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A flywheel with a mass of 4 kg has a radius of gyration of 1 m. Find the increase in energy stored in the flywheel when its speed increases from 40 rad/s to 50 rad/s
- a)3600 J
- b)1800 J
- c)900 J
- d)7200 J
Correct answer is option 'B'. Can you explain this answer?
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A flywheel with a mass of 4 kg has a radius of gyration of 1 m. Find t...
Additional energy stored =
= 1800 J
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A flywheel with a mass of 4 kg has a radius of gyration of 1 m. Find t...
Given data:
Mass of the flywheel (m) = 4 kg
Radius of gyration (k) = 1 m
Initial speed (ω₁) = 40 rad/s
Final speed (ω₂) = 50 rad/s
Formula:
The kinetic energy of a rotating body can be calculated using the formula:
KE = 0.5 * I * ω²
where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
Calculating the initial and final kinetic energy:
The moment of inertia (I) of a flywheel can be calculated using the formula:
I = mk²
Initial kinetic energy (KE₁) = 0.5 * I * ω₁²
Final kinetic energy (KE₂) = 0.5 * I * ω₂²
Calculating the increase in energy stored:
The increase in energy stored in the flywheel can be calculated by subtracting the initial kinetic energy from the final kinetic energy:
ΔKE = KE₂ - KE₁
Solution:
First, let's calculate the moment of inertia (I) of the flywheel:
I = mk²
= 4 kg * (1 m)²
= 4 kg * 1 m²
= 4 kg m²
Next, let's calculate the initial kinetic energy (KE₁):
KE₁ = 0.5 * I * ω₁²
= 0.5 * 4 kg m² * (40 rad/s)²
= 0.5 * 4 kg m² * 1600 rad²/s²
= 3200 J
Now, let's calculate the final kinetic energy (KE₂):
KE₂ = 0.5 * I * ω₂²
= 0.5 * 4 kg m² * (50 rad/s)²
= 0.5 * 4 kg m² * 2500 rad²/s²
= 5000 J
Finally, let's calculate the increase in energy stored (ΔKE):
ΔKE = KE₂ - KE₁
= 5000 J - 3200 J
= 1800 J
Therefore, the increase in energy stored in the flywheel when its speed increases from 40 rad/s to 50 rad/s is 1800 J. Hence, option B is the correct answer.
Mass of the flywheel (m) = 4 kg
Radius of gyration (k) = 1 m
Initial speed (ω₁) = 40 rad/s
Final speed (ω₂) = 50 rad/s
Formula:
The kinetic energy of a rotating body can be calculated using the formula:
KE = 0.5 * I * ω²
where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.
Calculating the initial and final kinetic energy:
The moment of inertia (I) of a flywheel can be calculated using the formula:
I = mk²
Initial kinetic energy (KE₁) = 0.5 * I * ω₁²
Final kinetic energy (KE₂) = 0.5 * I * ω₂²
Calculating the increase in energy stored:
The increase in energy stored in the flywheel can be calculated by subtracting the initial kinetic energy from the final kinetic energy:
ΔKE = KE₂ - KE₁
Solution:
First, let's calculate the moment of inertia (I) of the flywheel:
I = mk²
= 4 kg * (1 m)²
= 4 kg * 1 m²
= 4 kg m²
Next, let's calculate the initial kinetic energy (KE₁):
KE₁ = 0.5 * I * ω₁²
= 0.5 * 4 kg m² * (40 rad/s)²
= 0.5 * 4 kg m² * 1600 rad²/s²
= 3200 J
Now, let's calculate the final kinetic energy (KE₂):
KE₂ = 0.5 * I * ω₂²
= 0.5 * 4 kg m² * (50 rad/s)²
= 0.5 * 4 kg m² * 2500 rad²/s²
= 5000 J
Finally, let's calculate the increase in energy stored (ΔKE):
ΔKE = KE₂ - KE₁
= 5000 J - 3200 J
= 1800 J
Therefore, the increase in energy stored in the flywheel when its speed increases from 40 rad/s to 50 rad/s is 1800 J. Hence, option B is the correct answer.
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A flywheel with a mass of 4 kg has a radius of gyration of 1 m. Find the increase in energy stored in the flywheel when its speed increases from 40 rad/s to 50 rad/sa)3600 Jb)1800 Jc)900 Jd)7200 JCorrect answer is option 'B'. Can you explain this answer?
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