Explanation Given information : The mass m of the man is 75 kg . The coefficient of static friction μ s at A and B is 0.3 . The length a of the ladder is 2 .5 m . Show the free body diagram of the member A C as in Figure (1). Show the free body diagram of the member B C as in Figure (2). The slipping or tipping can take place either at end A or B of the ladder. Assume that the slipping occurs at end B . Calculate the friction force at B . F B = μ s N B (I) Here, the normal force at B is N B . Substitute 0.3 for N B in Equation (I). F B = 0.3 N B From Figure (2), Resolve the forces in x direction. + → ∑ F x = 0 F B C sin θ / 2 − F B = 0 (II) Here, the friction force between B and C is F B C . Substitute 0.3 N B for F B in Equation (II). F B C sin θ / 2 − 0.3 N B = 0 F B C sin θ / 2 = 0.3 N B (III) Resolve the forces in y direction. + ↑ ∑ F y = 0 N B − F B C cos θ / 2 = 0 F B C cos θ / 2 = N B (IV) Conclusion: Divide Equation (III) by Equation (IV). F B C sin θ / 2 F B C cos θ / 2 = 0.3 N B N B tan θ / 2 = 0.3 θ / 2 = tan − 1 ( 0.3 ) θ / 2 = 16.69 ° θ = 2 ( 16.69 ° ) θ = 33.4 ° Hence, the greatest angle θ so that the ladder does not slip is 33.4 ° _ . From Figure (1), Take a moment about A in anticlockwise direction. + ∑ M A = 0 F B C sin θ ( a ) − W b = 0 F B C sin θ ( a ) − m g b = 0 (V) Here, the acceleration due to gravity is g . Substitute 33.4 ° for θ , 2 .5 m for a , 75 kg for m , 9

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 8.2, Problem 54P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 8.2 - P81. Determine the friction force at the surface...Ch. 8.2 - P82. Determine M to cause impending motion of the...Ch. 8.2 - P83. Determine the force P to move block B.Ch. 8.2 - P84. Determine the force P needed to cause...Ch. 8.2 - F81. Determine the friction developed between the...Ch. 8.2 - F82. Determine the minimum force P to prevent the...Ch. 8.2 - Prob. 3FP Ch. 8.2 - F84. If the coefficient of static friction at...Ch. 8.2 - F85. Determine the maximum force P that can be...Ch. 8.2 - F86. Determine the minimum coefficient of static...

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The greatest angle θ so that the ladder does not slip.

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