(a) Explanation The mass of the disk A ( m A ) is 6 kg . The mass of the disk B ( m B ) is 3 kg . The initial angular velocity of the disk B ( ω B ) 0 is 360 rpm . The horizontal force of magnitude applied on disks ( F ) is 20 N . The coefficient of the kinetic friction ( μ k ) is 0.15 . The radius of the disk A ( r A ) is 80 mm . The radius of the disk B ( r B ) is 60 mm . Calculation: Consider the acceleration due to gravity ( g ) as 9.81 m / s 2 . Convert the unit of the radius of the disk A ( r A ) : r A = 80 mm × 10 − 3 m 1 mm = 0.08 m Convert the unit of the radius of the disk B ( r B ) : r B = 60 mm × 10 − 3 m 1 mm = 0.06 m While slipping occurs, a friction force F is applied to disk A , and F to disk B . Calculate the mass moment of inertia of the disk A ( I A ) : I A = 1 2 m A r A 2 Substitute 6 kg for m A and 0.08 m for r A . I A = 1 2 × 6 × ( 0.08 ) 2 = 0.0192 kg ⋅ m 2 Calculate the mass moment of inertia of the disk B ( I B ) : I B = 1 2 m B r B 2 Substitute 3 kg for m B and 0.06 m for r B . I B = 1 2 × 3 × ( 0.06 ) 2 = 5.4 × 10 − 3 kg ⋅ m 2 Show the free body diagram of the disk A as in Figure 1. Here, N is the horizontal force of the disk A and α A is the angular acceleration of the disk A . Refer to Figure 1. Calculate the horizontal forces by applying the equation of equilibrium: Sum of horizontal forces is equal to 0. ∑ F x = 0 N − 20 = 0 N = 20 N Calculate the magnitude of the friction force ( F ) : F = μ k N Substitute 20 N for N and 0 (b) To determine Find the final angular velocity of each disk ( ω A and ω B ) .

VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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Chapter 16.1, Problem 16.42P

(a)

To determine

Find the angular acceleration of each disk (αA and αB).

(b)

To determine

Find the final angular velocity of each disk (ωA and ωB).

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Chapter 16.1, Problem 16.41P

Chapter 16.1, Problem 16.43P

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VEC MECH 180-DAT EBOOK ACCESS(STAT+DYNA)

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Find the angular acceleration of each disk ( α A and α B ) .

Solution Summary: The author calculates the angular acceleration of each disk and the horizontal force of magnitude applied on disks.