Explanation Given information: The weight ( W ) of gears A and C is 2.5 lb. The weight ( W A B C ) of rod ABC is 4 lb. The radius ( r ) of gears A and C is 2 inch. The time ( t ) for produced required couple is 2.5 sec. The angular velocity ( ω ) of the rod is 240 rpm clockwise. Calculation: Find the mass ( m ) of the disks A and C using the equation: m = W g Substitute 2.5 lb for W and 32.2 ft/s 2 for g . m = 2.5 32.2 = 0.07764 lb ⋅ s 2 /ft Find the mass ( m A B C ) of the rod ABC using the equation: m A B C = W A B C g Substitute 4 lb for W and 32.2 ft/s 2 for g . m A B C = 7 32.2 = 0.12422 lb ⋅ s 2 /ft The mass moment of inertia of the disk A and C is same ( I ¯ A = I ¯ C = I ) . Write the equation of the mass moment of inertia ( I ¯ ) of the gears A and C . I ¯ = 1 2 m r 2 Write the equation of the mass moment of inertia ( I ¯ A B C ) of the rod ABC . I ¯ A B C = 1 12 m A B C ( A B C ) 2 Here, ABC is the length of rod ABC . Substitute 4 r for ABC . I ¯ A B C = 1 12 m A B C ( 4 r ) 2 = 4 3 m A B C r 2 Sketch the system with components of velocity as shown in Figure (1). Refer Figure (1), The gears A and C have the same mass ( m A = m C = m ) , radius ( r A = r C = r ) and angular velocity ( ω A = ω C = ω 1 ) . Hence, the velocity of gears A and C is same ( v ¯ A = v ¯ C = v ¯ ) . Write the equation of velocity ( v ¯ ) of gears A and C . v ¯ = ( B C ) ω Here, BC is the distance between the point A and C . Substitute 2 r for BC . v ¯ = 2 r ω The gears A and C roll on the fixed gear B . Write the equation of angular velocity ( ω 1 ) of gears A and C . ω 1 = v ¯ C r Substitute v ¯ for v ¯ C . ω 1 = v ¯ r Substitute 2 r ω for v ¯ . ω 1 = 2 r ω r = 2 ω Consider the principle of impulse and momentum in the gear C . Syst Momenta 1 + Syst Ext Imp 1y2 = Syst Momenta 2 Sketch the impulse and momentum diagram of the gear C as shown in Figure (2).

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

11th Edition

ISBN: 9781259639272

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 17.76P

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Find the magnitude of the couple M which must be applied to rod ABC.

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Chapter 17.2, Problem 17.75P

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Chapter 17 Solutions

Connect 1 Semester Access Card for Vector Mechanics for Engineers: Statics and Dynamics

Ch. 17.1 - A round object of mass m and radius r is released...Ch. 17.1 - Prob. 17.2CQ Ch. 17.1 - Prob. 17.3CQ Ch. 17.1 - Prob. 17.4CQ Ch. 17.1 - Slender bar A is rigidly connected to a massless...Ch. 17.1 - A 200-kg flywheel is at rest when a constant 300...Ch. 17.1 - The rotor of an electric motor has an angular...Ch. 17.1 - Prob. 17.3P Ch. 17.1 - Two disks of the same material are attached to a...Ch. 17.1 - Prob. 17.5P

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Find the magnitude of the couple M which must be applied to rod ABC .

Solution Summary: The author calculates the mass of the disks A and C using the equation: m=Wg Substitute 2.5 lb for W and 32.2ft/

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Find the magnitude of the couple M which must be applied to rod ABC.

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Chapter 17 Solutions