Question
A swinging pendulum eventually comes to rest. Does this violate the law of conservation of energy? Explain where the energy goes.
Solution — Step by Step
The law says energy cannot be created or destroyed — it only transforms from one form to another. It does not say a pendulum must swing forever. The key word students miss: the law applies to an isolated system (no external forces doing work).
When we pull the pendulum to one side, we give it gravitational potential energy (GPE). The moment we release it, that GPE converts to kinetic energy (KE) as it swings down. At the lowest point, KE is maximum; GPE is minimum. This conversion is perfect — if no energy escapes the system.
A real pendulum is not isolated. Two forces continuously steal energy:
- Air resistance — the bob has to push air molecules out of its way. This work done on air molecules appears as heat in the surrounding air.
- Friction at the pivot — the hinge rubs slightly with every swing, again producing heat and tiny vibrations (sound).
Each swing, a small fraction of mechanical energy leaks out as heat and sound.
Add it all up: Initial GPE = Final heat energy + Final sound energy + any remaining KE (which is zero when it stops). The total energy is conserved — it just isn’t in a useful mechanical form anymore. The pendulum stops; the air around it is imperceptibly warmer.
Energy is not lost — it is dissipated into the surroundings as thermal energy and sound. Conservation of energy is not violated. The pendulum stops because its mechanical energy transforms into forms we cannot recover easily.
Why This Works
The conservation of energy is one of the most tested concepts in NCERT Class 9 and it trips students because of one word: isolated. In an isolated system, mechanical energy (KE + PE) is conserved. But the moment friction or air resistance enters the picture, mechanical energy is no longer conserved by itself — total energy (mechanical + heat + sound) still is.
Think of it this way: a 100 rupee note doesn’t disappear when you spend it. It just moves to someone else’s pocket. Energy is the same — the pendulum’s “rupees” go into the air’s pocket as heat.
This is also why we call friction a non-conservative force. Work done against friction always produces heat that cannot be converted back to mechanical energy spontaneously. Conservative forces (like gravity) let you get the energy back; friction doesn’t.
Alternative Method
Instead of tracking energy form by form, use the work-energy theorem:
For the pendulum over many swings, (starts and ends at rest). So . But gravity and friction both do work. This means:
Over a full cycle, (conservative force, closed path). Therefore:
Wait — that can’t be right. These are negative values (energy removed from the system). So:
This confirms that all the initial GPE ends up as heat and sound. Same answer, different route.
Common Mistake
Many students write: “The pendulum stops because energy is destroyed by friction.” This is wrong — and will cost you marks in boards. Friction does not destroy energy; it converts mechanical energy into thermal energy. Always say dissipated or converted to heat, never “lost” or “destroyed”. Examiners specifically look for this distinction in 3-mark and 5-mark answers.
Board exams frequently ask: “Does a swinging pendulum violate conservation of energy?” The model answer structure is: (1) No, it does not. (2) Energy is dissipated as heat and sound due to air resistance and friction at pivot. (3) Total energy of the system + surroundings remains constant. Write exactly this for full marks.