# Work Done = (f)(d)

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1. Aug 4, 2015

So we did an experiment calculating work (w=fd) by 1)running and 2)walking upstairs and it turns out that running and walking the same distace(d) with the same weight(f) makes the work done also the same. It later on becomes different when it comes to talking about power but for now lets stick to work for now.

then this problem was mentioned:

Two persons with the same weight went to the top of a same building. One climbed using a spiral staircase and the other one used an elevator. Did the two person have the same work done?(just a simple analysis type question)

Our handouts (done by my school) says that the answer was yes, they both did the same work.

Now, I do not understand because for me, the one who exerted more work was the one who climbed using the stairs simply because that person lifted his own weight going to the top of the building thus he is the one doing work. On the other hand, the other person was lifted by an elevator meaning the elevator was the one who did the work.
Also , if work is going to be computed, isn't that the person who used the elevator is not just the weight to be computed but also the weight of the elevator since the elevator went up the building with him? Therefore I think that they don't have the same work done.

Of course all of this is just something based on my understanding and I don't have the courage to go against my instructor and handouts unless I have some valid or legit proof. But I'm not good with physics so I cant explain it properly.
I don't mind being wrong, however I would just want to be enlightened xD.

2. Aug 4, 2015

### tommyxu3

The one I think you have to accentuate is what is doing work, and you should realize the general definition of work: $\int_{\Gamma} \vec{F}\cdot\vec{dl}.$ Can you use these to clear what get you confused above?
Incidentally, one declaration is confirmed that the amount of the change of their "gravitational potential energy" is identical, for they have the same weight and have the same displacement parallel to the direction of the gravity.

3. Aug 5, 2015

### Qwertywerty

First part of quote - the question asks - ' Did they have the same work done ? ( I believe , on them ) ' .

So yes - they did . In the first case , the muscular energy of the body is changed into gravitational potential energy , and in the second , the normal from the elevator does work on the man , thus causing change in his gravitational potential energy .

Second part - Are you sure it says they both did the same work ?