Explanation Given information: The weight ( W ) of the crate is 1600 lb. Calculation: Show the Free body diagram of point D as in Figure 1. The force applied at the point A is T A B , T A C , T A D and W . Write the weight of the crate in vector as below: W = − 1600 j Express the vector A B → as below: A B → = − ( 36 in . ) i + ( 60 in . ) j − ( 27 in . ) k Calculate distance of the member DA as below: A B = ( − 36 ) 2 + 60 2 + ( − 27 ) 2 = 1296 + 3600 + 729 = 75 in . Calculate the unit vector ( λ A B ) using the relation: λ A B = A B → A B Substitute − ( 36 in . ) i + ( 60 in . ) j − ( 27 in . ) k for A B → and 75 in . for AB . λ A B = − ( 36 in . ) i + ( 60 in . ) j − ( 27 in . ) k 75 in . = − 0.48 i + 0.8 j − 0.36 k Calculate the tension force ( T A B ) in cable AB using the relation: T A B = T A B λ A B Substitute − 0.48 i + 0.8 j − 0.36 k for λ A B . T A B = ( − 0.48 i + 0.8 j − 0.36 k ) T A B Express the vector A C → as below: A C → = ( 60in . ) j + ( 32in . ) k Calculate distance of the member AC as below: A C = ( 60 ) 2 + ( 32 ) 2 = 3600 + 1024 = 68 in . Calculate the unit vector ( λ A C ) using the relation: λ A C = A C → A C Substitute ( 60in . ) j + ( 32in . ) k for A C → and 68 in . for AC . λ A C = ( 60in . ) j + ( 32in . ) k 68 in . = 0.8824 j + 0.4706 k Calculate the tension force ( T A C ) in Cable AC using the relation: T A C = T A C λ A C Substitute 0.8824 j + 0.4706 k for λ A C . T A C = ( 0.8824 j + 0.4706 k ) T A C Express the vector A D → as below: A D → = ( 40 in . ) i + ( 60in . ) j − ( 27in . ) k Calculate distance of the member AD as below: A D = ( 40 ) 2 + ( 60 ) 2 + ( − 27 ) 2 = 1600 + 3600 + 729 = 77 in

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

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Axial Load

When a bar of the uniform cross-section is acted by a load, such that the load acts along the longitudinal axis of the bar, such kinds of loadings are known as axial loadings. In general terms, a load is an external force acting on a component. An axial …

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Chapter 2.5, Problem 2.106P

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Find the tension in the cable AB(TAB), AC(TAC) and AD(TAD).

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Chapter 2.5, Problem 2.105P

Chapter 2.5, Problem 2.107P

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Chapter 2 Solutions

Vector Mechanics for Engineers: Statics, 11th Edition

Ch. 2.1 - Two forces are applied as shown to a hook....Ch. 2.1 - Two forces are applied as shown to a bracket...Ch. 2.1 - Prob. 2.3P Ch. 2.1 - Prob. 2.4P Ch. 2.1 - A stake is being pulled out of the ground by means...Ch. 2.1 - A telephone cable is clamped at A to the pole AB....Ch. 2.1 - A telephone cable is clamped at A to the pole AB....Ch. 2.1 - A disabled automobile is pulled by means of two...Ch. 2.1 - A disabled automobile is pulled by means of two...Ch. 2.1 - Two forces are applied as shown to a hook support....

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. 2.15P Ch. 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 - Prob. 2.19P Ch. 2.1 - Prob. 2.20P 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. 2.23P Ch. 2.2 - 2.23 and 2.24 Determine the x and y components of...Ch. 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 - The hydraulic cylinder BC exerts cm member AB a...Ch. 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 - Prob. 2.36P 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 - Prob. 2.39P Ch. 2.2 - Prob. 2.40P Ch. 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. 2.45P Ch. 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. 2.51P Ch. 2.3 - 2.52 Two forces P and Q are 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 - Free-Body Diagram...Ch. 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 - 2.65 Three forces are applied to a bracket as...Ch. 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 - Prob. 2.71P Ch. 2.4 - Prob. 2.72P 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. 2.75P Ch. 2.4 - Prob. 2.76P Ch. 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. 2.79P Ch. 2.4 - Prob. 2.80P Ch. 2.4 - 2.81 A force acts at the origin of a coordinate...Ch. 2.4 - A force acts at the origin of a coordinate system...Ch. 2.4 - A force F of magnitude 210 N acts at the origin of...Ch. 2.4 - Prob. 2.84P Ch. 2.4 - 2.85 A frame ABC is supported in part by cable DBE...Ch. 2.4 - Prob. 2.86P Ch. 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 - Find the magnitude and direction of the resultant...Ch. 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. 2.95P Ch. 2.4 - For the plate of Prob. 2.89; determine the...Ch. 2.4 - The boom OA carries a load P and is supported by...Ch. 2.4 - Prob. 2.98P 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. 2.103P Ch. 2.5 - Prob. 2.104P Ch. 2.5 - Prob. 2.105P Ch. 2.5 - Prob. 2.106P Ch. 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 - A rectangular plate is supported by three cables...Ch. 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. 2.118P Ch. 2.5 - Prob. 2.119P 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 - Knowing that the tension in cable AC of the system...Ch. 2.5 - Prob. 2.123P Ch. 2.5 - Prob. 2.124P Ch. 2.5 - Fig. P2.113 2.114 Solve Prob. 2.113 assuming that...Ch. 2.5 - Prob. 2.126P Ch. 2 - Prob. 2.127RP Ch. 2 - Prob. 2.128RP Ch. 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 - Knowing that the tension in cable AC is 2130 N,...Ch. 2 - Find the magnitude and direction of the resultant...Ch. 2 - Prob. 2.136RP Ch. 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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Find the tension in the cable AB ( T A B ) , AC ( T A C ) and AD ( T A D ) .

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Find the tension in the cable AB(TAB), AC(TAC) and AD(TAD).

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Chapter 2 Solutions