Explanation Draw the free body diagram for the pulley with the instantaneous center C . Figure-(1) Write the expression for the upward velocity of the supported mass. ω = v r i (I) Here, the inner radius of the pulley is r i and the angular velocity of the pulley is ω . Write the expression for the mass moment of inertia for pulley about O . I O = m k O 2 (II) Here, the mass of the grooved pulley is m and the centroidal radius of gyration of the pulley is k O . Write the expression for the conservation of the moment-angular momentum for the pulley about its centre O . H O 1 + F r o t − T a v r i t = I O ω (III) Here, the constant force is F , the time average value of the force in the cable is T a v , time period is t and the outer radius of the pulley is r o . Substitute v r i for ω in Equation (III). H O 1 + F r o t − T a v r i t = I O ( v r i ) (IV) Draw the free body diagram for the supported pulley. Figure-(2) Write the expression for the conservation of linear impulse momentum for the supported cylinder about its centre. T a v t − M g t = M v (V) Here, the mass of the cylinder is M and the acceleration due to gravity is g . Conclusion: Substitute 40 kg for m and 160 mm for K O in Equation (II). I O = ( 40 kg ) ( 160 mm ) 2 = ( 40 kg ) ( 160 mm ( 1 m 10 3 mm ) ) 2 = ( 40 kg ) ( 0.0256 m 2 ) = 1.024 kg ⋅ m 2 Substitute 1.024 kg ⋅ m 2 for I O , 3 s for t , 75 N for F , 225 mm for r o , 150 mm for r i , 0 for H C 1 in Equation (IV). ( 0 ) + ( 75 N ) ( 225 mm ) ( 3 s ) − T a v ( 150 mm ) ( 3 s ) = ( 1.024 kg ⋅ m 2 ) ( v 150 mm ) [ { ( 75 N ( 1 kg ⋅ m / s 2 1 N ) ) ( 225 mm ( 1 m 10 3 mm ) ) ( 3 s ) − T a v ( 150 mm ( 1 m 10 3 mm ) ) ( 3 s ) } = ( 1

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ISBN: 9781118885840

Author: James L. Meriam, L. G. Kraige, J. N. Bolton

Publisher: WILEY

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Chapter 6.9, Problem 177RP

To determine

The upward velocity of the supported mass after 3 seconds.

The average time value of the force to support the mass of $10 kg$ .

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Chapter 6.9, Problem 176RP

Chapter 6.9, Problem 178RP

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The upward velocity of the supported mass after 3 seconds.

The average time value of the force to support the mass of $10 kg$ .