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

11th Edition

ISBN: 9780073398242

Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self

Publisher: McGraw-Hill Education

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 17.2, Problem 17.85P

To determine

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 17.2, Problem 17.84P

Chapter 17.2, Problem 17.86P

Students have asked these similar questions

5. An 80 kg gymnast dismounts from a high bar. He starts the dismount at full extension, then tucks to complete a number of revolutions before landing. His moment of inertia when fully extended can be approximated as a rod of length 1.8 m and when in the tuck a rod of half that length. If his rotation rate at full extension is 1.0 rev/s and he enters the tuck when his center of mass is at 3.0 m height moving horizontally to the floor, how many revolutions can he execute if he comes out of the tuck at 1.8 m height? High bar 1.8 m 3 m ANS. Moment of inertia at full extension, I = 21.6 kg-m^2 Moment of inertia at the tuck I' = 5.4 kg-m^2 Angular velocity at the tuck = 4 rev/sec Time interval in the tuck = 0.5 sec i.e. In 0.5 s, he will be able to execute two revolutions at 4.0 rev/s.

The mass of gear A is 25 kg and its centroidal radius of gyration is 105 mm. The mass of gear B is 13 kg and its centroidal radius of gyration is 85 mm. Calculate the angular acceleration of gear B when a torque of 16 N·m is applied to the shaft of gear A. Neglect friction. The angular acceleration is positive if counterclockwise, negative if clockwise..

The arms of a Porter governor are 225 mm long. The upper and lower arms are pivoted to links of 35 mm and 45 mm respectively from the axis of rotation. Each ball has a mass of 4 kg and the sleeve mass is 35 kg. The force of friction on the sleeve of the mechanism is 44 N. Determine the range of speed of the governor for extreme radii of rotation of 115 mm and 145 mm.

Chapter 17 Solutions

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

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.

Concept explainers

Videos

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.

Want to see the full answer?

Chapter 17 Solutions