Quote:
Originally Posted by donkbluff
A smooth bead or ring with non-zero mass is threaded onto a light inextensible string that is tied at each end to hooks A and B on the ceiling of a room.
A force is applied to the ring such that the entire system is held in equilibrium, with each segment of string taut.
In such a scenario, is it correct to assume that the tension in both segments of string is the same due to the fact that the ring or bead is modeled as being smooth?
Thank you in advance for clarification.
Smoothness only means that you don't have to worry about friction of the hooks in your calculation.
It is true that each segment of the string will have the same tension (consider the force diagram at some point in the middle of the string -- you can't have a difference otherwise there's a net force). But it is not true that the entire string must have the same tension throughout.
Where you intuition might be leading you wrong is that you're mistaking the lack of friction between the string and the hook as meaning that the tension "passes through" the hook in some way (that the tension "curves around" the hook as if the hook isn't there). But that's not what's happening.
You want to think of the string and hook touching at a single point. If you cut that string at that exact point and then reconnect the strings to the hook there, you should see the exact same force diagram, but now you have two separate strings. And so all the calculations are the same for the connected string case as the two-string case.