Applied Science and Mathematics for Engineering
This section covers Applied Science and Mathematics for Engineering: SI units, force, work, power, energy, ratio, percentage, geometry and trigonometry used in workshop calculations. The exam tests unit-consistent calculation and interpretation.
Core rules
- SI units: length metre (m), mass kilogram (kg), time second (s), force newton (N), work/energy joule (J), power watt (W). Weight = mg, with g ≈ 9.81 m/s².
- Work = force × distance moved in the force direction. Power = work/time. Efficiency = useful output/input × 100%.
- 1 kW = 1000 W; 1 kWh = 3.6 MJ. Convert mm to m before using formulas in metres.
- For right triangles, sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent.
- Area and volume: circle area = πr²; cylinder volume = πr²h. Keep units consistent.
Worked example
A 20 kg load is lifted 1.5 m in 3 s. Force = mg = 20 × 9.81 = 196.2 N. Work = 196.2 × 1.5 = 294.3 J. Power = 294.3/3 = 98.1 W. If the motor input is 120 W, efficiency = 98.1/120 × 100% = 81.75%.
Traps
Do not use mass in kg as force in N. Do not mix mm and m. Do not treat kWh as a unit of power; it is energy. Do not omit the 9.81 factor when weight is required.