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Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.?
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Each arm of a porter governor is 200 mm long. The upper arm is pivoted...
Solution:
Given data:
Length of each arm (l) = 200 mm = 0.2 m
Distance of upper pivot point from the axis (r1) = 30 mm = 0.03 m
Distance of lower pivot point from the axis (r2) = 40 mm = 0.04 m
Mass of each ball (m) = 5 kg
Mass of the sleeve (Ms) = 50 kg
Force of friction (Ff) = Weight equivalent to 30 N
To determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm, we need to first calculate the speeds of the governor at these radii.
Calculation of speed:
The speed of the governor (N) is given by the formula:
N = (g × l × √(r1r2))/√(r1 + r2)
Where g is the acceleration due to gravity, which is taken as 9.81 m/s^2.
At r = 120 mm = 0.12 m:
N1 = (9.81 × 0.2 × √(0.03 × 0.04))/√(0.03 + 0.04)
N1 = 87.03 rad/s
At r = 140 mm = 0.14 m:
N2 = (9.81 × 0.2 × √(0.03 × 0.04))/√(0.03 + 0.04)
N2 = 91.49 rad/s
Calculation of centripetal force:
The centripetal force (Fc) acting on each ball is given by the formula:
Fc = m × r × ω^2
Where m is the mass of each ball, r is the distance of each ball from the axis, and ω is the angular velocity of the governor.
At r = 120 mm = 0.12 m:
Fc1 = 5 × 0.12 × (87.03)^2
Fc1 = 461.46 N
At r = 140 mm = 0.14 m:
Fc2 = 5 × 0.14 × (91.49)^2
Fc2 = 563.58 N
Calculation of forces acting on the sleeve:
The forces acting on the sleeve are the weight of the sleeve (Ws), the weight of the balls (Wb), and the force of friction (Ff).
Ws = Ms × g = 50 × 9.81 = 490.5 N
Wb = 2 × m × g = 2 × 5 × 9.81 = 98.1 N
The total force acting on the sleeve (Ft) is given by the formula:
Ft = Fc + Ws + Wb + Ff
At r = 120 mm = 0.12 m:
Ft1 = 461.46 + 490.5 + 98.1 + 30
Ft1 = 1080.06 N
At r = 140 mm = 0.14 m:
Ft2 = 563.58 + 490.5 + 98.1 + 30
Ft2 = 1182.18 N
Calculation of maximum and minimum speeds:
Given data:
Length of each arm (l) = 200 mm = 0.2 m
Distance of upper pivot point from the axis (r1) = 30 mm = 0.03 m
Distance of lower pivot point from the axis (r2) = 40 mm = 0.04 m
Mass of each ball (m) = 5 kg
Mass of the sleeve (Ms) = 50 kg
Force of friction (Ff) = Weight equivalent to 30 N
To determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm, we need to first calculate the speeds of the governor at these radii.
Calculation of speed:
The speed of the governor (N) is given by the formula:
N = (g × l × √(r1r2))/√(r1 + r2)
Where g is the acceleration due to gravity, which is taken as 9.81 m/s^2.
At r = 120 mm = 0.12 m:
N1 = (9.81 × 0.2 × √(0.03 × 0.04))/√(0.03 + 0.04)
N1 = 87.03 rad/s
At r = 140 mm = 0.14 m:
N2 = (9.81 × 0.2 × √(0.03 × 0.04))/√(0.03 + 0.04)
N2 = 91.49 rad/s
Calculation of centripetal force:
The centripetal force (Fc) acting on each ball is given by the formula:
Fc = m × r × ω^2
Where m is the mass of each ball, r is the distance of each ball from the axis, and ω is the angular velocity of the governor.
At r = 120 mm = 0.12 m:
Fc1 = 5 × 0.12 × (87.03)^2
Fc1 = 461.46 N
At r = 140 mm = 0.14 m:
Fc2 = 5 × 0.14 × (91.49)^2
Fc2 = 563.58 N
Calculation of forces acting on the sleeve:
The forces acting on the sleeve are the weight of the sleeve (Ws), the weight of the balls (Wb), and the force of friction (Ff).
Ws = Ms × g = 50 × 9.81 = 490.5 N
Wb = 2 × m × g = 2 × 5 × 9.81 = 98.1 N
The total force acting on the sleeve (Ft) is given by the formula:
Ft = Fc + Ws + Wb + Ff
At r = 120 mm = 0.12 m:
Ft1 = 461.46 + 490.5 + 98.1 + 30
Ft1 = 1080.06 N
At r = 140 mm = 0.14 m:
Ft2 = 563.58 + 490.5 + 98.1 + 30
Ft2 = 1182.18 N
Calculation of maximum and minimum speeds:
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Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.?
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Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.?.
Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.?.
Solutions for Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.? in English & in Hindi are available as part of our courses for Mechanical Engineering.
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Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.?, a detailed solution for Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.? has been provided alongside types of Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.? theory, EduRev gives you an
ample number of questions to practice Each arm of a porter governor is 200 mm long. The upper arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 30 mm from the axis and the lower arm is pivoted to link at 40 mm from the axis. Each ball has a mass of 5 kg and the mass of the sleeve is 50 kg. The force of friction and the operating gear of the mechanism is equivalent to the weight of 30 N on the sleeve. Determine the speed range of the governor for extreme radii of rotation of 120 mm and 140 mm.? tests, examples and also practice Mechanical Engineering tests.
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