Explanation Given information: The mass of the roller m r is 100 kg . The mass of the tube m t is 40 kg . The radius of the tube r is 150 mm or ( 0.1 5 m ) . The coefficient of static friction at contact surface A , μ A = 0.2 . The coefficient of static friction at contact surface B , μ B = 0.3 . The coefficient of static friction at contact surface C , μ C = 0.4 . Calculation: Show the free body diagram of the roller as in Figure 1. Show the free body diagram of the tube as in Figure 2. Conclusion: From Figure 1, Resolve the force in the x -direction. + → ∑ F x = 0 P − N A cos θ − F A sin θ − F C = 0 (1) Here, the friction force at A is F A , the friction force at C is F C , the angle of incline is θ , and the normal force at A is N A . Substitute 30 ° for θ in Equation (1). + → ∑ F x = 0 P − N A cos 30 ° − F A sin 30 ° − F C = 0 P − 0.866 N A − 0.5 F A − F C = 0 (2) Resolve the force in the y -direction. + ↑ ∑ F y = 0 N C + F A cos θ − N A sin θ − m r g = 0 (3) Here, the normal force at C is N C and the acceleration due to gravity is g . Substitute 9 .81 m / s 2 for g , 100 kg for m r , and 30 ° for θ in Equation (3). + ↑ ∑ F y = 0 N C + F A cos 30 ° − N A sin 30 ° − ( 100 ) ( 9.81 ) = 0 N C + 0.866 F A − 0.5 N A − 981 = 0 (4) Take the moment about point D in the anti-clockwise direction. + ∑ M D = 0 F A r − F C r = 0 (5) Substitute 150 mm for r in Equation (5). F A ( 150 mm ) − F C ( 150 mm ) = 0 F A [ ( 150 mm ) 1 m 1000 mm ] − F C [ ( 150 mm ) 1 m 1000 mm ] = 0 F A ( 0 .15 m ) − F C ( 0 .15 m ) = 0 0.15 F A − 0 .15 F C = 0 (6) From Figure 2, Resolve the force in the x -direction. + → ∑ F x = 0 N A − F B − m t g sin θ = 0 (7) Here, the friction force at B is F B . Substitute 40 kg for m t , 9 .81 m / s 2 for g , and 30 ° for θ in Equation (7). N A − F B − ( 40 ) ( 9.81 ) ( sin 30 ° ) = 0 N A − F B − 196.2 = 0 (8) Resolve the force in the y -direction. + ↑ ∑ F y = 0 N B − F A − m t g cos θ = 0 (9) Here, the normal force at B is N B . Substitute 9 .81 m / s 2 for g , 40 kg for m t , and 30 ° for θ in Equation (9). N B − F A − ( 40 ) ( 9

Statics And Mechanics Of Materials, Student Value Edition Plus Mastering Engineering With Pearson Etext -- Access Card Package (5th Edition)

5th Edition

ISBN: 9780134380704

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 4.8, Problem 62P

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Chapter 4.8, Problem 61P

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Statics And Mechanics Of Materials, Student Value Edition Plus Mastering Engineering With Pearson Etext -- Access Card Package (5th Edition)

Ch. 4.4 - Draw the free-body diagram of each object. Prob....Ch. 4.4 - Determine the horizontal and vertical components...Ch. 4.4 - Determine the horizontal and vertical components...Ch. 4.4 - The truss is supported by a pin at A and a roller...Ch. 4.4 - Determine the components of reaction at the fixed...Ch. 4.4 - The 25-kg bar has a center of mass at G. If it is...Ch. 4.4 - Determine the reactions at the smooth contact...Ch. 4.4 - Determine the components of the support reactions...Ch. 4.4 - Determine the reactions at the supports. Prob. 4-2 Ch. 4.4 - Determine the horizontal and vertical components...

Ch. 4.4 - Determine the reactions at the supports. Prob. 4-4 Ch. 4.4 - Determine the reactions at the supports. Prob. 4-5 Ch. 4.4 - Determine the reactions at the supports. Prob. 4-6 Ch. 4.4 - Determine the magnitude of force at the pin A and...Ch. 4.4 - The dimensions of a jib crane are given in the...Ch. 4.4 - The dimensions of a jib crane are given in the...Ch. 4.4 - The smooth pipe rests against the opening at the...Ch. 4.4 - The beam is horizontal and the springs are...Ch. 4.4 - The 10-kg uniform rod is pinned at end A. If it is...Ch. 4.4 - The man uses the hand truck to move material up...Ch. 4.4 - Three uniform books, each having a weight W and...Ch. 4.4 - Determine the reactions at the pin A and the...Ch. 4.4 - If rope BC will fail when the tension becomes 50...Ch. 4.4 - Prob. 17P Ch. 4.4 - Prob. 18P Ch. 4.4 - The cantilever footing is used to support a wall...Ch. 4.4 - Prob. 20P Ch. 4.4 - A boy stands out at the end of the diving board,...Ch. 4.4 - Prob. 22P Ch. 4.4 - Prob. 23P Ch. 4.4 - Prob. 24P Ch. 4.4 - Prob. 25P Ch. 4.4 - The man attempts to pull the four wheeler up the...Ch. 4.6 - Draw the free-body diagram of each object.Ch. 4.6 - In each case, write the moment equations about the...Ch. 4.6 - Prob. 7FP Ch. 4.6 - Prob. 8FP Ch. 4.6 - The rod is supported by smooth journal bearings at...Ch. 4.6 - Determine the support reactions at the smooth...Ch. 4.6 - Determine the force developed in the short link...Ch. 4.6 - Determine the components of reaction that the...Ch. 4.6 - The uniform load has a mass of 600 kg and is...Ch. 4.6 - Due to an unequal distribution of fuel in the wing...Ch. 4.6 - Determine the components of reaction at the fixed...Ch. 4.6 - The 50-lb mulching machine has a center of gravity...Ch. 4.6 - Prob. 30P Ch. 4.6 - The uniform concrete slab has a mass of 2400 kg....Ch. 4.6 - Prob. 32P Ch. 4.6 - Determine the tension in each cable and the...Ch. 4.6 - The bent rod is supported at A, B, and C by smooth...Ch. 4.6 - Prob. 35P Ch. 4.6 - The bar AB is supported by two smooth collars. At...Ch. 4.6 - The rod has a weight of 6 lb/ft. If it is...Ch. 4.6 - The sign has a mass of 100 kg with center of mass...Ch. 4.6 - Both pulleys cite fixed to the shaft and as the...Ch. 4.6 - Both pulleys are fixed to the shaft and as the...Ch. 4.6 - Prob. 41P Ch. 4.8 - Determine the friction force at the surface of...Ch. 4.8 - Determine the couple moment M needed to cause...Ch. 4.8 - Prob. 6PP Ch. 4.8 - Prob. 7PP Ch. 4.8 - Prob. 13FP Ch. 4.8 - Determine the minimum force P to prevent the 30-kg...Ch. 4.8 - Determine the maximum force P that can be applied...Ch. 4.8 - Prob. 16FP Ch. 4.8 - Prob. 17FP Ch. 4.8 - Prob. 18FP Ch. 4.8 - Prob. 19FP Ch. 4.8 - If the coefficient of static friction at all...Ch. 4.8 - Prob. 21FP Ch. 4.8 - Prob. 42P Ch. 4.8 - The tractor exerts a towing force T = 400 lb....Ch. 4.8 - The mine car and its contents have a total mass of...Ch. 4.8 - The winch on the truck is used to hoist the...Ch. 4.8 - Prob. 46P Ch. 4.8 - The automobile has a mass of 2 Mg and center of...Ch. 4.8 - Prob. 48P Ch. 4.8 - Prob. 49P Ch. 4.8 - Prob. 50P Ch. 4.8 - Determine the angle at which the applied force P...Ch. 4.8 - Prob. 52P Ch. 4.8 - The 180-lb man climbs up the ladder and stops at...Ch. 4.8 - The 180-lb man climbs up the ladder and stops at...Ch. 4.8 - The spool of wire having a weight of 300 lb rests...Ch. 4.8 - The spool of wire having a weight of 300 lb rests...Ch. 4.8 - The ring has a mass of 0.5 kg and is resting on...Ch. 4.8 - Determine the smallest force P that must be...Ch. 4.8 - The man having a weight of 200 lb pushes...Ch. 4.8 - The uniform hoop of weight W is subjected to the...Ch. 4.8 - Prob. 61P Ch. 4.8 - Prob. 62P Ch. 4.8 - Prob. 63P Ch. 4.8 - The coefficient of static Friction between the...Ch. 4 - If the roller at B can sustain a maximum load of 3...Ch. 4 - Determine the reactions at the supports A and B...Ch. 4 - Determine the normal reaction at the roller A and...Ch. 4 - Determine the horizontal and vertical components...Ch. 4 - Determine the x, y, z components of reaction at...Ch. 4 - Prob. 6RP Ch. 4 - Prob. 7RP Ch. 4 - The uniform 60-kg crate C rests uniformly on a...

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Chapter 4 Solutions