Principles and Theoretical Foundations
Principles and Theoretical Foundations checks whether you can apply the physical laws behind a procedure rather than memorise its steps: force and moment balance, energy conservation, Ohm's law, pressure and stress, and heat transfer. Expect short quantitative items where a single relationship decides the answer.
Core relationships
- Newton's second law: F = m·a. On a level surface with no acceleration, the normal force equals the weight.
- Static equilibrium: net force and net moment are both zero. For moments about a pivot, Σ(F × d) = 0 using perpendicular distance.
- Conservation of energy: input = useful output + losses. Efficiency η = useful output ÷ input, always below 1 in a real machine.
- Ohm's law, V = I·R, with power P = V·I = I²R = V²/R for resistive DC circuits.
- Pressure p = F/A in pascals; in a fluid column p = ρgh. Stress σ = F/A₀ uses the original area; strain ε = ΔL/L₀. Within the elastic limit, Hooke's law gives σ = E·ε.
- Heat transfers by conduction, convection, and radiation; conduction rises with area and temperature difference and falls with thickness.
Worked example
A beam pivots at one end. A 300 N load hangs 0.40 m from the pivot, and a downward effort is applied 1.20 m from the pivot. What effort balances it?
- Take moments about the pivot. Load moment = 300 N × 0.40 m = 120 N·m clockwise.
- For balance the effort moment must equal it anticlockwise: F × 1.20 m = 120 N·m.
- F = 120 ÷ 1.20 = 100 N. Check: mechanical advantage = load ÷ effort = 300 ÷ 100 = 3, matching the arm ratio 1.20 ÷ 0.40 = 3. The check traps inverted ratios: 0.33 would give 900 N, which is wrong.
Traps that cost marks
- Using a diameter where a radius belongs, giving a factor-of-four area error.
- Mixing millimetres and metres inside a moment or stress calculation.
- Quoting efficiency above 100% by confusing input with output.
- Leaving gauge pressure unconverted in a gas relationship.
- Applying ideal mechanical advantage when friction losses are stated.