1. What Is Mechanical Energy?
Mechanical energy is the total energy an object has because of its motion and position. It is made of two parts:
- Kinetic Energy (KE): energy of motion
- Potential Energy (PE): stored energy due to position
So mechanical energy simply tells us the combined effect of these two energies.
1.1. Formula for Mechanical Energy
The total mechanical energy is:
\( E_{mechanical} = KE + PE \)
This value changes only when non-conservative forces like friction act.
2. Why Mechanical Energy Is Useful
Many systems in nature and machines use a mixture of kinetic and potential energy. Mechanical energy helps us understand how energy moves around in such systems.
2.1. Examples of Systems with Mechanical Energy
- A swinging pendulum
- A roller coaster on a track
- A falling object
- A ball thrown upward
3. Mechanical Energy in a Swinging Pendulum
A pendulum changes its energy form continuously:
3.1. At the Top Positions
Speed is zero → KE = 0
Height is maximum → PE is maximum
3.2. At the Lowest Position
Speed is maximum → KE is maximum
Height is minimum → PE is minimum
3.3. Total Mechanical Energy
\( KE + PE \) remains the same (if there is no friction or air resistance).
4. Mechanical Energy in a Falling Object
When an object falls from a height:
4.1. Before Falling
Object has maximum potential energy and zero kinetic energy.
4.2. During the Fall
Potential energy decreases, while kinetic energy increases because the object speeds up.
4.3. Just Before Hitting the Ground
Potential energy is minimum, kinetic energy is maximum.
5. Mechanical Energy in a Roller Coaster
A roller coaster continuously converts potential energy to kinetic energy and back as it moves along the track.
5.1. At the Top of the Track
High PE, low KE.
5.2. At the Bottom of the Track
Low PE, high KE.
5.3. With No Friction
Total mechanical energy stays constant. This is why the coaster can climb back up smaller hills.
6. When Mechanical Energy Is Not Conserved
Mechanical energy changes when non-conservative forces act on the object:
6.1. Examples
- Friction converts mechanical energy into heat.
- Air resistance reduces mechanical energy of moving objects.
- Engine parts lose energy due to friction without lubrication.
7. Units of Mechanical Energy
The SI unit of mechanical energy is the Joule (J), the same as other forms of energy.
7.1. Everyday Example
A 2 kg ball lifted 5 m above the ground stores about \( PE = mgh = 2 \times 10 \times 5 = 100 \) Joules of potential energy.