(a) Explanation Given information: The coefficient of static friction between the rope and the horizontal pipe is ( μ s ) h = 0.30 . The smallest value of P for which the equilibrium is maintained is P min = 80 N . Calculation: Show the free-body diagram of the horizontal pipe as in Figure (1). Find the angle the rope wounded around the pipe as follows: β = 1 4 × 2 π = π 2 Find the force P using the equation. P Q = e ( μ s ) h β Substitute π 2 for β . P Q = e ( μ s ) h × π 2 (1) Find the angle the rope wounded around the pipe as follows: β = 1 4 × 2 π = π 2 Find the force S using the equation. S 400 = e ( μ s ) h β Substitute π 2 for β . S 400 = e ( μ s ) h × π 2 (2) Show the free-body diagram of the vertical pipe as in Figure (2). Find the angle the rope wounded around the pipe as follows: β = 1 2 × 2 π = π Find the force Q using the equation. Q S = e ( μ s ) v β Substitute π for β . Q S = e ( μ s ) v × π (3) Multiply the equations (1), (2), and (3). P Q × S 400 × Q S = e ( μ s ) h × π 2 × e ( μ s ) h × π 2 × e ( μ s ) v × π P 400 = e ( μ s ) h × π 2 × e ( μ s ) h × π 2 × e ( μ s ) v × π (b) To determine Find the coefficient of static friction between the rope and the vertical pipe.

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ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 8.4, Problem 8.108P

(a)

To determine

Find the largest value of P for which the equilibrium s maintained.

(b)

To determine

Find the coefficient of static friction between the rope and the vertical pipe.

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Chapter 8.4, Problem 8.107P

Chapter 8.4, Problem 8.109P

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