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What will be efficiency of the screw in case of raising the load when coefficient of friction is 0.1553 and tangent of helix angle is 0.0813?
- a)34%
- b)45%
- c)54%
- d)43%
Correct answer is option 'A'. Can you explain this answer?
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What will be efficiency of the screw in case of raising the load when ...
Explanation: Efficiency= tanἀ(1-0.1553 x tan ἀ)/(0.1553+tanἀ).
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What will be efficiency of the screw in case of raising the load when ...
Understanding Efficiency of a Screw Mechanism
To determine the efficiency of a screw in raising a load, we utilize the relationship between the coefficient of friction, the tangent of the helix angle, and the mechanical advantage of the screw.
Key Concepts:
- Coefficient of Friction (μ): This is given as 0.1553. It represents the frictional resistance encountered when the screw rotates.
- Tangent of Helix Angle (tan θ): This value is 0.0813. It is crucial as it indicates the angle at which the screw's helix is inclined.
Efficiency Formula:
The efficiency (η) of a screw can be calculated using the formula:
η = (tan θ) / (tan θ + μ)
Substituting the given values:
- μ = 0.1553
- tan θ = 0.0813
Calculating Efficiency:
1. Calculate the Denominator:
- tan θ + μ = 0.0813 + 0.1553 = 0.2366
2. Calculate Efficiency:
- η = 0.0813 / 0.2366
3. Final Calculation:
- η ≈ 0.3438 or 34.38%
Thus, rounding off gives us approximately 34% as the efficiency of the screw in raising the load.
Conclusion:
The efficiency of the screw mechanism, considering the provided values for the coefficient of friction and the tangent of the helix angle, confirms that the correct answer is indeed option 'A' (34%). Understanding these parameters helps in optimizing the design and operation of screw mechanisms in mechanical systems.
To determine the efficiency of a screw in raising a load, we utilize the relationship between the coefficient of friction, the tangent of the helix angle, and the mechanical advantage of the screw.
Key Concepts:
- Coefficient of Friction (μ): This is given as 0.1553. It represents the frictional resistance encountered when the screw rotates.
- Tangent of Helix Angle (tan θ): This value is 0.0813. It is crucial as it indicates the angle at which the screw's helix is inclined.
Efficiency Formula:
The efficiency (η) of a screw can be calculated using the formula:
η = (tan θ) / (tan θ + μ)
Substituting the given values:
- μ = 0.1553
- tan θ = 0.0813
Calculating Efficiency:
1. Calculate the Denominator:
- tan θ + μ = 0.0813 + 0.1553 = 0.2366
2. Calculate Efficiency:
- η = 0.0813 / 0.2366
3. Final Calculation:
- η ≈ 0.3438 or 34.38%
Thus, rounding off gives us approximately 34% as the efficiency of the screw in raising the load.
Conclusion:
The efficiency of the screw mechanism, considering the provided values for the coefficient of friction and the tangent of the helix angle, confirms that the correct answer is indeed option 'A' (34%). Understanding these parameters helps in optimizing the design and operation of screw mechanisms in mechanical systems.
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What will be efficiency of the screw in case of raising the load when coefficient of friction is 0.1553 and tangent of helix angle is 0.0813?a)34%b)45%c)54%d)43%Correct answer is option 'A'. Can you explain this answer?
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