The discussion revolves around a problem involving a variable mass system, specifically focusing on the dynamics of a rope being pulled. Participants are exploring the relationships between velocity, force, and mass in the context of conservation laws.
Some participants have offered insights into the complexities of applying conservation principles, noting potential discrepancies in outcomes. There is an ongoing exploration of different interpretations of the problem, with no clear consensus reached yet.
Participants mention the challenges of understanding the problem due to its complexity and the varying levels of familiarity with the concepts involved. There are references to specific assumptions about the rope's behavior and the forces at play, which are still under discussion.
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!erobz said: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:
$$ dW = F~dx = \frac{1}{2} \lambda ( x + dx) v^2 - \frac{1}{2} \lambda x v^2 = \frac{1}{2}\lambda v^2 dx $$
$$ \implies F = \frac{1}{2}\lambda v^2$$
?
Well... if it hasn't been shouted down by the pros around here yet it might be ok.Callumnc1 said: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!