# Work done raising an object. Calculus needed.

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1. Jun 15, 2016

### knownothing

1. The problem statement, all variables and given/known data
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.

3. 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.

2. Jun 15, 2016

### SteamKing

Staff Emeritus
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?

3. Jun 15, 2016

### Ray Vickson

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).

Last edited: Jun 15, 2016
4. Jun 17, 2016

### rude man

No calculus needed ...