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A system of beam supports a motor of mass 1000 kg including unbalance mass. The resonance occurs at a speed of 2400 rpm. If the amplitude of vibration at the motor’s operating speed of 1200 rpm is 0.1 mm. The magnitude of the unbalance mass (in kg) located at 8 cm radius is (damping factor is 0.15)
- a)3.5
- b)4
Correct answer is between '3.5,4'. Can you explain this answer?
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A system of beam supports a motor of mass 1000 kg including unbalance...
The steady state amplitude (X) in the rotating unbalance machine is given as
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Where, X = 0.1mm = 0.0001m
m0 = unbalance mass in kg m = 1000kg
e = 8cm = 0.08m
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A system of beam supports a motor of mass 1000 kg including unbalance...
Resonance occurs when the natural frequency of a system matches the excitation frequency, resulting in a significant increase in amplitude. In this case, the resonance occurs at a speed of 2400 rpm, which is twice the operating speed of the motor at 1200 rpm.
To find the magnitude of the unbalance mass, we can use the formula for the amplitude of vibration in a rotating system:
Amplitude = (unbalance mass × radius) / (motor mass × damping factor)
Given that the amplitude at the operating speed of 1200 rpm is 0.1 mm, we can substitute the values into the formula and solve for the unbalance mass:
0.1 mm = (unbalance mass × 8 cm) / (1000 kg × 0.15)
Converting the units to meters and solving the equation gives us:
0.1 × 10^-3 m = (unbalance mass × 0.08 m) / (1000 kg × 0.15)
Simplifying the equation further:
0.1 × 10^-3 m × 1000 kg × 0.15 = unbalance mass × 0.08 m
0.015 kg = unbalance mass × 0.08 m
unbalance mass = 0.015 kg / 0.08 m
unbalance mass ≈ 0.1875 kg
Therefore, the magnitude of the unbalance mass located at an 8 cm radius is approximately 0.1875 kg.
Since the correct answer is between 3.5 and 4 kg, it seems that there may be an error in the calculations or the given values. Please double-check the given information and review the calculations to ensure accuracy.
To find the magnitude of the unbalance mass, we can use the formula for the amplitude of vibration in a rotating system:
Amplitude = (unbalance mass × radius) / (motor mass × damping factor)
Given that the amplitude at the operating speed of 1200 rpm is 0.1 mm, we can substitute the values into the formula and solve for the unbalance mass:
0.1 mm = (unbalance mass × 8 cm) / (1000 kg × 0.15)
Converting the units to meters and solving the equation gives us:
0.1 × 10^-3 m = (unbalance mass × 0.08 m) / (1000 kg × 0.15)
Simplifying the equation further:
0.1 × 10^-3 m × 1000 kg × 0.15 = unbalance mass × 0.08 m
0.015 kg = unbalance mass × 0.08 m
unbalance mass = 0.015 kg / 0.08 m
unbalance mass ≈ 0.1875 kg
Therefore, the magnitude of the unbalance mass located at an 8 cm radius is approximately 0.1875 kg.
Since the correct answer is between 3.5 and 4 kg, it seems that there may be an error in the calculations or the given values. Please double-check the given information and review the calculations to ensure accuracy.
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A system of beam supports a motor of mass 1000 kg including unbalance mass. The resonance occurs at a speed of 2400 rpm. If the amplitude of vibration at the motor’s operating speed of 1200 rpm is 0.1 mm. The magnitude of the unbalance mass (in kg) located at 8 cm radius is (damping factor is 0.15)a)3.5b)4Correct answer is between '3.5,4'. Can you explain this answer?
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A system of beam supports a motor of mass 1000 kg including unbalance mass. The resonance occurs at a speed of 2400 rpm. If the amplitude of vibration at the motor’s operating speed of 1200 rpm is 0.1 mm. The magnitude of the unbalance mass (in kg) located at 8 cm radius is (damping factor is 0.15)a)3.5b)4Correct answer is between '3.5,4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A system of beam supports a motor of mass 1000 kg including unbalance mass. The resonance occurs at a speed of 2400 rpm. If the amplitude of vibration at the motor’s operating speed of 1200 rpm is 0.1 mm. The magnitude of the unbalance mass (in kg) located at 8 cm radius is (damping factor is 0.15)a)3.5b)4Correct answer is between '3.5,4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system of beam supports a motor of mass 1000 kg including unbalance mass. The resonance occurs at a speed of 2400 rpm. If the amplitude of vibration at the motor’s operating speed of 1200 rpm is 0.1 mm. The magnitude of the unbalance mass (in kg) located at 8 cm radius is (damping factor is 0.15)a)3.5b)4Correct answer is between '3.5,4'. Can you explain this answer?.
A system of beam supports a motor of mass 1000 kg including unbalance mass. The resonance occurs at a speed of 2400 rpm. If the amplitude of vibration at the motor’s operating speed of 1200 rpm is 0.1 mm. The magnitude of the unbalance mass (in kg) located at 8 cm radius is (damping factor is 0.15)a)3.5b)4Correct answer is between '3.5,4'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about A system of beam supports a motor of mass 1000 kg including unbalance mass. The resonance occurs at a speed of 2400 rpm. If the amplitude of vibration at the motor’s operating speed of 1200 rpm is 0.1 mm. The magnitude of the unbalance mass (in kg) located at 8 cm radius is (damping factor is 0.15)a)3.5b)4Correct answer is between '3.5,4'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A system of beam supports a motor of mass 1000 kg including unbalance mass. The resonance occurs at a speed of 2400 rpm. If the amplitude of vibration at the motor’s operating speed of 1200 rpm is 0.1 mm. The magnitude of the unbalance mass (in kg) located at 8 cm radius is (damping factor is 0.15)a)3.5b)4Correct answer is between '3.5,4'. Can you explain this answer?.
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