The problem involves three identical balls connected by light inextensible strings on a smooth horizontal surface, where the middle ball is given an initial velocity. The objective is to determine the velocity of one of the balls at the moment of collision with another ball, focusing on the principles of conservation of momentum and the effects of tension in the strings.
The discussion is ongoing, with participants providing insights into the conservation laws applicable to the system. There is a recognition of the complexities introduced by tension and the need for careful consideration of the initial and final states of the system. Multiple interpretations of the problem are being explored, particularly regarding the velocities of the balls at the moment of collision.
Participants note that the initial conditions involve only the middle ball having a velocity, while the others start from rest. The discussion also highlights the impulsive nature of tension and its implications for energy conservation in the system.
This in no way invalidates my argument. It is just an argument for why your argument works. In this case, there is no tension before the middle ball is hit and there is no tension immedeately after. There is no impulse change of the outer balls and therefore no violation of work conservation. The balls would have to change their speed at the instant of the hit for this to occur.haruspex said:I disagree.
Suppose there is a mass on a frictionless table, attached to a taut string that passes over a pulley to a suspended mass. Initially, the first mass is held in place, then released. There is nonzero tension right from the start, but acceleration is smooth, no sudden jumps in speed, so work is conserved.
I think you are saying that because the tension increases gradually from zero, it follows that there is no sudden change in speed. That is true, but my quibble with your wording in post #25 is that it might give the reader the impression that such a profile for the tension is the key requisite for work conservation here. I contend that it is not. The tension could have been nonzero right from the start yet work be conserved. Moreover, tension could suddenly change from zero to nonzero yet work be conserved. The key consideration is a sudden change in speed.Orodruin said:This in no way invalidates my argument. It is just an argument for why your argument works. In this case, there is no tension before the middle ball is hit and there is no tension immedeately after. There is no impulse change of the outer balls and therefore no violation of work conservation. The balls would have to change their speed at the instant of the hit for this to occur.
Yes.Titan97 said:So in this case, work is conserved since there is no sudden change in speed (acceleration is finite).