Explanation Given: The mass of the spool S is 2 kg . The coefficient of static friction μ s is 0.2 . The distance from A to S is 0.25 m . Write the equation of centripetal acceleration a = υ 2 r Here, centripetal acceleration is a , the velocity is υ and the radius is r . The distance from A to S is shown in Figure (1). From the Figure (1) write the equation to determine the angle of inclination tan θ = 3 4 θ = tan − 1 ( 3 4 ) θ = 36.87 ° From the Figure (1) write the equation to determine the radius of curvature. r = A S cos θ = x cos θ (I). Draw the free body diagram spool as shown in Figure (2). Write the formula for equation of motion for spool in the vertical direction. ∑ F y = m a = m ( 0 ) = 0 Here, summation of total force acting on vertical direction is ∑ F y mass is m and acceleration in the vertical direction is a y . Refer Figure (2) calculate the normal force on the spool in the vertical direction. ∑ F y = N cos θ − μ s N sin θ − m g (II). Write the formula for equation of motion in the horizontal direction. ∑ F x = m a x (III). Here, summation of total force acting on horizontal direction is ∑ F x mass is m and acceleration in the horizontal direction is a x . Refer Figure (2) resolve the forces in the horizontal direction. ∑ F x = N sin θ + μ s N cos θ (IV). Conclusion: Substitute 0.25 m for x and 36.87 ° for θ in Equation (I). r = x cos θ = 0.25 cos 36.87 ° = 0.2 m Substitute υ 2 r for a in Equation (III)

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

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Chapter 13.5, Problem 59P

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The minimum constant speed of the spool.

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Chapter 13.5, Problem 58P

Chapter 13.5, Problem 60P

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Engineering Mechanics: Statics & Dynamics (14th Edition)

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The minimum constant speed of the spool.

Solution Summary: The author explains the minimum and maximum constant speed of the spool. The distance from A to S is shown in Figure (1).

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Chapter 13 Solutions