(a) Explanation Given information: The mass ( m ) of double pulley is 3 kg. The radius of gyration ( k ) of double pulley is 100 mm. The outer radius ( r C ) of the double pulley is 150 mm. The inner radius ( r B ) of the double pulley is 80 mm. The magnitude force P applied on cord B is 24 N. Calculation: Find the mass moment of inertia ( I ¯ ) of double pulley using the equation: I ¯ = m k 2 Substitute 3 kg for m and 100 mm for k . I ¯ = 3 ( 100 mm × 1 m 1 , 000 mm ) 2 = 0.03 kg ⋅ m 2 Consider point C is the instantaneous center of the pulley. Write the equation of velocity ( v ¯ ) of the center of the pulley after 1.5 s using kinematics. v ¯ = r C ω (1) Consider principle of impulse and momentum. Syst Momenta 1 + Syst Ext Imp 1 → 2 = Syst Momenta 2 Sketch the impulse and moment diagram of double pulley as shown in Figure (1). Here, Q is the tension in the cord C . Refer Figure (1), Take moment about C . 0 + P t ( r C + r B ) − m g t r C = I ¯ ω + m v ¯ r C Substitute r C ω for v ¯ . 0 + P t ( r C + r B ) − m g t r C = I ¯ ω + m ( r C ω ) r C P t ( r C + r B ) − m g t r C = ω ( I ¯ + m r C 2 ) ω = P t ( r C + r B ) − m g t r C I ¯ + m r C 2 Substitute 24 N for P , 1 (b) To determine Find the tension in cord C .

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 17.71P

(a)

To determine

The velocity of the center of the pulley after 1.5 s.

(b)

To determine

Find the tension in cord C.

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Chapter 17.2, Problem 17.70P

Chapter 17.2, Problem 17.72P

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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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