📌 Quick Answer
Mechanical energy is the sum of the kinetic energy and potential energy of an object: ME = KE + PE.
It is the energy a body has because of its motion and its position, and in the absence of friction (only conservative forces) it stays constant.
🔹 Key Takeaways
- Mechanical energy ME = KE + PE.
- Kinetic energy KE = ½mv²; gravitational potential energy PE = mgh.
- SI unit is the joule (J).
- It is conserved when only conservative forces (like gravity) act.
What Is Mechanical Energy?
Mechanical energy is the energy associated with the motion and position of an object. It is the sum of two forms: kinetic energy (energy of motion) and potential energy (stored energy of position or configuration).
Formula and Types of Mechanical Energy
| Type | Formula | Depends on |
|---|---|---|
| Kinetic energy (KE) | ½mv² | Mass and speed |
| Gravitational potential energy (PE) | mgh | Mass, gravity and height |
| Elastic potential energy | ½kx² | Spring constant and extension |
Total mechanical energy = KE + PE.
Conservation of Mechanical Energy
The law of conservation of mechanical energy states that when only conservative forces act on a body, its total mechanical energy remains constant. As an object falls, its potential energy converts into kinetic energy, but the sum stays the same.
Worked Example
A 2 kg ball is dropped from a height of 5 m. Its potential energy at the top is PE = mgh = 2 × 9.81 × 5 = 98.1 J. Just before it hits the ground, all of this has become kinetic energy, so KE = 98.1 J and the total mechanical energy is conserved at 98.1 J.
Applications and Examples
- A swinging pendulum continuously trades PE and KE.
- A roller-coaster car at the top of a hill (high PE) speeds up going down (high KE).
- Hydroelectric power converts the PE of stored water into electrical energy.
Frequently Asked Questions
What is mechanical energy?
Mechanical energy is the sum of an object’s kinetic energy and potential energy: ME = KE + PE.
What is the formula for mechanical energy?
ME = KE + PE = ½mv² + mgh for an object with speed v at height h.
What are the two types of mechanical energy?
Kinetic energy (energy of motion) and potential energy (stored energy of position or configuration).
Is mechanical energy always conserved?
It is conserved only when non-conservative forces such as friction and air resistance are absent; otherwise some mechanical energy converts to heat.
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