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A circular disc mounted on a shaft carries three attached masses of 4kg, 3kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured counter clockwise from the reference line along the x - axis. The amount of the counter mass at a radial distance of 70mm required for the static balance will be ________ (in kg)
Correct answer is between '3.85,4.2'. Can you explain this answer?
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A circular disc mounted on a shaft carries three attached masses of 4k...
°, 135° and 300° respectively. The disc rotates at a constant speed of 1200 rpm. Find the magnitude and direction of the resultant centrifugal force acting on the disc.
We can start by finding the centrifugal force acting on each of the masses, using the formula:
Fc = mrω^2
where Fc is the centrifugal force, m is the mass, r is the radial distance, and ω is the angular velocity in radians per second.
Converting the rotational speed of the disc from rpm to radians per second:
ω = 2π × 1200/60 = 125.66 rad/s
Centrifugal force acting on the 4kg mass:
Fc1 = 4 × 0.075 × (125.66)^2 = 471.5 N
Centrifugal force acting on the 3kg mass:
Fc2 = 3 × 0.085 × (125.66)^2 = 484.8 N
Centrifugal force acting on the 2.5kg mass:
Fc3 = 2.5 × 0.050 × (125.66)^2 = 261.6 N
Next, we can find the x and y components of each centrifugal force, using the angles given:
Fx1 = Fc1 cos 45° = 333.8 N
Fy1 = Fc1 sin 45° = 333.8 N
Fx2 = Fc2 cos 135° = -342.0 N
Fy2 = Fc2 sin 135° = 342.0 N
Fx3 = Fc3 cos 300° = -130.8 N
Fy3 = Fc3 sin 300° = -225.4 N
Note that the negative sign for Fx2 and Fx3 indicates that these forces act in the opposite direction to the positive x-axis.
To find the resultant x and y components of the centrifugal forces, we can add up the x and y components separately:
Fx = Fx1 + Fx2 + Fx3 = -139.0 N
Fy = Fy1 + Fy2 + Fy3 = 450.4 N
The magnitude of the resultant centrifugal force is given by:
Fres = √(Fx^2 + Fy^2) = 472.2 N
The direction of the resultant centrifugal force can be found using the inverse tangent function:
θ = tan^-1(Fy/Fx) = tan^-1(-3.24) = -71.6°
Note that the negative sign for θ indicates that the direction of the resultant force is in the opposite direction to the positive x-axis.
Therefore, the magnitude of the resultant centrifugal force acting on the disc is 472.2 N, and its direction is 71.6° to the left of the positive x-axis.
We can start by finding the centrifugal force acting on each of the masses, using the formula:
Fc = mrω^2
where Fc is the centrifugal force, m is the mass, r is the radial distance, and ω is the angular velocity in radians per second.
Converting the rotational speed of the disc from rpm to radians per second:
ω = 2π × 1200/60 = 125.66 rad/s
Centrifugal force acting on the 4kg mass:
Fc1 = 4 × 0.075 × (125.66)^2 = 471.5 N
Centrifugal force acting on the 3kg mass:
Fc2 = 3 × 0.085 × (125.66)^2 = 484.8 N
Centrifugal force acting on the 2.5kg mass:
Fc3 = 2.5 × 0.050 × (125.66)^2 = 261.6 N
Next, we can find the x and y components of each centrifugal force, using the angles given:
Fx1 = Fc1 cos 45° = 333.8 N
Fy1 = Fc1 sin 45° = 333.8 N
Fx2 = Fc2 cos 135° = -342.0 N
Fy2 = Fc2 sin 135° = 342.0 N
Fx3 = Fc3 cos 300° = -130.8 N
Fy3 = Fc3 sin 300° = -225.4 N
Note that the negative sign for Fx2 and Fx3 indicates that these forces act in the opposite direction to the positive x-axis.
To find the resultant x and y components of the centrifugal forces, we can add up the x and y components separately:
Fx = Fx1 + Fx2 + Fx3 = -139.0 N
Fy = Fy1 + Fy2 + Fy3 = 450.4 N
The magnitude of the resultant centrifugal force is given by:
Fres = √(Fx^2 + Fy^2) = 472.2 N
The direction of the resultant centrifugal force can be found using the inverse tangent function:
θ = tan^-1(Fy/Fx) = tan^-1(-3.24) = -71.6°
Note that the negative sign for θ indicates that the direction of the resultant force is in the opposite direction to the positive x-axis.
Therefore, the magnitude of the resultant centrifugal force acting on the disc is 472.2 N, and its direction is 71.6° to the left of the positive x-axis.
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A circular disc mounted on a shaft carries three attached masses of 4kg, 3kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured counter clockwise from the reference line along the x - axis. The amount of the counter mass at a radial distance of 70mm required for the static balance will be ________ (in kg)Correct answer is between '3.85,4.2'. Can you explain this answer?
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A circular disc mounted on a shaft carries three attached masses of 4kg, 3kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured counter clockwise from the reference line along the x - axis. The amount of the counter mass at a radial distance of 70mm required for the static balance will be ________ (in kg)Correct answer is between '3.85,4.2'. Can you explain this answer? 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 A circular disc mounted on a shaft carries three attached masses of 4kg, 3kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured counter clockwise from the reference line along the x - axis. The amount of the counter mass at a radial distance of 70mm required for the static balance will be ________ (in kg)Correct answer is between '3.85,4.2'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular disc mounted on a shaft carries three attached masses of 4kg, 3kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured counter clockwise from the reference line along the x - axis. The amount of the counter mass at a radial distance of 70mm required for the static balance will be ________ (in kg)Correct answer is between '3.85,4.2'. Can you explain this answer?.
A circular disc mounted on a shaft carries three attached masses of 4kg, 3kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured counter clockwise from the reference line along the x - axis. The amount of the counter mass at a radial distance of 70mm required for the static balance will be ________ (in kg)Correct answer is between '3.85,4.2'. Can you explain this answer? 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 A circular disc mounted on a shaft carries three attached masses of 4kg, 3kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured counter clockwise from the reference line along the x - axis. The amount of the counter mass at a radial distance of 70mm required for the static balance will be ________ (in kg)Correct answer is between '3.85,4.2'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A circular disc mounted on a shaft carries three attached masses of 4kg, 3kg and 2.5 kg at radial distance of 75 mm, 85 mm and 50mm and at the angular positions of 45°, 135° and 240° respectively. The angular positions are measured counter clockwise from the reference line along the x - axis. The amount of the counter mass at a radial distance of 70mm required for the static balance will be ________ (in kg)Correct answer is between '3.85,4.2'. Can you explain this answer?.
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