Explanation Given: The weight of the wheel ( W ) is 20 lb. The weight of the homogeneous block ( W B ) is 30 lb. The coefficient of static friction at B ( μ B ) is 0.2. The coefficient of static friction at D ( μ D ) is 0.3. Show the free body diagram of the wheel as in Figure (1). Using Figure (1), Assume the slipping at B, Find the friction force at B. F B = μ B × N B (I) Determine the smallest force ( P ). Take summation of the moment about A is equal to zero. ∑ M A = 0 F B + T = P (II) Determine the tractive force ( T ) using the Equation of equilibrium. Along the horizontal direction: ∑ F x = 0 F B − T = 0 F B = T (III) Determine the normal reaction at B ( N B ) using the Equation of equilibrium. Along the vertical direction: ∑ F y = 0 N B − W − P = 0 N B = W + P (IV) Conclusion: Substitute 0.2 for μ B in Equation (I). F B = 0.2 × N B (V) Substitute F B + T for P in Equation (IV). N B = W + ( F B + T ) Substitute F B for T . N B = W + ( F B + F B ) = W + 2 F B (VI) Substitute 20 lb for W and 0.2 × N B for F B in Equation (VI). N B = 20 + 2 ( 0.2 × N B ) N B − 0.4 N B = 20 0.6 N B = 20 N B = 20 0.6 N B = 33.33 lb Substitute 33.33 lb for N B in Equation (V). F B = 0.2 × 33.33 = 6.67 lb Substitute 6

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 8.2, Problem 55P

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The smallest vertical force (P).

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Chapter 8 Solutions

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 smallest vertical force ( P ).

Solution Summary: The author shows the free body diagram of the wheel as in Figure (1).

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