. 32PCh. 7.1 - Prob. 33PCh. 7.1 - Prob. 34PCh. 7.1 - Prob. 35PCh. 7.1 - Prob. 36PCh. 7.1 - Prob. 37PCh. 7.1 - Prob. 38PCh. 7.1 - Prob. 39PCh. 7.1 - Prob. 40PCh. 7.1 - Determine the x, y, z components of force and...Ch. 7.1 - z components of force and moment at point C in the...Ch. 7.1 - Prob. 43PCh. 7.1 - Prob. 44PCh. 7.2 - Determine the shear and moment as a function of x,...Ch. 7.2 - Determine the shear and moment as a function of x,...Ch. 7.2 - Determine the shear and moment as a function of x,...Ch. 7.2 - Determine the shear and moment as a function of x,...Ch. 7.2 - Determine the shear and moment as a function of x,...Ch. 7.2 - Determine the shear and moment as a function of x,...Ch. 7.2 - Prob. 45PCh. 7.2 - Draw the shear and moment diagrams for the beam...Ch. 7.2 - Draw the shear and moment diagrams for the beam...Ch. 7.2 - Draw the shear and moment diagrams of the beam (a)...Ch. 7.2 - If L = 9 m, the beam will fail when the maximum...Ch. 7.2 - Draw the shear and moment diagrams for the...Ch. 7.2 - Prob. 51PCh. 7.2 - Prob. 52PCh. 7.2 - Draw the shear and moment diagrams for the beam....Ch. 7.2 - Prob. 54PCh. 7.2 - Draw the shear and bending-moment diagrams for the...Ch. 7.2 - Prob. 56PCh. 7.2 - Draw the shear and bending-moment diagrams for...Ch. 7.2 - Draw the shear and moment diagrams for the...Ch. 7.2 - Prob. 59PCh. 7.2 - The shaft is supported by a smooth thrust bearing...Ch. 7.2 - Prob. 61PCh. 7.2 - Prob. 62PCh. 7.2 - Prob. 63PCh. 7.2 - Prob. 64PCh. 7.2 - Prob. 65PCh. 7.2 - Draw the shear and moment diagrams for the beam....Ch. 7.2 - Prob. 67PCh. 7.2 - Prob. 68PCh. 7.2 - Express the internal shear and moment components...Ch. 7.3 - Draw the shear and moment diagrams for the beam....Ch. 7.3 - Draw the shear and moment diagrams for the beam....Ch. 7.3 - Draw the shear and moment diagrams for the beam....Ch. 7.3 - Draw the shear and moment diagrams for the beam....Ch. 7.3 - Draw the shear and moment diagrams for the beam....Ch. 7.3 - Draw the shear and moment diagrams for the beam....Ch. 7.3 - Prob. 70PCh. 7.3 - Prob. 71PCh. 7.3 - Draw the shear and moment diagrams for the beam....Ch. 7.3 - Prob. 73PCh. 7.3 - Draw the shear and moment diagrams for the...Ch. 7.3 - Draw the shear and moment diagrams for the beam....Ch. 7.3 - Prob. 76PCh. 7.3 - Prob. 77PCh. 7.3 - Draw the shear and moment diagrams for the shaft....Ch. 7.3 - Draw the shear and moment diagrams for the beam....Ch. 7.3 - Prob. 80PCh. 7.3 - Prob. 81PCh. 7.3 - Prob. 82PCh. 7.3 - Prob. 83PCh. 7.3 - Prob. 84PCh. 7.3 - Prob. 85PCh. 7.3 - Prob. 86PCh. 7.3 - Prob. 87PCh. 7.3 - Prob. 88PCh. 7.3 - Prob. 89PCh. 7.3 - Prob. 90PCh. 7.3 - Prob. 91PCh. 7.3 - Prob. 92PCh. 7.3 - Prob. 93PCh. 7.4 - Prob. 94PCh. 7.4 - Prob. 95PCh. 7.4 - Determine the tension in each segment of the cable...Ch. 7.4 - Prob. 97PCh. 7.4 - Prob. 98PCh. 7.4 - Prob. 99PCh. 7.4 - If cylinder E has a mass of 20 kg and each cable...Ch. 7.4 - Prob. 101PCh. 7.4 - Prob. 102PCh. 7.4 - If yB = 1.5 ft. determine the largest weight of...Ch. 7.4 - The cable AB is subjected to a uniform loading of...Ch. 7.4 - Determine the maximum uniform loading w, measured...Ch. 7.4 - The cable is subjected to a uniform loading of w =...Ch. 7.4 - Prob. 107PCh. 7.4 - Prob. 108PCh. 7.4 - If the pipe has a mass per unit length of 1500...Ch. 7.4 - Prob. 110PCh. 7.4 - Prob. 111PCh. 7.4 - Prob. 112PCh. 7.4 - Prob. 113PCh. 7.4 - A telephone line (cable) stretches between two...Ch. 7.4 - Prob. 115PCh. 7.4 - Prob. 116PCh. 7.4 - Prob. 117PCh. 7.4 - A cable has a weight of 5 lb/ft. If it can span...Ch. 7.4 - Prob. 119PCh. 7.4 - The power transmission cable weighs 10 lb/fl. If...Ch. 7.4 - The power transmission cable weighs 10 lb/ft. If h...Ch. 7.4 - Prob. 122PCh. 7.4 - Prob. 123PCh. 7.4 - The man picks up the 52-ft chain and holds it just...Ch. 7.4 - Determine the internal normal force, shear force,...Ch. 7.4 - Draw the shear and moment diagrams for the beam....Ch. 7.4 - Prob. 127RPCh. 7.4 - Prob. 128RPCh. 7.4 - Prob. 129RPCh. 7.4 - Prob. 130RPCh. 7.4 - Prob. 131RPCh. 7.4 - Prob. 132RPCh. 7.4 - Draw the shear and moment diagrams for the beam....Ch. 7.4 - Determine the normal force, shear force, and...Ch. 7.4 - Draw the shear and moment diagrams for the beam....Ch. 7.4 - Prob. 137RPCh. 7.4 - Prob. 138RPCh. 7.4 - Prob. 139RP
Knowledge Booster
Background pattern image
Recommended textbooks for you
Text book image
Elements Of Electromagnetics
Mechanical Engineering
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Oxford University Press
Text book image
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:9780134319650
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:9781259822674
Author:Yunus A. Cengel Dr., Michael A. Boles
Publisher:McGraw-Hill Education
Text book image
Control Systems Engineering
Mechanical Engineering
ISBN:9781118170519
Author:Norman S. Nise
Publisher:WILEY
Text book image
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:9781337093347
Author:Barry J. Goodno, James M. Gere
Publisher:Cengage Learning
Text book image
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:9781118807330
Author:James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:WILEY