The discussion centers on the conditions for static equilibrium of a uniform sphere on an incline, specifically addressing the role of friction. Participants conclude that for static equilibrium to be achieved, the net torque must be zero, which occurs when friction is absent. The analysis reveals that at angles θ = 0 and θ = π/2, equilibrium cannot be maintained without friction, as the normal force cannot counterbalance the forces acting on the sphere. The conversation emphasizes the importance of understanding the relationship between applied forces, normal force, and friction in achieving equilibrium.
PREREQUISITESPhysics students, mechanical engineers, and anyone interested in understanding the dynamics of forces and equilibrium in physical systems.
But then an infinitesimal displacement away from vertical it is?Orodruin said:
Within the model yes. But as I have already stated - repeatedly - it is obvious that the model breaks down well before that. Just as the rope model does before the rope becomes horizontal.erobz said:
Ok, I wasn't picking up on that. My point was this model has a window of validity, but it isn't obvious where exactly that is with what is exposed to us in manipulatable variables. I feel a "better" model is the alternative to this, which is what I think you (ultimately) believe too.Orodruin said:
But that is exactly what you have been arguing against!erobz said:
Worse, he is inadvertently providing some upward force with his hand in addition to the intended horizontal force.Orodruin said:
To me it feels worse than what I've encountered in the past... infinite forces from infinitesimal deviations seems unsavory. I'm not an academic. I'm still trying to probe my parents to see if Santa Clause is real or not.Orodruin said:
I'm aware of that too, but I don't think that helps the argument against reducing the amount of idealization, does it?jbriggs444 said:
It helps clarify matters. We do not need to model exotic things like deformation and off center contact forces if the reality primarily involves equal vertical support forces on either side.erobz said:
Yeah, friction at both contact point works that of the wall and the ball and the friction of the thing applying the force. My point was its like the model is like fine,fine,fine,...adinfinitum. Suddenly friction is necessary at 90.000000000000000... I still want to spit it out, instead of chewing it. Its too philosophical in flavor to be good food IMO.jbriggs444 said:
In reality there is no such thing as a vertical wall. Or an exact angle of the wall. Or even an unambiguous definition of the "wall". There is no point in pushing reality that far.erobz said:
But that's the whole ball game!jbriggs444 said:
Yeah, so long as it is admitted that good enough is mostly fuzzy in this sport, and new stuff can be found in the fuzz that is groundbreaking. I'm not suggesting that here, but to say you guys don't adjust/fine tune is a bit defeatist. Maybe we teach what is "good enough", but I don't think we truly ever except what is good enough.jbriggs444 said:
It most definitely isn’t. The whole ball game is making useful predictions. That includes both accuracy (good enough for the purpose), reliability, and ease of performing the prediction.erobz said:
I think you are missing the entire point here. This is a post in the introductory homework forum. The point is helping the OP solve the problem within the constraints of the given model. A discussion of what refinements the model could use in particular limits (or even how the model behaves in those limits) is not part of the problem. It might have been in a more advanced setting, but here that discussion is not productive to the OP because the entire purpose is understanding the simplified model, not to consider where it breaks down and why or what possible refinements could be made to resolve the issues.erobz said:
Understood.haruspex said:
Yes, the one already established: there is no frictional force.Lnewqban said: