1. What Is the Law of Conservation of Mechanical Energy?
The law of conservation of mechanical energy states that:
If only conservative forces (like gravity or spring force) act on a system, the total mechanical energy remains constant.
Mechanical energy includes:
- Kinetic energy (KE)
- Potential energy (PE)
So we can write:
\( KE + PE = \text{constant} \)
1.1. Meaning of the Law
Energy shifts between kinetic and potential forms, but the total amount stays the same. Nothing is lost or gained — it simply changes type.
2. When Is Mechanical Energy Conserved?
Mechanical energy is conserved only when no non-conservative forces act on the object. These include:
- Friction
- Air resistance
- Applied forces
If these forces are absent or negligible, total mechanical energy remains constant.
2.1. Conservative Forces
A conservative force stores and releases energy without loss. Examples:
- Gravitational force
- Spring/elastic force
3. Example: A Falling Object
This is the simplest and most common example of mechanical energy conservation.
3.1. At the Top
Speed = 0 → KE = 0
Height maximum → PE maximum
3.2. During the Fall
Speed increases → KE increases
Height decreases → PE decreases
3.3. Just Before Reaching the Ground
PE minimum → almost zero
KE maximum
3.4. Total Energy Check
\( KE + PE = \text{constant} \)
Energy just changes form — nothing is lost.
4. Example: Swinging Pendulum
A pendulum constantly exchanges potential and kinetic energy while swinging.
4.1. Extreme Positions (Left and Right)
Speed = 0 → KE = 0
Height is maximum → PE maximum
4.2. Lowest Position
Speed maximum → KE maximum
Height minimum → PE minimum
4.3. Total Mechanical Energy
Despite the continuous change between KE and PE, the total mechanical energy stays constant (ignoring air resistance).
5. Example: Roller Coaster
Roller coasters provide a clear demonstration of energy conservation as they go up and down the track.
5.1. At the Highest Point
PE maximum
KE minimum
5.2. At the Lowest Point
KE maximum
PE minimum
5.3. Moving Up the Next Hill
KE converts back to PE as the coaster rises.
6. When Mechanical Energy Is Not Conserved
In real life, some mechanical energy often gets converted into other forms due to:
- Friction
- Air resistance
- Sound
- Heat
In these cases, total mechanical energy changes, but total energy is still conserved.
6.1. Examples
- Friction in a sliding block reduces mechanical energy; energy becomes heat.
- A ball bouncing loses height each time due to energy lost as sound and heat.
7. Equation for Conservation of Mechanical Energy
For a closed system where only gravity acts:
\( KE_1 + PE_1 = KE_2 + PE_2 \)
This equation helps solve many problems involving falling objects, projectiles, and pendulums.
7.1. Interpretation
The sum is the same at every point; only the distribution between KE and PE changes.