Read a Sliding Chain: Let the Hanging Length Drive It
As a chain slides off a frictionless table, the gravitational potential energy of the hanging segment changes continuously. Treat the entire chain as the system.
Energy of a Sliding Chain is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the condition
If y hangs, its mass is λ y and its centre of mass is y/2 below the edge. Write the gravitational potential energy from this geometry before using energy conservation.
Build the governing relation
All segments share the same speed, so kinetic energy is one-half λ L v². Compare the initial and final hanging lengths.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Do not use only the mass currently hanging in the kinetic-energy term; the whole moving chain has the same speed.
Ready to try the pattern?
100% coverage across the linked question.
Practise the linked question