The discussion centers on the dynamics of a variable mass system, specifically a massive rope being pulled. Participants debate the relationship between the acceleration of the rope's segments and their velocities, particularly focusing on the average speed being v0/2. The conservation of work versus momentum is analyzed, revealing that while momentum calculations yield a force F=λv0²/2, work conservation suggests F=λv0²/4. The conversation highlights the complexities of internal forces and the effects of tension in the rope, ultimately concluding that the momentum argument is flawed due to assumptions about forces acting on the rope.
PREREQUISITESPhysics students, educators, and anyone interested in advanced mechanics, particularly those studying variable mass systems and the intricacies of force dynamics in flexible bodies.
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!