Vector Mechanics for Engineers: Statics and Dynamics
Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Chapter 2, Problem 2.136RP
To determine

The magnitude of P and Q.

Expert Solution & Answer
Check Mark

Answer to Problem 2.136RP

The magnitude of P and Q are 131.2N_ and 29.6N_ respectively.

Explanation of Solution

Given information:

The weight (W) is 376 N.

Calculation:

Draw the free body diagram of point A as in Figure (1).

<x-custom-btb-me data-me-id='1725' class='microExplainerHighlight'>Vector</x-custom-btb-me> Mechanics for Engineers: Statics and Dynamics, Chapter 2, Problem 2.136RP

The force applied at the point A is TAB,TAC,W, Q, and P.

Write vector form of P as below:

P=Pi

Write vector form of Q as below:

Q=Qk

Write vector form of W as below:

W=(367N)j

Since the tension in cable AB and AC is equal,

TAB=TAC=T

Express the vector AB as below:

AB=(130mm)i+(400mm)j+(160mm)k

Calculate distance of the member AB as below:

AB=(130)2+(400)2+(160)2=16,900+160,000+25,600=450mm

Calculate the unit vector (λAB) using the relation:

λAB=ABAB

Substitute (130mm)i+(400mm)j+(160mm)k for AB and 450mm for AB.

λAB=(130mm)i+(400mm)j+(160mm)k450mm=0.2889i+0.889j+0.3556k

Calculate the tension force (TAB) in cable AB using the relation:

TAB=TλAB

Substitute 0.2889i+0.889j+0.355k for λAB.

TAB=(0.2889i+0.889j+0.3556k)T

Express the vector AC as below:

AC=(150mm)i+(400mm)j+(240mm)k

Calculate distance of the member AC as below:

AC=(150)2+(400)2+(240)2=22,500+160,000+57,600=490mm

Calculate the unit vector (λAC) using the relation:

λAC=ACAC

Substitute (150mm)i+(400mm)j+(240mm)k for AC and 490 mm for AC.

λAC=(150mm)i+(400mm)j+(240mm)k490mm=0.3061i+0.8163j0.4898k

Calculate the tension force (TAC) in Cable AC using the relation:

TAC=TλAC

Substitute 0.3061i+0.8163j0.4898k for λAC.

TAC=(0.3061i+0.8163j0.4898k)T

Calculate the tension in the cable using the relation:

Use the equilibrium condition,

F=0

TAB+TAC+Q+P+W=0

Substitute (0.2889i+0.889j+0.3556k)T for TAB, (0.3061i+0.8163j0.4898k)T for TAC, Pi for P, Qk for Q, and (376N)j for W.

{(0.2889i+0.889j+0.3556k)T+(0.3061i+0.8163j0.4898k)T+Pi+Qk+(376N)j}=0{(0.2889T0.3061T+P)i+(0.889T+0.8163T376)j+(0.3556T0.4898T+Q)k}=0{(0.595T+P)i+(1.7053T376)j+(0.1342T+Q)k}=0

Equate the component i, j and k to zero,

0.595T+P=0 (1)

1.7053T376=0 (2)

0.1342T+Q=0 (3)

Calculate tension in cable (T) as below:

Solve Equation (2).

1.7053T367=0T=3761.7053T=220.5N

Calculate magnitude of P as below:

Substitute 220.5 N for T in Equation (1).

0.595(220.5)+P=0P=131.2N

Calculate magnitude of Q as below:

Substitute 220.5 N for T in Equation (2).

0.1342(220.5)+Q=0Q=29.6N

Thus, the magnitude P and Q are 131.2N_ and 29.6N_ respectively.

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Chapter 2 Solutions

Vector Mechanics for Engineers: Statics and Dynamics

Ch. 2.1 - A steel tank is to be positioned in an excavation....Ch. 2.1 - A steel tank is to be positioned in an excavation....Ch. 2.1 - A steel tank is to be positioned in an excavation....Ch. 2.1 - For the hook support of Prob. 2.10, determine by...Ch. 2.1 - Prob. 2.15PCh. 2.1 - Solve Prob. 2.1 by trigonometry.Ch. 2.1 - Solve Prob. 2.4 by trigonometry.Ch. 2.1 - For the stake of Prob. 2.5, knowing that the...Ch. 2.1 - 2.19 Two forces P and Q are applied to the lid of...Ch. 2.1 - 2.20 Two forces P and Q are applied to the lid of...Ch. 2.2 - Determine the x and y components of each of the...Ch. 2.2 - Determine the x and y components of each of die...Ch. 2.2 - Prob. 2.23PCh. 2.2 - Prob. 2.24PCh. 2.2 - Member BC exerts on member AC a force P directed...Ch. 2.2 - Member BD exerts on member ABC a force P directed...Ch. 2.2 - Prob. 2.27PCh. 2.2 - Cable AC exerts on beam AD a force P directed...Ch. 2.2 - The hydraulic cylinder BD exerts on member ABC a...Ch. 2.2 - The guy wire BD exerts on the telephone pole AC a...Ch. 2.2 - Determine the resultant of the three forces of...Ch. 2.2 - Determine the resultant of the three forces of...Ch. 2.2 - Determine the resultant of the three forces of...Ch. 2.2 - Determine the resultant of the three forces of...Ch. 2.2 - Knowing that = 35, determine the resultant of the...Ch. 2.2 - 2.36 Knowing that the tension in rope AC is 365 N,...Ch. 2.2 - Knowing that = 40, determine the resultant of the...Ch. 2.2 - Knowing that = 75, determine the resultant of the...Ch. 2.2 - 2.39 For the collar of Prob. 2.35, determine (a)...Ch. 2.2 - Prob. 2.40PCh. 2.2 - PROBLEM 2.41 Determine (a) the required tension in...Ch. 2.2 - PROBLEM 2.42 For the block of Problems 2.37 and...Ch. 2.3 - Two cables are tied together at C and loaded as...Ch. 2.3 - Two forces of magnitude TA = 8 kips and TB = 15...Ch. 2.3 - The 60-lb collar A can slide on a frictionless...Ch. 2.3 - A chairlift has been stopped in the position...Ch. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - Prob. 2.45PCh. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - 2 .47 Two cables are tied together at C and are...Ch. 2.3 - Knowing that = 20, determine the tension (a) in...Ch. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - Two cables are tied together at C and are loaded...Ch. 2.3 - Prob. 2.51PCh. 2.3 - 2.52 Two forces P and Q arc applied as shown to an...Ch. 2.3 - A welded connection is in equilibrium under the...Ch. 2.3 - A welded connection is in equilibrium under the...Ch. 2.3 - A sailor is being rescued using a boatswains chair...Ch. 2.3 - A sailor is being rescued using a boatswains chair...Ch. 2.3 - For the cables of Prob. 2.44, find the value of ...Ch. 2.3 - For the cables of Prob. 2.46, it is known that the...Ch. 2.3 - For the situation described in Fig. P2.48,...Ch. 2.3 - 2 .60 Two cables tied together at C are loaded as...Ch. 2.3 - A movable bin and its contents have a combined...Ch. 2.3 - Prob. 2.62PCh. 2.3 - Collar A is connected as shown to a 50-lb load and...Ch. 2.3 - Collar A is connected as shown to a 50-lb load and...Ch. 2.3 - Prob. 2.65PCh. 2.3 - A 200-kg crate is to be supported by the...Ch. 2.3 - A 600-lb crate is supported by several...Ch. 2.3 - Solve parts b and d of Prob. 2.67, assuming that...Ch. 2.3 - A load Q is applied to the pulley C, which can...Ch. 2.3 - An 1800-N load Q is applied to pulley C, which can...Ch. 2.4 - 2.71 Determine (a) the x, y, and z components of...Ch. 2.4 - 2. 72 Determine (a) the x, y, and z components of...Ch. 2.4 - A gun is aimed at a point A located 35 east of...Ch. 2.4 - Solve Prob. 2.73 assuming that point A is located...Ch. 2.4 - Prob. 2.75PCh. 2.4 - Prob. 2.76PCh. 2.4 - Cable AB is 65 ft long, and the tension in that...Ch. 2.4 - PROBLEM 2.78 Cable AC is 70 ft long, and the...Ch. 2.4 - Prob. 2.79PCh. 2.4 - Prob. 2.80PCh. 2.4 - Prob. 2.81PCh. 2.4 - Prob. 2.82PCh. 2.4 - Prob. 2.83PCh. 2.4 - Prob. 2.84PCh. 2.4 - 2.85 A frame ABC is supported in part by cable DBE...Ch. 2.4 - Prob. 2.86PCh. 2.4 - In order to move a wrecked truck, two cables are...Ch. 2.4 - In order to move a wrecked truck, two cables are...Ch. 2.4 - A rectangular plate is supported by three cables...Ch. 2.4 - A rectangular plate is supported by three cables...Ch. 2.4 - Find the magnitude and direction of the resultant...Ch. 2.4 - Prob. 2.92PCh. 2.4 - Knowing that the tension is 425 lb in cable AB and...Ch. 2.4 - Knowing that the tension is 510 lb in cable AB and...Ch. 2.4 - Prob. 2.95PCh. 2.4 - Prob. 2.96PCh. 2.4 - The boom OA carries a load P and is supported by...Ch. 2.4 - Fig. P2.97 2.98 For the boom and loading of Prob....Ch. 2.5 - Three cables are used to tether a balloon as...Ch. 2.5 - A container of mass m = 120 kg is supported by...Ch. 2.5 - A 150-lb cylinder is supported by two cables AC...Ch. 2.5 - A transmission tower is held by three guy wires...Ch. 2.5 - A container is supported by three cables that are...Ch. 2.5 - A container is supported by three cables that are...Ch. 2.5 - Three cables are used to tether a balloon as...Ch. 2.5 - Three cables are used to tether a balloon as...Ch. 2.5 - Prob. 2.103PCh. 2.5 - Prob. 2.104PCh. 2.5 - Prob. 2.105PCh. 2.5 - Prob. 2.106PCh. 2.5 - Three cables are connected at A, where the forces...Ch. 2.5 - Fig. P2.107 and P2.108 2.108 Three cables are...Ch. 2.5 - Prob. 2.109PCh. 2.5 - A rectangular plate is supported by three cables...Ch. 2.5 - A transmission tower is held by three guy wires...Ch. 2.5 - A transmission tower is held by three guy wires...Ch. 2.5 - In trying to move across a slippery icy surface, a...Ch. 2.5 - Fig. P2.113 2.114 Solve Prob. 2.113 assuming that...Ch. 2.5 - For the rectangular plate of Probs. 2.109 and...Ch. 2.5 - PROBLEM 2.116 For the cable system of Problems...Ch. 2.5 - PROBLEM 2.117 For the cable system of Problems...Ch. 2.5 - Prob. 2.118PCh. 2.5 - For the transmission tower of Probs. 2.111 and...Ch. 2.5 - Three wires are connected at point D, which is...Ch. 2.5 - A container of weight W is suspended from ring A,...Ch. 2.5 - Prob. 2.122PCh. 2.5 - Prob. 2.123PCh. 2.5 - Prob. 2.124PCh. 2.5 - Fig. P2.113 2.114 Solve Prob. 2.113 assuming that...Ch. 2.5 - Prob. 2.126PCh. 2 - Prob. 2.127RPCh. 2 - Prob. 2.128RPCh. 2 - A hoist trolley is subjected to the three forces...Ch. 2 - Knowing that = 55 and that boom AC exerts on pin...Ch. 2 - Two cables are tied together at C and loaded as...Ch. 2 - Two cables tied together at C are loaded as shown....Ch. 2 - The end of the coaxial cable AE is attached to the...Ch. 2 - Prob. 2.134RPCh. 2 - Find the magnitude and direction of the resultant...Ch. 2 - Prob. 2.136RPCh. 2 - Collars A and B are connected by a 25-in.-lang...Ch. 2 - Fig. P2.137 and P2.138 2.138 Collars A and B are...
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