Vector Mechanics for Engineers: Statics, 11th Edition
Vector Mechanics for Engineers: Statics, 11th Edition
11th Edition
ISBN: 9780077687304
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek
Publisher: McGraw-Hill Education
bartleby

Videos

Question
Book Icon
Chapter 7.5, Problem 7.148P
To determine

Find the distance a.

Expert Solution & Answer
Check Mark

Answer to Problem 7.148P

The distance a is 5.71ft_.

Explanation of Solution

Given information:

The length of the cable AB is L=10ft.

The value of angle θ is 45°.

The collar at A is slides freely and the collar at B is prevented from the moving.

Calculation:

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

Vector Mechanics for Engineers: Statics, 11th Edition, Chapter 7.5, Problem 7.148P

Refer Equation 7.16 in the textbook.

Write the equation of the catenary cable as follows;

y=ccoshxc

Differentiate the equation with x;

dydx=sinhxc

The slope at point A is;

tanθ=|dydx|A=sinhxAcxAc=sinh(tan(90°θ))xA=csinh1(tan(90°θ)) (1)

The length of the portion AC is;

AC=csinh(xAc)

The length of the portion CB is;

CB=csinh(xBc)

Find the distance xB using the relation.

L=AC+CB

Substitute 10 ft for L, csinh(xAc) for AC, and csinh(xBc) for CB.

10=csinh(xAc)+csinh(xBc)csinh(xBc)=10csinh(xAc)sinh(xBc)=10csinh(xAc)xB=csinh1[10csinh(xAc)] (2)

Find the distance (yA) using the relation.

yA=ccosh(xAc) (3)

Find the distance (yB) using the relation.

yB=ccosh(xBc) (4)

Consider the triangle ABD;

Find the value of tanθ using the relation.

tanθ=OppositesideAdjacentside=yByAxB+xA (5)

Find the distance a using the relation.

a=yByA (6)

Use the trial and error procedure to find the value of a.

Consider the value of c and for the given value of θ=45°.

Find the angle θ in the equation (5). The calculated value of angle θ and the given value of θ=45° should be equal.

Trial 1:

Consider a trial value of 1.60 ft for c.

c=1.60ft

Substitute 1.60 ft for c and 45° for θ in Equation (1).

xA=1.60×sinh1(tan(90°45°))=1.410ft

Substitute 1.60 ft for c and 1.410 ft for xA in Equation (2).

xB=1.60×sinh1[101.60sinh(1.4101.60)]=3.777ft

Substitute 1.60 ft for c and 1.410 ft for xA in Equation (3).

yA=1.60×cosh(1.4101.60)=2.263ft

Substitute 1.60 ft for c and 3.777 ft for xB in Equation (4).

yB=1.60×cosh(3.7771.60)=8.551ft

Substitute 1.410 ft for xA, 3.777 ft for xB, 2.263 ft for yA, and 8.551 ft for yB in Equation (5).

tanθ=8.5512.2633.777+1.410θ=50.483°

The calculated value of θ=50.483° is not equal to the given value of θ=45°

Trial 2:

Consider a trial value of 1.70 ft for c.

c=1.70ft

Substitute 1.70 ft for c and 45° for θ in Equation (1).

xA=1.70×sinh1(tan(90°45°))=1.498ft

Substitute 1.70 ft for c and 1.498 ft for xA in Equation (2).

xB=1.70×sinh1[101.70sinh(1.4981.70)]=3.891ft

Substitute 1.70 ft for c and 1.498 ft for xA in Equation (3).

yA=1.70×cosh(1.4981.70)=2.404ft

Substitute 1.70 ft for c and 3.891 ft for xB in Equation (4).

yB=1.70×cosh(3.8911.70)=8.472ft

Substitute 1.498 ft for xA, 3.891 ft for xB, 2.404 ft for yA, and 8.472 ft for yB in Equation (5).

tanθ=8.4722.4043.891+1.498θ=48.388°

The calculated value of θ=48.388° is not equal to the given value of θ=45°

Trial 3:

Consider a trial value of 1.8652 ft for c.

c=1.8652ft

Substitute 1.8652 ft for c and 45° for θ in Equation (1).

xA=1.8652×sinh1(tan(90°45°))=1.644ft

Substitute 1.8652 ft for c and 1.644 ft for xA in Equation (2).

xB=1.8652×sinh1[101.8652sinh(1.6441.8652)]=4.064ft

Substitute 1.8652 ft for c and 1.644 ft for xA in Equation (3).

yA=1.8652×cosh(1.6441.8652)=2.638ft

Substitute 1.8652 ft for c and 4.064 ft for xB in Equation (4).

yB=1.8652×cosh(4.0641.8652)=8.346ft

Substitute 1.644 ft for xA, 4.064 ft for xB, 2.638 ft for yA, and 8.346 ft for yB in Equation (5).

tanθ=8.3462.6384.064+1.644θ=45°

The calculated value of θ=45° is equal to the given value of θ=45°

Therefore, the value of c is 1.8652 ft.

Substitute 2.638 ft for yA, and 8.346 ft for yB in Equation (6).

a=8.3462.638=5.708ft5.71ft

Therefore, the distance a is 5.71ft_.

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!
Students have asked these similar questions
Continuity equation A y x dx D T معادلة الاستمرارية Ly X Q/Prove that ди хе + ♥+ ㅇ? he me ze ོ༞“༠ ?
Q Derive (continuity equation)? I want to derive clear mathematics.
motor supplies 200 kW at 6 Hz to flange A of the shaft shown in Figure. Gear B transfers 125 W of power to operating machinery in the factory, and the remaining power in the shaft is mansferred by gear D. Shafts (1) and (2) are solid aluminum (G = 28 GPa) shafts that have the same diameter and an allowable shear stress of t= 40 MPa. Shaft (3) is a solid steel (G = 80 GPa) shaft with an allowable shear stress of t = 55 MPa. Determine: a) the minimum permissible diameter for aluminum shafts (1) and (2) b) the minimum permissible diameter for steel shaft (3). c) the rotation angle of gear D with respect to flange A if the shafts have the minimum permissible diameters as determined in (a) and (b).

Chapter 7 Solutions

Vector Mechanics for Engineers: Statics, 11th Edition

Ch. 7.1 - A semicircular rod is loaded as shown. Determine...Ch. 7.1 - Fig. P7.11 and P7.12 7.12 A semicircular rod is...Ch. 7.1 - The axis of the curved member AB is a parabola...Ch. 7.1 - Knowing that the axis of the curved member AB is a...Ch. 7.1 - Prob. 7.15PCh. 7.1 - 7.16 Knowing that the radius of each pulley is 200...Ch. 7.1 - A 5-in.-diameter pipe is supported every 9 ft by a...Ch. 7.1 - For the frame of Prob. 7.17, determine the...Ch. 7.1 - Knowing that the radius of each pulley is 200 mm...Ch. 7.1 - Fig. P7.19 and P7.20 7.20 Knowing that the radius...Ch. 7.1 - and 7.22 A force P is applied to a bent rod that...Ch. 7.1 - and 7.22 A force P is applied to a bent rod that...Ch. 7.1 - A quarter-circular rod of weight W and uniform...Ch. 7.1 - For the rod of Prob. 7.23, determine the magnitude...Ch. 7.1 - A semicircular rod of weight W and uniform cross...Ch. 7.1 - A semicircular rod of weight W and uniform cross...Ch. 7.1 - 7.27 and 7.28 A half section of pipe rests on a...Ch. 7.1 - 7.27 and 7.28 A half section of pipe rests on a...Ch. 7.2 - Prob. 7.29PCh. 7.2 - Prob. 7.30PCh. 7.2 - 7.29 through 7.32 For the beam and loading shown,...Ch. 7.2 - 7.29 through 7.32 For the beam and loading shown,...Ch. 7.2 - 7.33 and 7.34 For the beam and loading shown, (a)...Ch. 7.2 - 7.33 and 7.34 For the beam and loading shown, (a)...Ch. 7.2 - 7.35 and 7.36 For the beam and loading shown, (a)...Ch. 7.2 - 7.35 and 7.36 For the beam and loading shown, (a)...Ch. 7.2 - 7.37 and 7.38 For the beam and loading shown, (a)...Ch. 7.2 - 7.37 and 7.38 For the beam and loading shown, (a)...Ch. 7.2 - For the beam and loading shown, (a) draw the shear...Ch. 7.2 - 7.39 through 7.42 For the beam and loading shown,...Ch. 7.2 - For the beam and loading shown, (a) draw the shear...Ch. 7.2 - Prob. 7.42PCh. 7.2 - Assuming the upward reaction of the ground on beam...Ch. 7.2 - Solve Problem 7.43 knowing that P = 3wa. PROBLEM...Ch. 7.2 - Assuming the upward reaction of the ground on beam...Ch. 7.2 - Solve Prob. 7.45 assuming that the 12-kip load has...Ch. 7.2 - Prob. 7.47PCh. 7.2 - Prob. 7.48PCh. 7.2 - Prob. 7.49PCh. 7.2 - Prob. 7.50PCh. 7.2 - Prob. 7.51PCh. 7.2 - Prob. 7.52PCh. 7.2 - Two small channel sections DF and EH have been...Ch. 7.2 - Solve Prob. 7.53 when = 60. PROBLEM 7.53 Two...Ch. 7.2 - For the structural member of Prob. 7.53, determine...Ch. 7.2 - For the beam of Prob. 7.43, determine (a) the...Ch. 7.2 - Determine (a) the distance a for which the maximum...Ch. 7.2 - For the beam and loading shown, determine (a) the...Ch. 7.2 - A uniform beam is to be picked up by crane cables...Ch. 7.2 - Knowing that P = Q = 150 lb, determine (a) the...Ch. 7.2 - Knowing that P = Q = 150 lb, determine (a) the...Ch. 7.2 - In order to reduce the bending moment in the...Ch. 7.3 - 7.63 Using the method of Sec. 7.3, solve Prob....Ch. 7.3 - Prob. 7.64PCh. 7.3 - 7.65 Using the method of Sec. 7.3, solve Prob....Ch. 7.3 - Prob. 7.66PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.33....Ch. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.34....Ch. 7.3 - Prob. 7.69PCh. 7.3 - Prob. 7.70PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.39....Ch. 7.3 - Prob. 7.72PCh. 7.3 - Using the method of Sec. 7.3, solve Prob. 7.41....Ch. 7.3 - Prob. 7.74PCh. 7.3 - Prob. 7.75PCh. 7.3 - Prob. 7.76PCh. 7.3 - 7.77 and 7.78 For the beam and loading shown, (a)...Ch. 7.3 - Prob. 7.78PCh. 7.3 - Prob. 7.79PCh. 7.3 - For the beam and loading shown, (a) draw the shear...Ch. 7.3 - Prob. 7.81PCh. 7.3 - For the beam and loading shown, (a) draw the shear...Ch. 7.3 - (a) Draw the shear and bending-moment diagrams for...Ch. 7.3 - Solve Prob. 7.83 assuming that the 300-lb force...Ch. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - 7.85 and 7.86 For the beam and loading shown, (a)...Ch. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - For the beam and loading shown, (a) write the...Ch. 7.3 - *7.89 The beam AB is subjected to the uniformly...Ch. 7.3 - Prob. 7.90PCh. 7.3 - Prob. 7.91PCh. 7.3 - Prob. 7.92PCh. 7.4 - Three loads are suspended as shown from the cable...Ch. 7.4 - Knowing that the maximum tension in cable ABCDE is...Ch. 7.4 - Prob. 7.95PCh. 7.4 - Prob. 7.96PCh. 7.4 - Prob. 7.97PCh. 7.4 - Prob. 7.98PCh. 7.4 - Prob. 7.99PCh. 7.4 - Prob. 7.100PCh. 7.4 - Knowing that mB = 70 kg and mC = 25 kg, determine...Ch. 7.4 - Fig. P7.101 and P7.102 7.102 Knowing that mB = 18...Ch. 7.4 - Cable ABC supports two loads as shown. Knowing...Ch. 7.4 - Prob. 7.104PCh. 7.4 - If a = 3 m, determine the magnitudes of P and Q...Ch. 7.4 - If a = 4 m, determine the magnitudes of P and Q...Ch. 7.4 - An electric wire having a mass per unit length of...Ch. 7.4 - The total mass of cable ACB is 20 kg. Assuming...Ch. 7.4 - The center span of the George Washington Bridge,...Ch. 7.4 - The center span of the Verrazano-Narrows Bridge...Ch. 7.4 - Each cable of the Golden Gate Bridge supports a...Ch. 7.4 - Two cables of the same gauge are attached to a...Ch. 7.4 - A 76-m length of wire having a mass per unit...Ch. 7.4 - A cable of length L + is suspended between two...Ch. 7.4 - The total mass of cable AC is 25 kg. Assuming that...Ch. 7.4 - Cable ACB supports a load uniformly distributed...Ch. 7.4 - Each cable of the side spans of the Golden Gate...Ch. 7.4 - A steam pipe weighing 45 lb/ft that passes between...Ch. 7.4 - A cable AB of span L and a simple beam AB of the...Ch. 7.4 - Making use of the property established in Prob....Ch. 7.4 - Prob. 7.121PCh. 7.4 - 7.120 through 7.123 Making use of the property...Ch. 7.4 - Prob. 7.123PCh. 7.4 - Prob. 7.124PCh. 7.4 - Using the property indicated in Prob. 7.124,...Ch. 7.4 - If the weight per unit length of the cable AB is...Ch. 7.5 - A 25-ft chain with a weight of 30 lb is suspended...Ch. 7.5 - A 500-ft-long aerial tramway cable having a weight...Ch. 7.5 - A 40-m cable is strung as shown between two...Ch. 7.5 - A 50-m steel surveying tape has a mass of 1.6 kg....Ch. 7.5 - Prob. 7.131PCh. 7.5 - Prob. 7.132PCh. 7.5 - A 20-m length of wire having a mass per unit...Ch. 7.5 - Determine the sag of a 30-ft chain that is...Ch. 7.5 - Prob. 7.135PCh. 7.5 - Prob. 7.136PCh. 7.5 - A cable weighing 2 lb/ft is suspended between two...Ch. 7.5 - Prob. 7.138PCh. 7.5 - Prob. 7.139PCh. 7.5 - Fig. P7.139 and P7.140 7.140 A motor M is used to...Ch. 7.5 - Prob. 7.141PCh. 7.5 - Prob. 7.142PCh. 7.5 - Prob. 7.143PCh. 7.5 - Prob. 7.144PCh. 7.5 - To the left of point B, the long cable ABDE rests...Ch. 7.5 - Fig. P7.145 and P7.146 7.146 To the left of point...Ch. 7.5 - The 10-ft cable AB is attached to two collars as...Ch. 7.5 - Prob. 7.148PCh. 7.5 - Prob. 7.149PCh. 7.5 - (a) Determine the maximum allowable horizontal...Ch. 7.5 - A cable has a mass per unit length of 3 kg/m and...Ch. 7.5 - Determine the sag-to-span ratio for which the...Ch. 7.5 - Prob. 7.153PCh. 7 - Knowing that the turnbuckle has been tightened...Ch. 7 - Knowing that the turnbuckle has been tightened...Ch. 7 - Two members, each consisting of a straight and a...Ch. 7 - Knowing that the radius of each pulley is 150 mm,...Ch. 7 - For the beam shown, determine (a) the magnitude P...Ch. 7 - For the beam and loading shown, (a) draw the shear...Ch. 7 - For the beam and loading shown, (a) draw the shear...Ch. 7 - For the beam shown, draw the shear and...Ch. 7 - The beam AB, which lies on the ground, supports...Ch. 7 - Two loads are suspended as shown from the cable...Ch. 7 - A wire having a mass per unit length of 0.65 kg/m...Ch. 7 - A 10-ft rope is attached to two supports A and B...
Knowledge Booster
Background pattern image
Mechanical Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
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
How to balance a see saw using moments example problem; Author: Engineer4Free;https://www.youtube.com/watch?v=d7tX37j-iHU;License: Standard Youtube License