Energy

1. Definition of Energy

• Energy is the ability to do work.
• It is a scalar quantity (has magnitude but no direction).
• The SI unit of energy is the Joule (J).

2. Types of Mechanical Energy

a) Kinetic Energy $(KE)$

• Energy possessed by a moving object.

• Formula: where: $KE = \frac{1}{2} m v^2$

  • $KE$ $=$ Kinetic energy $(J)$
  • $m$ $=$ Mass of object $(kg)$
  • $v$ $=$ Velocity $(m·s⁻¹)$

b) Potential Energy $(PE)$

• Energy stored due to position in a gravitational field.

• Formula: where: $PE = mgh$

  • $PE =$ Potential energy $(J)$
  • $m =$ Mass $(kg)$
  • $g =$ Gravitational acceleration $(9.8 m·s⁻²)$
  • $h =$ Height above a reference point $(m)$

3. Principle of Conservation of Mechanical Energy

• Total mechanical energy (sum of $KE$ and $PE$) in an isolated system remains constant, provided no external forces (e.g., friction) do work on the system.

• Equation: $KE_i + PE_i = KE_f + PE_f$

  • If no external forces act, energy is only transferred between kinetic and potential forms.

4. Work Done by Forces and Energy Changes

a) Conservative Forces

• Forces for which work done is independent of the path taken.
• Examples: Gravitational force, electrostatic force, spring force.
• Work done by gravity is reversible (can convert between $PE$ and $KE$ ).

b) Non-Conservative Forces

• Forces that cause energy loss (e.g., friction, air resistance).
• Example: A moving object slows down due to friction.
• Work done by non-conservative forces leads to energy dissipation (e.g., heat, sound).

5. Work-Energy Theorem

• The net work done on an object is equal to its change in kinetic energy: $W_{\text{net}} = \Delta KE = KE_f - KE_i$

• If : The object gains energy. $W_{\text{net}} > 0$

• If : The object loses energy. $W_{\text{net}} < 0$

6. Key Takeaways

✔ Energy is conserved in an isolated system.

✔ Mechanical energy = Kinetic energy + Potential energy.

✔ Conservative forces do not remove energy from the system.

✔ Non-conservative forces cause energy loss.

✔ The net work done on an object changes its kinetic energy.

Exam Tip

💡 Identify whether a force is conservative or non-conservative before solving energy problems.