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A cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)
Correct answer is '2.1'. Can you explain this answer?
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Most Upvoted Answer
A cast iron flywheel is required to absorb 25000 N - m of energy as s...
Given:
- Energy to be absorbed: 25000 N-m
- Initial speed: 120 rpm
- Final speed: 125 rpm
- Diameter of the flywheel: 8 times its thickness
- Density of cast iron: 7200 kg/m³
To find:
The diameter of the flywheel
Solution:
Step 1: Calculate the change in kinetic energy:
The change in kinetic energy (ΔKE) can be calculated using the formula:
ΔKE = 0.5 * I * (ωf² - ωi²)
Where:
I = moment of inertia of the flywheel
ωi = initial angular velocity (in rad/s)
ωf = final angular velocity (in rad/s)
Given:
Initial speed = 120 rpm
Final speed = 125 rpm
Converting the speeds to rad/s:
ωi = 120 * 2π / 60
ωf = 125 * 2π / 60
ΔKE = 0.5 * I * ((125 * 2π / 60)² - (120 * 2π / 60)²)
Step 2: Calculate the moment of inertia:
The moment of inertia (I) of a solid disc can be calculated using the formula:
I = 0.5 * m * r²
Where:
m = mass of the flywheel
r = radius of the flywheel
Step 3: Calculate the mass of the flywheel:
The mass of the flywheel (m) can be calculated using the formula:
m = V * ρ
Where:
V = volume of the flywheel
ρ = density of cast iron
Step 4: Calculate the volume of the flywheel:
The volume of the flywheel (V) can be calculated using the formula:
V = π * r² * h
Where:
r = radius of the flywheel
h = thickness of the flywheel
Step 5: Find the radius of the flywheel:
Given:
Diameter of the flywheel = 8 times its thickness
Let the thickness of the flywheel be x.
Therefore, the diameter of the flywheel = 8x
The radius of the flywheel (r) can be calculated using the formula:
r = (8x) / 2 = 4x
Step 6: Solve the equations:
Substituting the values calculated in steps 2, 3, 4, and 5 into the equation from step 1, we can solve for x:
ΔKE = 0.5 * (0.5 * (V * ρ) * (4x)²) * ((125 * 2π / 60)² - (120 * 2π / 60)²)
Simplifying the equation, we get:
ΔKE = 0.5 * (0.5 * (π * x² * 7200) * (4x)²) * ((125 * 2π / 60)² - (120 * 2π / 60)²)
Since the density of cast iron and the change in kinetic energy are known, we can solve for x:
25000 =
- Energy to be absorbed: 25000 N-m
- Initial speed: 120 rpm
- Final speed: 125 rpm
- Diameter of the flywheel: 8 times its thickness
- Density of cast iron: 7200 kg/m³
To find:
The diameter of the flywheel
Solution:
Step 1: Calculate the change in kinetic energy:
The change in kinetic energy (ΔKE) can be calculated using the formula:
ΔKE = 0.5 * I * (ωf² - ωi²)
Where:
I = moment of inertia of the flywheel
ωi = initial angular velocity (in rad/s)
ωf = final angular velocity (in rad/s)
Given:
Initial speed = 120 rpm
Final speed = 125 rpm
Converting the speeds to rad/s:
ωi = 120 * 2π / 60
ωf = 125 * 2π / 60
ΔKE = 0.5 * I * ((125 * 2π / 60)² - (120 * 2π / 60)²)
Step 2: Calculate the moment of inertia:
The moment of inertia (I) of a solid disc can be calculated using the formula:
I = 0.5 * m * r²
Where:
m = mass of the flywheel
r = radius of the flywheel
Step 3: Calculate the mass of the flywheel:
The mass of the flywheel (m) can be calculated using the formula:
m = V * ρ
Where:
V = volume of the flywheel
ρ = density of cast iron
Step 4: Calculate the volume of the flywheel:
The volume of the flywheel (V) can be calculated using the formula:
V = π * r² * h
Where:
r = radius of the flywheel
h = thickness of the flywheel
Step 5: Find the radius of the flywheel:
Given:
Diameter of the flywheel = 8 times its thickness
Let the thickness of the flywheel be x.
Therefore, the diameter of the flywheel = 8x
The radius of the flywheel (r) can be calculated using the formula:
r = (8x) / 2 = 4x
Step 6: Solve the equations:
Substituting the values calculated in steps 2, 3, 4, and 5 into the equation from step 1, we can solve for x:
ΔKE = 0.5 * (0.5 * (V * ρ) * (4x)²) * ((125 * 2π / 60)² - (120 * 2π / 60)²)
Simplifying the equation, we get:
ΔKE = 0.5 * (0.5 * (π * x² * 7200) * (4x)²) * ((125 * 2π / 60)² - (120 * 2π / 60)²)
Since the density of cast iron and the change in kinetic energy are known, we can solve for x:
25000 =
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Community Answer
A cast iron flywheel is required to absorb 25000 N - m of energy as s...
We have ρ = 7200 kg/m3, D = 8t, ∆E = 25000 N - m, 125 rpm and N2 = 120 rpm.
Fluctuation of energy ∆E = 1/2I(ω12 - ω22)
25000 = 1/2 x I[(13.08)2 - (12.56)2]
So, moment of inertia, I = 3750.94 kg - m2
Also, for solid disc I = mD2/8
and m = ρ x v (i.e. Density x Volume)
= ρ x (area x thickness)
Therefore, I = m x D2/8 = ρ x π/32 x D3 x D2/8
= π/256 x ρ x D5
Or 3750.94 = π/256 x 7200 x D5
Or D5 = 42.472
Hence, diameter of flywheel, D = 2.1 m
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A cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. Can you explain this answer?
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A cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. 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 cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. 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 cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. Can you explain this answer?.
A cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. 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 cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. 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 cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. Can you explain this answer?.
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A cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. Can you explain this answer?, a detailed solution for A cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. Can you explain this answer? has been provided alongside types of A cast iron flywheel is required to absorb 25000 N - m of energy as speed is increased from 120 to 125 rpm. If the flywheel is to be solid disc having a diameter 8 times its thickness and the density of cast iron is 7200 kg/m3, the diameter (in m) of the flywheel is ______. (Answer up to one decimal place)Correct answer is '2.1'. Can you explain this answer? theory, EduRev gives you an
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