(a) To determine The resulting velocity of the carriage. Explanation Given information: The radius ( r ) of the cylinder A is 9 in . . The weight ( W A ) of the cylinder A is 18 lb. The weight ( W B ) of the carriage B is 6 lb. The force ( P ) applied on the system is 2.5 lb. The time ( t ) is 1.2 s. Calculation: Find the mass of the cylinder A using the equation: m A = W A g Substitute 18 lb for W A and 32.2 ft/s 2 for g . m A = 18 32.2 = 0.559 lb ⋅ s 2 /ft Find the mass of the carriage B using the equation: m B = W B g Substitute 6 lb for W A and 32.2 ft/s 2 for g . m B = 6 32.2 = 0.18634 lb ⋅ s 2 /ft Find the moment of inertia ( I ¯ ) of the cylinder using the equation: I ¯ = 1 2 m A r 2 Substitute 0.559 lb ⋅ s 2 /ft for m A and 9 in. for r . I ¯ = 1 2 ( 0.559 ) ( 9 in . × 1 ft 12 in . ) 2 = 0.15722 slug ⋅ ft 2 Consider principle of impulse and momentum. Syst Momenta 1 + Syst Ext Imp 1 → 2 = Syst Momenta 2 Sketch the impulse and moment diagram of cylinder alone as shown in Figure (1). Refer Figure (1), Take moment about C (Anticlockwise moment as positive). 0 + P t r = I ¯ ω + m A v A r Here, ω is the angular velocity of the cylinder A and v A is the velocity of the cylinder A . Substitute 2.5 lb for P , 1.2 s for t , 9 in. for r , 0.15722 slug ⋅ ft 2 for I ¯ , and 0.559 lb ⋅ s 2 /ft for m A . 0 + ( 2.5 ) ( 1.2 ) ( 9 in . × 1 ft 12 in . ) = ( 0 (b) To determine Find the resulting velocity at the center of the cylinder.

Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

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Chapter 17.2, Problem 17.73P

(a)

To determine

The resulting velocity of the carriage.

(b)

To determine

Find the resulting velocity at the center of the cylinder.

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Chapter 17.2, Problem 17.72P

Chapter 17.2, Problem 17.74P

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