Why is Rope Distance Not Part of the Equation?

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In summary, the question is about the difference in the use of distance in pump problems and rope problems. While pump problems involve the distance traveled by water, rope problems do not have a specific representation for the distance traveled by the rope. This is because the distance in rope problems is relative to the point where the rope is hanging, whereas in pump problems it is relative to the starting point of the water.
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EV33
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This is not really a homework problem but just a question.

How come while doing pump problems distance is part of the equation but rope problems distance is not...


For example your rope integral might look like integral from zero to fifty of (25-(.5)x) dx

Here all that 25-(.5)x is the weight of the rope...


But a pump integral may look like the integral from zero to three of ((8x)(9.8)(1000)(5-x))dx

Here (5-x) represents the distance the water travels...


How come there is nothing that represents the distance the rope travels in the rope problem?
 
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  • #2
If the actual questions to the examples I gave would make my question more understandable I can write them out, but I figured it was probably not necessary.
 
  • #3
If you are talking about the work required to lift a rope that is hanging down up to the point from which it is hanging, and x represents the height of a point on the rope then the "piece" of rope is lifted L- x where L is the length of the rope. If, instead, x is the distance from the point on the rope to the point where it is hanging, the distance is x.
 

FAQ: Why is Rope Distance Not Part of the Equation?

Why is rope distance not considered in equations?

Rope distance is not typically included in equations because it does not have a significant effect on the outcome of most scientific experiments or calculations. Rope distance is usually considered negligible compared to other factors that are more important in determining the results.

What is the role of rope distance in experiments?

The role of rope distance in experiments is usually to connect objects or to provide a means of measuring distance. It is not usually a factor that needs to be considered in the actual calculations or analysis of the experiment.

Are there any situations where rope distance is important in equations?

There may be some situations where rope distance needs to be considered in equations, such as experiments involving tension or elasticity of ropes. However, these situations are not very common and can be easily accounted for in the calculations.

How can I determine if rope distance should be included in my calculations?

If you are unsure whether rope distance should be included in your calculations, it is best to consult with a mentor or reference materials. In general, if the rope distance is relatively small compared to other factors and does not significantly affect the outcome, it can be ignored in the equations.

Is there a specific formula for incorporating rope distance into equations?

No, there is no specific formula for incorporating rope distance into equations. It is not a standard variable in most scientific equations and should only be included if it is a significant factor in the experiment or calculation.

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