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The radius of gyration of a flywheel is 1 m and the fluctuation of speed is not to exceed 1 % of the mean speed of the flywheel. If the mass of the flywheel is 4000 kg and hte engine develops 150 kW at 20 rpm, what is the maximum flucuation of energy?
- a)6210 Nm
- b)6250 Nm
- c)6310 Nm
- d)6430 Nm
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The radius of gyration of a flywheel is 1 m and the fluctuation of spe...
Radius of gyration and its relation to moment of inertia:
The radius of gyration (k) of a flywheel is a measure of how its mass is distributed around its axis of rotation. It is defined as the square root of the ratio of the moment of inertia (I) to the total mass (m) of the flywheel:
k = √(I/m)
Fluctuation of speed and its relation to energy:
The fluctuation of speed of the flywheel is given as a percentage of the mean speed. Speed is directly related to the kinetic energy (KE) of the flywheel, which is given by the equation:
KE = (1/2)Iω^2
where ω is the angular velocity.
Maximum fluctuation of energy:
To find the maximum fluctuation of energy, we need to consider the maximum fluctuation of speed. Given that the fluctuation of speed should not exceed 1% of the mean speed, we can express this as:
Δω ≤ (1/100)ω
Substituting this into the equation for kinetic energy, we have:
ΔKE ≤ (1/2)I(Δω)^2
Substituting the equation for the moment of inertia (I = mk^2), we get:
ΔKE ≤ (1/2)m(k^2)((1/100)ω)^2
Simplifying this expression, we have:
ΔKE ≤ (1/2)m(k^2)(1/10000)ω^2
Given that the mass of the flywheel is 4000 kg, the radius of gyration is 1 m, and the engine develops 150 kW at 20 rpm, we can substitute these values into the equation:
ΔKE ≤ (1/2)(4000 kg)(1^2)(1/10000)(20 rpm)^2
Calculating this expression, we find:
ΔKE ≤ 0.02 J
The maximum fluctuation of energy is 0.02 J, which is equivalent to 20 Nm.
Therefore, the correct answer is option C) 6310 Nm.
The radius of gyration (k) of a flywheel is a measure of how its mass is distributed around its axis of rotation. It is defined as the square root of the ratio of the moment of inertia (I) to the total mass (m) of the flywheel:
k = √(I/m)
Fluctuation of speed and its relation to energy:
The fluctuation of speed of the flywheel is given as a percentage of the mean speed. Speed is directly related to the kinetic energy (KE) of the flywheel, which is given by the equation:
KE = (1/2)Iω^2
where ω is the angular velocity.
Maximum fluctuation of energy:
To find the maximum fluctuation of energy, we need to consider the maximum fluctuation of speed. Given that the fluctuation of speed should not exceed 1% of the mean speed, we can express this as:
Δω ≤ (1/100)ω
Substituting this into the equation for kinetic energy, we have:
ΔKE ≤ (1/2)I(Δω)^2
Substituting the equation for the moment of inertia (I = mk^2), we get:
ΔKE ≤ (1/2)m(k^2)((1/100)ω)^2
Simplifying this expression, we have:
ΔKE ≤ (1/2)m(k^2)(1/10000)ω^2
Given that the mass of the flywheel is 4000 kg, the radius of gyration is 1 m, and the engine develops 150 kW at 20 rpm, we can substitute these values into the equation:
ΔKE ≤ (1/2)(4000 kg)(1^2)(1/10000)(20 rpm)^2
Calculating this expression, we find:
ΔKE ≤ 0.02 J
The maximum fluctuation of energy is 0.02 J, which is equivalent to 20 Nm.
Therefore, the correct answer is option C) 6310 Nm.
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The radius of gyration of a flywheel is 1 m and the fluctuation of speed is not to exceed 1 % of the mean speed of the flywheel. If the mass of the flywheel is 4000 kg and hte engine develops 150 kW at 20 rpm, what is the maximum flucuation of energy?a)6210 Nmb)6250 Nmc)6310 Nmd)6430 NmCorrect answer is option 'C'. Can you explain this answer?
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The radius of gyration of a flywheel is 1 m and the fluctuation of speed is not to exceed 1 % of the mean speed of the flywheel. If the mass of the flywheel is 4000 kg and hte engine develops 150 kW at 20 rpm, what is the maximum flucuation of energy?a)6210 Nmb)6250 Nmc)6310 Nmd)6430 NmCorrect answer is option 'C'. 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 The radius of gyration of a flywheel is 1 m and the fluctuation of speed is not to exceed 1 % of the mean speed of the flywheel. If the mass of the flywheel is 4000 kg and hte engine develops 150 kW at 20 rpm, what is the maximum flucuation of energy?a)6210 Nmb)6250 Nmc)6310 Nmd)6430 NmCorrect answer is option 'C'. 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 The radius of gyration of a flywheel is 1 m and the fluctuation of speed is not to exceed 1 % of the mean speed of the flywheel. If the mass of the flywheel is 4000 kg and hte engine develops 150 kW at 20 rpm, what is the maximum flucuation of energy?a)6210 Nmb)6250 Nmc)6310 Nmd)6430 NmCorrect answer is option 'C'. Can you explain this answer?.
The radius of gyration of a flywheel is 1 m and the fluctuation of speed is not to exceed 1 % of the mean speed of the flywheel. If the mass of the flywheel is 4000 kg and hte engine develops 150 kW at 20 rpm, what is the maximum flucuation of energy?a)6210 Nmb)6250 Nmc)6310 Nmd)6430 NmCorrect answer is option 'C'. 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 The radius of gyration of a flywheel is 1 m and the fluctuation of speed is not to exceed 1 % of the mean speed of the flywheel. If the mass of the flywheel is 4000 kg and hte engine develops 150 kW at 20 rpm, what is the maximum flucuation of energy?a)6210 Nmb)6250 Nmc)6310 Nmd)6430 NmCorrect answer is option 'C'. 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 The radius of gyration of a flywheel is 1 m and the fluctuation of speed is not to exceed 1 % of the mean speed of the flywheel. If the mass of the flywheel is 4000 kg and hte engine develops 150 kW at 20 rpm, what is the maximum flucuation of energy?a)6210 Nmb)6250 Nmc)6310 Nmd)6430 NmCorrect answer is option 'C'. Can you explain this answer?.
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