Cambridge Syllabus Notes

Energy and Control Systems

Objective

Understand the five main forms of energy used in design and technology: kinetic, potential, thermal, electrical, and chemical. Learn how to calculate, compare, and convert between them, and how they influence control systems.

Kinetic Energy (KE)

Energy of motion. Think of a ⚽️ rolling ball or a 🚀 blasting off.

Formula: $K = \frac{1}{2} m v^2$

Mass (m) in kilograms (kg)
Velocity (v) in metres per second (m/s)
Units: Joules (J)

Example: A 0.5 kg toy car moving at 4 m/s has KE = 0.5 × 0.5 × 4² = 4 J.

Potential Energy (PE)

Stored energy due to position or configuration. Like a 🎈 hanging high or a spring compressed.

Types:

Gravitational: $U_g = mgh$
Elastic (spring): $U_s = \frac{1}{2} k x^2$

m = mass (kg)
g = 9.81 m/s²
h = height (m)
k = spring constant (N/m)
x = displacement (m)

Example: A 2 kg book 3 m above the ground has U_g = 2 × 9.81 × 3 ≈ 58.86 J.

Thermal Energy (Heat)

Energy due to the motion of atoms and molecules. Think of a ☕️ steaming hot or a 🔥 burning coal.

Heat capacity: $Q = mc\Delta T$

m = mass (kg)
c = specific heat capacity (J/kg·K)
ΔT = temperature change (K)

Example: Heating 0.3 kg of water from 20 °C to 80 °C (ΔT = 60 K) with c = 4184 J/kg·K gives Q = 0.3 × 4184 × 60 ≈ 75 kJ.

Electrical Energy (E)

Energy carried by electrons. Picture a ⚡️ lightning bolt or a battery powering a phone.

Formula: $E = V I t$

V = voltage (V)
I = current (A)
t = time (s)
Units: Joules (J) or Watt‑seconds (Ws)

Example: A 12 V battery supplying 2 A for 30 s delivers E = 12 × 2 × 30 = 720 J.

Chemical Energy

Stored in bonds of molecules. Think of a 🍎 apple or a 🚗 gasoline tank.

Energy released in combustion: $Q = \Delta H$

ΔH = enthalpy change (kJ/mol)
Positive ΔH: endothermic (absorbs heat)
Negative ΔH: exothermic (releases heat)

Example: Burning 1 mol of methane releases ΔH ≈ –890 kJ.

Energy Conversion in Control Systems

Control systems often convert one energy form to another to perform work or regulate processes.

Mechanical to electrical: Generators (e.g., wind turbines)
Electrical to mechanical: Motors (e.g., electric cars)
Chemical to thermal: Combustion engines
Thermal to electrical: Thermoelectric generators

Key concept: Energy conservation – total energy remains constant; it only changes form.

Exam Tips Box

Remember:

Always write units with the numerical answer.
Check that the formula matches the energy type.
Use the correct sign for ΔH (negative for exothermic).
Show all steps clearly; partial credit is awarded.

Summary Table

Energy Type	Formula	Example	Units
Kinetic	$K = \frac{1}{2} m v^2$	Toy car (0.5 kg, 4 m/s)	J
Potential (gravitational)	$U_g = mgh$	Book (2 kg, 3 m)	J
Thermal	$Q = mc\Delta T$	Water (0.3 kg, 20 °C → 80 °C)	J
Electrical	$E = V I t$	Battery (12 V, 2 A, 30 s)	J
Chemical	$Q = \Delta H$	Methane combustion (1 mol)	kJ/mol

Different forms of energy, including: kinetic, potential, thermal, electrical, chemical.