Work done raising an object. Calculus needed.

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Homework Help Overview

The problem involves calculating the work done in lifting a piano, supported by a rope, over a specified distance. The context includes considerations of gravitational force and the weight of the rope itself, which introduces complexity to the calculation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relevance of a specific formula for work done against gravity and question the necessity of gravitational constant in this context. There is an exploration of how to account for the weight of the rope in the work calculation.

Discussion Status

Some participants have offered insights into the definition of work and suggested that simpler methods may exist for calculating the work done. There is an ongoing exploration of different interpretations of the problem, particularly regarding the role of the rope's weight.

Contextual Notes

Participants note that the problem may not fit standard calculus techniques due to the mass/length relationship involved, and there is a mention of potential assumptions that could affect the calculations.

knownothing
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Homework Statement


A 50-meter rope weighing 2 N/m supports a piano weighing 600 N. Find the work done in lifting the piano 25 meters

2. Relevant equation.
None of the calculus equation, techniques covers this type of question with mass/length involved.

The Attempt at a Solution


I know the formula $W=GMm(1/r-1/r_i)$ for work done by gravity pulling an object downward. The reverse can be used for raising an object. But since $G$ is not given, I assume this formula is irrelevant.
 
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knownothing said:

Homework Statement


A 50-meter rope weighing 2 N/m supports a piano weighing 600 N. Find the work done in lifting the piano 25 meters

2. Relevant equation.
None of the calculus equation, techniques covers this type of question with mass/length involved.

The Attempt at a Solution


I know the formula $W=GMm(1/r-1/r_i)$ for work done by gravity pulling an object downward. The reverse can be used for raising an object. But since $G$ is not given, I assume this formula is irrelevant.
Even if this formula were relevant, you should understand that G is the universal gravitational constant, and its value can be looked up, even on the internet.

Getting back to the problem, even if the work performed lifting the rope were neglected, how would you calculate how much work it takes to lift the piano 25 meters?

In other words, what is the definition of work?
 
knownothing said:

Homework Statement


A 50-meter rope weighing 2 N/m supports a piano weighing 600 N. Find the work done in lifting the piano 25 meters

2. Relevant equation.
None of the calculus equation, techniques covers this type of question with mass/length involved.

The Attempt at a Solution


I know the formula $W=GMm(1/r-1/r_i)$ for work done by gravity pulling an object downward. The reverse can be used for raising an object. But since $G$ is not given, I assume this formula is irrelevant.

It is correct in principle, but using it is a severe case of "overkill". If all you want is a numerical answer accurate to more precision than you can measure, there is a much, much simpler (approximate) formula that people have been using for the past 400 years. Google "earth's gravitational force".

Besides, the formula above looks only at the plane, and neglects the mass of the rope. The point is that the part of the rope hanging down lessens as the plane is raised up (assuming, for example, that the rope is gradually wound up around a roller), so that portion of the work will be less straightfoward (although simple to obtain using calculus).
 
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