Rings threaded onto strings

Question

This is a follow up question to a question I asked a few weeks ago (Normal contact force with a light string)

When a ring is threaded onto a light string, we know it experiences a contact force. Does it also experience tension? In the previous question, I thought - and was told- no, it doesn't. But I ran into a question in which a smooth ring is threaded onto a vertical string, being  pulled to one side by a horizontal force. The ring is in equilibrium. If I just consider the forces on the ring here, that no tension idea runs into trouble since the ring will have a net vertical force that way. ( This is only out of interest. The answer to questions like these can be found by simply treating the ring and the bit of string as one body, there is no confusion then)

What I would like to know is exactly how a taut string interacts with a ring threaded onto it. About the contact force and tension in particular.

Abhi7731756 · Answer

Consider the taut string threaded around ring. What is tension in thread? Is it constant? No. It increases when it takes turns around the ring. This tension has some net vertical component. By Newton's third law,there should be some reaction force. This is the normal force pointing in opposite direction to the net vertical tension. If the ring is at rest,these forces cancel out. If we consider dynamics of only ring,then to simplify,we can take force only from that we are applying. By symmetry,we can cancel all the tension force(Assume there is no knot,the windings are completely circular). Hence,it is reasonable to neglect the contact forces.

Answered by Abhi7731756 on December 15, 2020

Rings threaded onto strings

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