Explanation Given information : The mass of the crate is m = 80 kg . The coefficient of static friction between the crate and the floor is μ s = 0.3 . Show the free body diagram of the angles and forces created by ropes as in Figure (1). Show the free body diagram of the crate as in Figure (2). Conclusion: From Figure (1), Resolve the forces in x direction, + → ∑ F x = 0 T 1 cos α − T 1 cos β − T 2 sin θ = 0 (I) Here, the tension force developed by ropes are T 1 and T 2 . Substitute 30 ° for α and 45 ° for β in Equation (I). T 1 cos 30 ° − T 1 cos 45 ° − T 2 sin θ = 0 T 1 ( cos 30 ° − cos 45 ° ) = T 2 sin θ T 2 sin θ = 0.159 T 1 (II) Resolve the forces in y direction, + ↑ ∑ F y = 0 T 1 sin α + T 1 sin β − T 2 cos θ = 0 (III) Substitute 30 ° for α and 45 ° for β in Equation (III). T 1 sin 30 ° + T 1 sin 45 ° − T 2 cos θ = 0 T 1 ( sin 30 ° + sin 45 ° ) = T 2 cos θ T 2 cos θ = 1.207 T 1 (IV) Divide Equation (II) by Equation (IV) to get, T 2 sin θ T 2 cos θ = 0.159 T 1 1.207 T 1 tan θ = 0.13173 θ = 7.50 ° Hence, the angle θ for the moment when the smallest force the man exerted on the rope to move the crate is 7.50 ° _ . From Figure (2), Resolve the forces in y direction, + ↑ ∑ F y = 0 N + T 2 cos θ − W = 0 N + T 2 cos θ − m g = 0 (V) Here, normal force on crate is N , weight is W and acceleration due to gravity is g

Engineering Mechanics: Statics and Study Pack (13th Edition)

13th Edition

ISBN: 9780133027990

Author: Russell C. Hibbeler

Publisher: Prentice Hall

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Question

Chapter 8.2, Problem 39P

To determine

The smallest force the man must exert on the rope to move the crate and the angle θ at this moment.

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Chapter 8.2, Problem 38P

Chapter 8.2, Problem 40P

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Chapter 8 Solutions

Engineering Mechanics: Statics and Study Pack (13th Edition)

Ch. 8.2 - Determine the friction developed between the 50-kg...Ch. 8.2 - Determine the minimum force P to prevent the 30-kg...Ch. 8.2 - Determine the maximum force P that can be applied...Ch. 8.2 - If the coefficient of static friction at contact...Ch. 8.2 - Determine the maximum force P that can be applied...Ch. 8.2 - Prob. 6FP Ch. 8.2 - Blocks A, B, and C have weights of 50 N, 25 N, and...Ch. 8.2 - If the coefficient of static friction at all...Ch. 8.2 - Using the coefficients of static friction...Ch. 8.2 - Prob. 1P

Ch. 8.2 - The tractor exerts a towing force T=400 lb....Ch. 8.2 - The winch on the truck is used to hoist the...Ch. 8.2 - Prob. 4P Ch. 8.2 - Prob. 5P Ch. 8.2 - Prob. 6P Ch. 8.2 - The block brake consists of a pin-connected lever...Ch. 8.2 - The block brake consists of a pin-connected lever...Ch. 8.2 - Prob. 9P Ch. 8.2 - Prob. 10P Ch. 8.2 - The block brake is used to stop the wheel from...Ch. 8.2 - If a torque of M=300 Nm is applied to the...Ch. 8.2 - The cam is subjected to a couple moment of 5N m....Ch. 8.2 - Determine the maximum weight W the man can lift...Ch. 8.2 - The car has a mass of 1.6 Mg and center of mass at...Ch. 8.2 - Prob. 16P Ch. 8.2 - Prob. 17P Ch. 8.2 - Prob. 18P Ch. 8.2 - Prob. 19P Ch. 8.2 - Prob. 20P Ch. 8.2 - Prob. 21P Ch. 8.2 - Prob. 22P Ch. 8.2 - A 35-kg disk rests on an inclined surface for...Ch. 8.2 - The man has a weight of 200 lb, and the...Ch. 8.2 - Prob. 25P Ch. 8.2 - Prob. 26P Ch. 8.2 - Prob. 27P Ch. 8.2 - Prob. 28P Ch. 8.2 - Prob. 29P Ch. 8.2 - Prob. 30P Ch. 8.2 - If the coefficient of static friction at A and B...Ch. 8.2 - Prob. 32P Ch. 8.2 - Prob. 33P Ch. 8.2 - Prob. 34P Ch. 8.2 - Prob. 35P Ch. 8.2 - Prob. 36P Ch. 8.2 - Prob. 37P Ch. 8.2 - Prob. 38P Ch. 8.2 - Prob. 39P Ch. 8.2 - Two blocks A and B have a weight of 10 Ib and 6...Ch. 8.2 - Two blocks A and B have a weight of 10 Ib and 6...Ch. 8.2 - Prob. 42P Ch. 8.2 - Prob. 43P Ch. 8.2 - Prob. 44P Ch. 8.2 - Prob. 45P Ch. 8.2 - The beam AB has a negligible mass and thickness...Ch. 8.2 - It is supported at one end by a pin and at the...Ch. 8.2 - Prob. 48P Ch. 8.2 - Prob. 49P Ch. 8.2 - Prob. 50P Ch. 8.2 - Prob. 51P Ch. 8.2 - Prob. 52P Ch. 8.2 - The wheel weights 20 lb and rests on a surface for...Ch. 8.2 - Prob. 54P Ch. 8.2 - Determine the greatest angle so that the ladder...Ch. 8.2 - Prob. 56P Ch. 8.2 - Prob. 57P Ch. 8.2 - Prob. 4CP Ch. 8.4 - Determine the largest angle that will cause the...Ch. 8.4 - If the beam AD is loaded as shown, determine the...Ch. 8.4 - Prob. 60P Ch. 8.4 - Prob. 61P Ch. 8.4 - If P=250 N, determine the required minimum...Ch. 8.4 - Determine the minimum applied force P required to...Ch. 8.4 - Prob. 64P Ch. 8.4 - Prob. 65P Ch. 8.4 - Prob. 66P Ch. 8.4 - Prob. 67P Ch. 8.4 - If the clamping force on the boards is 600 lb,...Ch. 8.4 - Prob. 69P Ch. 8.4 - If the force F is removed from the handle of the...Ch. 8.4 - If the clamping force at G is 900 N, determine the...Ch. 8.4 - If a horizontal force of F = 50 N is applied...Ch. 8.4 - Prob. 73P Ch. 8.4 - Prob. 74P Ch. 8.4 - The shaft has a square-threaded screw with a lead...Ch. 8.4 - Prob. 76P Ch. 8.4 - Prob. 77P Ch. 8.4 - Prob. 78P Ch. 8.4 - If a horizontal force of P = 100 N is applied...Ch. 8.4 - Determine the horizontal force P that must be...Ch. 8.4 - Prob. 81P Ch. 8.4 - Prob. 82P Ch. 8.5 - A cylinder having a mass of 250 kg is to be...Ch. 8.5 - A cylinder having a mass of 250 kg is to be...Ch. 8.5 - Prob. 85P Ch. 8.5 - Prob. 86P Ch. 8.5 - Prob. 87P Ch. 8.5 - The coefficient of static friction between the...Ch. 8.5 - Prob. 89P Ch. 8.5 - Prob. 90P Ch. 8.5 - Prob. 91P Ch. 8.5 - Prob. 92P Ch. 8.5 - Prob. 93P Ch. 8.5 - Determine the weight of the cylinder if the...Ch. 8.5 - If slipping does not occur at the wall, determine...Ch. 8.5 - Prob. 96P Ch. 8.5 - Prob. 97P Ch. 8.5 - Show that the frictional relationship between the...Ch. 8.5 - Prob. 99P Ch. 8.5 - Determine the largest angles so that the cord...Ch. 8.5 - Prob. 101P Ch. 8.5 - Determine the smallest counterclockwise twist or...Ch. 8.5 - Prob. 103P Ch. 8.5 - Prob. 104P Ch. 8.5 - Determine the smallest stretch of the spring...Ch. 8.5 - Idler pulley A, and motor pulley B. If the motor...Ch. 8.8 - Prob. 107P Ch. 8.8 - Prob. 108P Ch. 8.8 - Prob. 109P Ch. 8.8 - Prob. 110P Ch. 8.8 - Prob. 111P Ch. 8.8 - Prob. 112P Ch. 8.8 - Prob. 113P Ch. 8.8 - Prob. 114P Ch. 8.8 - Prob. 116P Ch. 8.8 - Prob. 117P Ch. 8.8 - Prob. 118P Ch. 8.8 - Prob. 119P Ch. 8.8 - Prob. 120P Ch. 8.8 - Prob. 121P Ch. 8.8 - Prob. 122P Ch. 8.8 - Prob. 123P Ch. 8.8 - Prob. 124P Ch. 8.8 - Prob. 125P Ch. 8.8 - Prob. 126P Ch. 8.8 - Prob. 127P Ch. 8.8 - The vehicle has a weight of 2600 lb and center of...Ch. 8.8 - The tractor has a weight of 16 000 lb and the...Ch. 8.8 - Prob. 130P Ch. 8.8 - Prob. 131P Ch. 8.8 - Prob. 132P Ch. 8.8 - Prob. 133RP Ch. 8.8 - Prob. 134RP Ch. 8.8 - Prob. 135RP Ch. 8.8 - Prob. 136RP Ch. 8.8 - The three stone blocks have weights of, WA =...Ch. 8.8 - The uniform 60-kg crate C rests uniformly on a...Ch. 8.8 - Prob. 139RP Ch. 8.8 - Prob. 140RP Ch. 8.8 - Prob. 141RP Ch. 8.8 - Prob. 142RP Ch. 8.8 - Prob. 143RP Ch. 8.8 - Prob. 144RP

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