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The ratio of tension on the tight side to that on the slack side in a flat belt drive is
- a)Proportional to the product of coefficient of friction and lap angle
- b)An exponential function of the product of coefficient of friction and lap angle.
- c)Proportional to the lap angle
- d)Proportional to the coefficient of friction
Correct answer is option 'B'. Can you explain this answer?
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The ratio of tension on the tight side to that on the slack side in a flat belt drive is an important parameter to determine the power transmission capability of the belt drive. This ratio is given by the following formula:
Tight side tension / Slack side tension = e^(μθ)
Where,
μ = Coefficient of friction between the belt and pulley
θ = Lap angle of the belt
Explanation:
Exponential function:
The above formula shows that the ratio of tensions in a flat belt drive is an exponential function of the product of coefficient of friction and lap angle. This means that as either μ or θ increases, the ratio of tensions increases exponentially.
Effect of coefficient of friction:
The coefficient of friction between the belt and pulley is a measure of the frictional resistance offered by the belt to the pulley. A higher coefficient of friction means that the belt will offer more resistance to slipping on the pulley. Therefore, a higher value of μ will result in a higher ratio of tensions.
Effect of lap angle:
The lap angle of the belt is the angle formed between the two sections of the belt that are in contact with the pulley. A larger lap angle means that the belt will have more surface area in contact with the pulley, resulting in a higher frictional force. Therefore, a higher value of θ will result in a higher ratio of tensions.
Limitations of the formula:
The above formula assumes that the belt is perfectly flexible and inextensible, and that the pulleys are perfectly cylindrical. However, in real-life situations, these assumptions may not hold true. Therefore, the actual ratio of tensions may vary from the theoretical value predicted by the formula.
Conclusion:
In conclusion, the ratio of tension on the tight side to that on the slack side in a flat belt drive is an exponential function of the product of coefficient of friction and lap angle. This formula is useful in determining the power transmission capacity of the belt drive, but it should be used with caution and the limitations should be kept in mind.
Tight side tension / Slack side tension = e^(μθ)
Where,
μ = Coefficient of friction between the belt and pulley
θ = Lap angle of the belt
Explanation:
Exponential function:
The above formula shows that the ratio of tensions in a flat belt drive is an exponential function of the product of coefficient of friction and lap angle. This means that as either μ or θ increases, the ratio of tensions increases exponentially.
Effect of coefficient of friction:
The coefficient of friction between the belt and pulley is a measure of the frictional resistance offered by the belt to the pulley. A higher coefficient of friction means that the belt will offer more resistance to slipping on the pulley. Therefore, a higher value of μ will result in a higher ratio of tensions.
Effect of lap angle:
The lap angle of the belt is the angle formed between the two sections of the belt that are in contact with the pulley. A larger lap angle means that the belt will have more surface area in contact with the pulley, resulting in a higher frictional force. Therefore, a higher value of θ will result in a higher ratio of tensions.
Limitations of the formula:
The above formula assumes that the belt is perfectly flexible and inextensible, and that the pulleys are perfectly cylindrical. However, in real-life situations, these assumptions may not hold true. Therefore, the actual ratio of tensions may vary from the theoretical value predicted by the formula.
Conclusion:
In conclusion, the ratio of tension on the tight side to that on the slack side in a flat belt drive is an exponential function of the product of coefficient of friction and lap angle. This formula is useful in determining the power transmission capacity of the belt drive, but it should be used with caution and the limitations should be kept in mind.
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The ratio of tension on the tight side to that on the slack side in a flat belt drive isa)Proportional to the product of coefficient of friction and lap angleb)An exponential function of the product of coefficient of friction and lap angle.c)Proportional to the lap angled)Proportional to the coefficient of frictionCorrect answer is option 'B'. Can you explain this answer?
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