Explanation Given information: The length of the slender steel rod is L = 225 mm . The coefficient of static friction between the rod and the pipe is μ s = 0.20 . Calculation: Find the friction force at point A and B as follows. F A = μ s N A F B = μ s N B Here, the normal force at point A is N A and the normal force at point B is N B . Show the free-body diagram of the slender steel rod as in Figure 1. Resolve the horizontal component of forces. ∑ F x = 0 N A − N B sin θ − F B cos θ = 0 N A − N B sin θ − μ s N B cos θ = 0 N A = N B sin θ + μ s N B cos θ Resolve the vertical component of forces. ∑ F y = 0 − F A + N B cos θ − F B sin θ − W = 0 − μ s N A + N B cos θ − μ s N B sin θ − W = 0 Substitute ( N B sin θ + μ s N B cos θ ) for N A . − μ s ( N B sin θ + μ s N B cos θ ) + N B cos θ − μ s N B sin θ − W = 0 − μ s N B sin θ − μ s 2 N B cos θ + N B cos θ − μ s N B sin θ − W = 0 N B ( − 2 μ s sin θ − μ s 2 cos θ + cos θ ) − W = 0 N B = W − 2 μ s sin θ + ( 1 − μ s 2 ) cos θ Take moment about point A

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ISBN: 9781259633133

Author: BEER

Publisher: MCG

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Chapter 8.1, Problem 8.45P

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Find the smallest value of θ for which the rod will not fall into the pipe.

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Chapter 8.1, Problem 8.44P

Chapter 8.1, Problem 8.46P

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Find the smallest value of θ for which the rod will not fall into the pipe.

Solution Summary: The author shows the free-body diagram of the slender steel rod as in Figure 1. Resolve the horizontal component of forces.

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Find the smallest value of θ for which the rod will not fall into the pipe.

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