Work (it is NOT a homework question!!)?

Question

How much work is done by the person while going from the position 1 to position 2? See the picture for details

http://www.geocities.com/jsjm61/questionForWork.JPG

Thanks

Answer 1

There isn't enough information in the picture, although I can provide what is missing (to a reasonable approximation.)

By pulling on the string, the person is lifting the centre of mass (where the downward force mg can be thought of as acting) through some height difference, h. (The pivot is frictionless, so that's all that's happening. Everything is stationary at the beginning and the end.)

So the work being done (against gravity) is: mgh.

Unfortunately, h can't really be found from the pictures as they are currently annotated. Note also that the length of the distance labelled 'b' CHANGES from diagram 1 to diagram 2! That should be disallowed. (The length 'a' is irrelevant: if you have a smaller lever arm, the force you actually need to apply will be greater --- Archimedes, and all that --- but you'll then move the point of attachment through a correspondingly smaller length, in lifting the whole arrangement. But all such minute detail evens out in the wash; no matter how it is done, in detail, the work is exactly what it takes to lift the weight through the distance that it IS lifted.)

Let's now suppose the following:

1. The length 'b' DOESN'T change half-way through this problem; and

2. The rod is angled down at 45 deg. from the vertical initially, and is horizontal finally. (Both of these assumptions look fairly good.) ***

Then h = b / sqrt(2) or b 2^(-1/2). (Write it how you prefer.)

So the work done is then: W = m g h / sqrt(2) or m g h 2^(-1/2).

Live long and prosper.

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*** POSTSCRIPT: If you don't like assuming that the rod is angled down at 45 deg., simply start with it angled down at an angle theta relative to the horizontal. Then replace the factors 1/sqrt(2) or 2^(-1/2) by sin (theta); that gives you the general result.

Live long and prosper.

Answer 2

i cant understand anything from the picture