Explanation Given information: The weight ( W C ) of carriage C is 3 lb. The weight ( W ) of each disk A and B is 2 lb. The radius ( r ) of each disk A and B is 3 in.. The time ( t ) for required velocity is 0.5 s. The force ( P ) applied on the carriage is 0.2 lb. Calculation: Find the mass ( m C ) of the carriage C using the equation: m C = W C g Substitute 3 lb for W and 32.2 ft/s 2 for g . m C = 3 32.2 = 0.093168 lb ⋅ s 2 /ft Find the mass ( m ) of the disks A and B using the equation: m = W g Substitute 2 lb for W and 32.2 ft/s 2 for g . m = 2 32.2 = 0.06211 lb ⋅ s 2 /ft Write the equation mass moment of inertia ( I ¯ G ) of the disks using the equation: I ¯ G = 1 2 m r 2 Sketch the velocity components of the system as shown in Figure (1). Refer Figure (1). The radius of each disk is same. Therefore, the angular velocity of the each disk is also same. ω A = ω B = ω Find the equation of angular velocity ( ω ) of the disks A and B using kinematics. v C = ω ( r ) ω = v C r Here, v C is the velocity of carriage C . Find the velocity ( v A ) of disk A using kinematics. v A = v C Consider the principle of impulse and momentum in the carriage C . Syst Momenta 1 + Syst Ext Imp 1y2 = Syst Momenta 2 Sketch the impulse and momentum diagram of the carriage C as shown in Figure 1. Refer Figure (1). Consider the components along x -axis. 0 + P t − F 1 Δ t − F 2 Δ t = m C v C (1) Consider the principle of impulse and momentum in the disk A . Syst Momenta 1 + Syst Ext Imp 1y2 = Syst Momenta 2 Sketch the impulse and momentum diagram of the disk A as shown in Figure (2). Refer Figure (2). Consider sum of moments about C . ( F 1 Δ t ) ( 2 r ) = I G ω A + m A v A r Substitute ω for ω A and m for m A

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

12th Edition

ISBN: 9781260916942

Author: BEER

Publisher: MCG

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Chapter 17.2, Problem 17.73P

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Find the velocity of the carriage 0.5 s after the 0.2-lb force P has been applied.

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Chapter 17.2, Problem 17.72P

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Chapter 17 Solutions

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

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Find the velocity of the carriage 0.5 s after the 0.2-lb force P has been applied.

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Find the velocity of the carriage 0.5 s after the 0.2-lb force P has been applied.

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