While integrating work we write dw = INT. F.ds. But why can't we write dw = INT. dF.s ?
The definition of work is ##work = force \times distance## and while the force can change over position and over time as we move along some path a distance s, we can generalize it as an integral over the path with ds being a very small distance to handle non-linear paths.
However dF isn't a force its a change in force and if used breaks the definition of work which is ##work = force \times distance## not ##work = change in force \times distance ##.
First what do you mean by dF multiplied by s....give the physical interpretation...
Isn't by definition ##\displaystyle w = \int_C f\cdot ds## ?
Yes, it is so...
Check integration by parts. You will see that f.ds is not the same as df.s but there is a relation between them. That is math. then you will have to see if that has physical sense.
The same question was recently asked in the General Physics section.
That thread was closed yesterday. Is this an attempt to re-open the same discussion?
Thread closed. @Gurasees, please take a look at the thread in the link that @nasu posted.
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