Explanation Given: The pipe weight is W . The applied force is P . Show the free body diagram of the pipe which pulls up the inclined plane of slope using a force as in Figure (1). Using Figure (1), Determine the normal reaction ( N ) using the Equations of equilibrium. Along the vertical direction: ∑ F y = 0 N + P sin ϕ − W cos α = 0 N = W cos α − P sin ϕ (I) Here, the inclined plane of slop is α and the angle of inclination is ϕ . Derive the applied force equation using the Equations of equilibrium. Along the horizontal direction: ∑ F x = 0 P cos ϕ − W sin α − α N = 0 Here, the co-efficient of the kinetic friction is μ k . Substitute tan θ N for α N . P cos ϕ − W sin α − tan θ N = 0 (II) Here, the angle of static friction is θ . Formulas used: 1 + tan θ = ( cos θ + sin θ ) cos ( A − B ) = cos A cos B + sin A sin B sin ( A + B ) = sin A cos B + cos A sin B Conclusion: Substitute W cos α − P sin ϕ for N in Equation (II). P cos ϕ − W sin α − tan θ ( W cos α − P sin ϕ ) = 0 P cos ϕ − W sin α − tan θ W cos α + tan θ P sin ϕ = 0 P cos ϕ − tan θ P sin ϕ = W sin α + tan θ W cos α P ( cos ϕ + tan θ sin ϕ ) = W ( sin α + tan θ cos α ) (III) Substitute ( cos θ + sin θ ) for 1 + tan θ in Equation (III)

Engineering Mechanics: Statics and Modified Mastering Engineering with eText and Access Card (14th Edition)

14th Edition

ISBN: 9780134229287

Author: Russell C. Hibbeler

Publisher: PEARSON

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The column is described as a vertical member of the structure that carries an axial compressive load, and buckling is a lateral deformation of the column under the application of load.

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Chapter 8.2, Problem 10P

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To derive: The angle ϕ and the applied force equation.

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Chapter 8 Solutions

Engineering Mechanics: Statics and Modified Mastering Engineering with eText and Access Card (14th Edition)

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 - Determine the maximum force P the connection can...Ch. 8.2 - The tractor exerts a towing force T=400 lb....Ch. 8.2 - Prob. 3P Ch. 8.2 - The winch on the truck is used to hoist the...Ch. 8.2 - The automobile has a mass of 2 Mg and center of...Ch. 8.2 - The automobile has a mass of 2 Mg and canter of...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 - Determine the maximum weight W the man can lift...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 car has a mass of 1.6 Mg and center of mass at...Ch. 8.2 - Prob. 15P Ch. 8.2 - The 180-Ib man climbs up the ladder and stops at...Ch. 8.2 - The 180-Ib man climbs up the ladder and stops at...Ch. 8.2 - The spool of wire having a weight of 300 Ib rests...Ch. 8.2 - Prob. 19P Ch. 8.2 - The ring has a mass of 0.5 kg and is resting on...Ch. 8.2 - A man attempts to support a stack of books...Ch. 8.2 - The tongs are used to lift the 150-kg crate, whose...Ch. 8.2 - The beam is supported by a pin at A and a roller...Ch. 8.2 - The uniform thin pole has a weight of 30 Ib and a...Ch. 8.2 - The uniform pole has a weight of 30 Ib and a...Ch. 8.2 - The block brake is used to stop the wheel from...Ch. 8.2 - Solve Prob. 8-26 if the couple moment M0 is...Ch. 8.2 - A worker walks up the sloped roof that is defined...Ch. 8.2 - Prob. 29P 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 - Determine the smallest force P that must be...Ch. 8.2 - The man having a weight of 200 Ib pushes...Ch. 8.2 - The uniform hoop of weight W is subjected to the...Ch. 8.2 - Prob. 35P Ch. 8.2 - Determine the minimum force P needed to push the...Ch. 8.2 - Prob. 37P Ch. 8.2 - The coefficient of static friction between the...Ch. 8.2 - Determine the smallest coefficient of static...Ch. 8.2 - Prob. 40P Ch. 8.2 - If the coefficient of static friction at A and B...Ch. 8.2 - The 100-kg disk rests on a surface for which, B =...Ch. 8.2 - Investigate whether the equilibrium can be...Ch. 8.2 - Prob. 44P 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 - Crates A and B weigh 200 Ib and 150 Ib,...Ch. 8.2 - Two blocks A and B, each having a mass of 5 kg,...Ch. 8.2 - The uniform crate has a mass of 150 kg. If the...Ch. 8.2 - The uniform crate has a mass of 150 kg. If the...Ch. 8.2 - Beam AB has a negligible mass and thickness, and...Ch. 8.2 - Beam AB has a negligible mass and thickness, and...Ch. 8.2 - Determine the smallest couple moment that can be...Ch. 8.2 - Determine the greatest angle so that the ladder...Ch. 8.2 - The wheel weights 20 lb and rests on a surface for...Ch. 8.2 - Prob. 56P Ch. 8.2 - The man has a weight of 200 lb, and the...Ch. 8.2 - Prob. 1CP Ch. 8.2 - Prob. 4CP Ch. 8.2 - Explain how to find the maximum force this man can...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 - The wedge is used to level the member. Determine...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 - If the coefficient of static friction between all...Ch. 8.4 - Determine the smallest force P needed to lift the...Ch. 8.4 - Prob. 66P 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. 69P Ch. 8.4 - If the force F is removed from the handle of the...Ch. 8.4 - Prob. 71P Ch. 8.4 - If the clamping force on the boards is 600 lb,...Ch. 8.4 - Prob. 73P Ch. 8.4 - The square-threaded bolt is used to join two...Ch. 8.4 - The shaft has a square-threaded screw with a lead...Ch. 8.4 - If couple forces of F=35 N are applied to the...Ch. 8.4 - Prob. 77P Ch. 8.4 - The device is used to pull the battery cable...Ch. 8.4 - Determine the clamping force on the board A if the...Ch. 8.4 - If the required clamping force on the board A is...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. 8.5 - 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 - A 180-lb farmer tries to restrain the cow from...Ch. 8.5 - The 100-lb boy at A is suspended from the cable...Ch. 8.5 - The 100-lb boy at A is suspended from the cable...Ch. 8.5 - Prob. 88P Ch. 8.5 - A cable is attached to the 20-kg plate B, passes...Ch. 8.5 - Prob. 90P Ch. 8.5 - Prob. 91P Ch. 8.5 - Determine the force P that must be applied to the...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 - The coefficient of static friction between the...Ch. 8.5 - Prob. 97P Ch. 8.5 - Show that the frictional relationship between the...Ch. 8.5 - The wheel is subjected to a torque of M = 50 N m...Ch. 8.5 - Using the coefficients of static friction...Ch. 8.5 - If the coefficient of static friction between the...Ch. 8.5 - Idler pulley A, and motor pulley B. If the motor...Ch. 8.5 - Using the coefficient of static friction...Ch. 8.5 - Determine the smallest counterclockwise twist or...Ch. 8.5 - Determine the largest angles so that the cord...Ch. 8.5 - Determine the smallest stretch of the spring...Ch. 8.8 - If the coefficient of static is, s = 0.3,...Ch. 8.8 - Prob. 108P Ch. 8.8 - Prob. 109P Ch. 8.8 - Prob. 110P Ch. 8.8 - Prob. 111P Ch. 8.8 - Prob. 113P Ch. 8.8 - Prob. 114P Ch. 8.8 - Prob. 115P Ch. 8.8 - Prob. 116P Ch. 8.8 - Prob. 117P Ch. 8.8 - If the coefficient of static friction is. k....Ch. 8.8 - If the coefficient of static friction between the...Ch. 8.8 - If the coefficient of kinetic friction between the...Ch. 8.8 - if the force P is applied horizontally to the...Ch. 8.8 - Prob. 122P Ch. 8.8 - Prob. 123P Ch. 8.8 - Prob. 124P Ch. 8.8 - Prob. 125P Ch. 8.8 - The bell crank fits loosely into a 0.5-in-diameter...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 - The 1.4-Mg machine is to be moved over a level...Ch. 8.8 - Prob. 1RP Ch. 8.8 - The uniform 60-kg crate C rests uniformly on a...Ch. 8.8 - A 35-kg disk rests on an inclined surface for...Ch. 8.8 - The cam is subjected to a couple moment of 5N m....Ch. 8.8 - The three stone blocks have weights of, WA =...Ch. 8.8 - Prob. 6RP Ch. 8.8 - Prob. 7RP Ch. 8.8 - Prob. 8RP

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To derive : The angle ϕ and the applied force equation.

Solution Summary: The author shows the free body diagram of the pipe which pulls up the inclined plane of slope using a force as in Figure (1).

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To derive: The angle ϕ and the applied force equation.

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Chapter 8 Solutions