The discussion centers on the conservation of momentum and the dynamics of three identical balls connected by inextensible strings on a smooth surface. When the middle ball B is given an initial velocity \(v_0\), the challenge is to determine the velocity of ball A at the moment it collides with ball C. Key insights include the application of conservation laws, specifically that momentum is conserved for the system as a whole, despite tension being an external force affecting individual balls. The final velocity of ball A is derived as \(v_A = \frac{2v_0}{3}\) when considering the system's dynamics and constraints.
PREREQUISITESStudents of physics, particularly those studying mechanics, as well as educators and anyone interested in understanding the dynamics of interconnected systems and the application of conservation laws in real-world scenarios.
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).