Conservation of Mechanical Energy
Senior 2 · Physics
Conservation of Mechanical Energy
Lesson 1 of 4
15 min
Before you can say where energy goes, you must decide what you are watching. A physicist draws an imaginary line around the part of the world she is studying: a falling mango, a pot of beans on a charcoal stove, the water behind a dam. Everything inside that line is the system. Everything outside it is the surroundings. The line itself is the boundary.
Whether energy seems to be "kept" or "lost" depends on where you drew that line. Draw it well and energy problems become simple bookkeeping. Draw it carelessly and energy seems to vanish or to appear from nowhere. Every lesson in this unit depends on this one.
On a cold morning in Musanze, Keza pours hot tea into three containers.
These three cups are the three kinds of system.
| System | Can MATTER cross the boundary? | Can ENERGY cross the boundary? | Examples |
|---|---|---|---|
| Open system | Yes | Yes | An open pot of boiling beans; the human body (you eat, breathe and sweat); a moto engine (fuel and air in, exhaust gas and heat out) |
| Closed system | No | Yes | A sealed bottle of juice warming in the sun; a sealed bicycle tyre; a pressure cooker while its valve is shut |
| Isolated system | No | No | A perfect vacuum flask (real flasks come close); the whole universe |
No real object on Earth is perfectly isolated: heat always leaks a little. We treat a system as isolated when the energy crossing its boundary is too small to matter in the time we are studying it.
In mechanics, energy usually enters or leaves a system as work done by a force from outside: a push, a pull, friction from the ground, or the drag of the air. When you study a falling stone, choose the system to be the stone and the Earth together. Gravity then acts inside the system, and the potential energy belongs to the stone–Earth pair.
If no outside force does work on this system and there is no friction or air resistance, the system is mechanically isolated. Its energy can change from one form to another inside the boundary, but the total cannot change. That is the idea the next lessons build on.
Classify each system and give the reason.
(a) The engine of a moving moto. Open: petrol and air enter, exhaust gases leave (matter crosses), and heat and work leave (energy crosses).
(b) A sealed plastic bottle of water left in the sun at the market. Closed: sunlight brings energy in and the water warms, but no water or air gets in or out.
(c) A stone and the Earth, with the stone falling where air resistance is negligible. Isolated (mechanically): no outside force does work, so the energy only changes form inside the system.
(d) Hot milk in a good vacuum flask for one hour. Approximately isolated: very little heat and no matter cross the boundary in that time.
Tip
Ask two questions at the boundary
1. Can matter cross? 2. Can energy cross?
Memory hook: Open lets both, Closed lets one (energy), Isolated lets none. In an exam, a classification with no reason earns little. Always add "because matter … and energy …".
Classify a candle burning in open air.
Solution: Open. Wax vapour and oxygen enter the flame and carbon dioxide and water vapour leave, so matter crosses. Heat and light leave, so energy crosses.
A glass jar is tightly sealed and then heated in a pan of water. What kind of system is the jar and its contents?
Solution: Closed. Heat enters through the glass, but no matter can get in or out while the lid stays sealed.
Why can a real vacuum flask never be a perfectly isolated system?
Solution: Some heat always escapes, mainly by conduction through the stopper and the neck of the flask, and a little by radiation. That is why tea in a flask is cooler the next morning. A real flask is only approximately isolated.
A pendulum swinging in the classroom slowly stops. Is the pendulum–Earth system isolated?
Solution: No. The air is outside the system, and air resistance (plus friction at the pivot) does work on the pendulum. That work carries energy out of the system as heat, so the pendulum's mechanical energy falls.
Mugisha says: "The human body is a closed system because the skin keeps everything inside." Evaluate his claim.
Solution: He is wrong. You breathe in oxygen and breathe out carbon dioxide, you eat and drink, and you sweat. Matter crosses the boundary all the time, and so does energy (you give out heat). The body is an open system.
Remember
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