If the belt is rubber, the friction is high enough, even when the system is starting from zero. (Assuming pulleys shaped like the ones linked above, of course.)
Whether a frictionless pulley is useless or not depends largely upon whether you are using it to change the direction of the line, adding tension to it, or using it to perform work. Such a pulley is only useless for the latter, such as a belt turning a drum, but a frictionless block and tackle or tensioning pulley would be incredibly useful.
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I wonder at what point you start getting a convex pulley having a (local) optimum in terms of how likely the belt is to stay on the pulley?
For low speed / low friction between belt and pulley, you'll just pull the belt off of the pulley if the pulley is convex.
And for high speed / high friction you'll end up with the above effect.
So I wonder: where does it transition?
If the belt is rubber, the friction is high enough, even when the system is starting from zero. (Assuming pulleys shaped like the ones linked above, of course.)
Is that the case even for a (mythical and completely useless) frictionless pulley?
Whether a frictionless pulley is useless or not depends largely upon whether you are using it to change the direction of the line, adding tension to it, or using it to perform work. Such a pulley is only useless for the latter, such as a belt turning a drum, but a frictionless block and tackle or tensioning pulley would be incredibly useful.
Good point.
So my question isn't as odd as it might first appear then.