Applied Science and Mathematics relevant to the Trade
Domain 6 tests the science and arithmetic behind shop decisions: force, torque, power, pressure, thermal efficiency, electrical circuits, gear ratios and unit conversion.
Core rules
- Torque = force × perpendicular distance; power = torque × angular velocity. Use N·m, N and rad/s, or convert rpm.
- Pressure = force ÷ area; in hydraulics, Pascal's law means pressure is transmitted equally, so force is multiplied by piston-area ratio.
- Thermal efficiency = useful work ÷ heat supplied; diesel cycle efficiency rises with compression ratio and falls with heat loss.
- Ohm's law: V = IR; power P = VI. A 12 V circuit drawing 5 A consumes 60 W.
- Gear ratio = driven teeth ÷ driving teeth; speed falls and torque rises in the same ratio.
Worked example
A hydraulic lift ram has a piston area of 0.0025 m². The pump supplies 8 MPa. Force = pressure × area = 8,000,000 Pa × 0.0025 m² = 20,000 N. If the implement weighs 15,000 N, the pressure needed is 15,000 ÷ 0.0025 = 6,000,000 Pa = 6 MPa. Reasoning: convert MPa to Pa before multiplying; the ram can lift 20 kN, so the 15 kN load is within capacity, ignoring friction and dynamic effects.
Traps
Using mm² instead of m²; mixing gauge and absolute pressure; confusing torque with power; forgetting that hydraulic force depends on area, not pump flow.