Variable mass, uniform body, force -- pulling a massive rope

[member 731016]

For some reason, I'm not getting that.

The differential work $dW$ done by the force as it moves a distance $dx$ should be the change in kinetic energy of the pulled rope:

$$ dW = F~dx = \frac{1}{2} \lambda ( x + dx) v^2 - \frac{1}{2} \lambda x v^2 = \frac{1}{2}\lambda v^2 dx $$

$$ \implies F = \frac{1}{2}\lambda v^2$$

?

Is that setting the differential work equal to the differential change in kinetic energy? I did not know the work energy theorem could be applied for differentials!

Many thanks!

 

[erobz]

Is that setting the differential work equal to the differential change in kinetic energy? I did not know the work energy theorem could be applied for differentials!

Many thanks!

Well... if it hasn't been shouted down by the pros around here yet it might be ok.