Explanation Given information: The initial angular velocity ( ω 1 ) of the main blades is 180 rpm. The final angular velocity ( ω 2 ) of the main blades is 240 rpm. The centroidal moment of inertia ( I C ) of the cab is. 650 lb ⋅ ft ⋅ s 2 . The length ( L ) of the blade is 14 ft . The weight ( W C ) of the cab is 1,250 lb. The weight ( W B ) of the cab is 55 lb. The radius of the cab ( r ) about y -axis is 16 ft. Calculation: Find the mass ( m ) of the system using the equation: m = W C g + 4 W B g Substitute 1,250 lb for W , 32.2 ft/s 2 for g , and 55 lb for W B . m = 1 , 250 32.2 + 4 55 32.2 = 45.65217 lb ⋅ s 2 /ft Find the moment of inertia ( I B ) of the blades using the equation: I B = 4 ( 1 3 m L 2 ) Substitute 1.708075 lb ⋅ s 2 /ft for m and 14 ft for L . I B = 4 ( 1 3 1.708075 × 14 2 ) = 446.38 lb ⋅ ft ⋅ s 2 Assume the initial ( Ω 1 ) and final ( Ω 1 ) angular velocity of the cab is zero. Therefore, the cab does not rotate. Consider the principle of impulse and momentum. Syst Momenta 1 + Syst Ext Imp 1y2 = Syst Momenta 2 I B ( ω 1 + Ω 1 ) + I C Ω 1 + F r t = I B ( ω 2 + Ω 2 ) + I C Ω 2 Substitute 0 for Ω 1 and 0 for Ω 2

Vector Mechanics for Engineers: Statics and Dynamics

12th Edition

ISBN: 9781259977251

Author: BEER

Publisher: MCG

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Chapter 17.2, Problem 17.85P

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Find the final horizontal velocity of the cab when the speed of the main blades is changed from 180 to 240 rpm and also find the force exerted by the tail propeller if the change in speed takes place uniformly in 12 sec.

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Chapter 17.2, Problem 17.84P

Chapter 17.2, Problem 17.86P

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Find the final horizontal velocity of the cab when the speed of the main blades is changed from 180 to 240 rpm and also find the force exerted by the tail propeller if the change in speed takes place uniformly in 12 sec.

Solution Summary: The author calculates the final horizontal velocity and force exerted by the tail propeller if the change in speed takes place uniformly in 12 sec.

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Find the final horizontal velocity of the cab when the speed of the main blades is changed from 180 to 240 rpm and also find the force exerted by the tail propeller if the change in speed takes place uniformly in 12 sec.

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Chapter 17 Solutions