Mechanical Reasoning - FRNSW Cognitive Test
Mechanical reasoning in the FRNSW cognitive test examines intuitive physics: levers, pulleys, gears, pressure, force, friction and mechanical advantage. Questions are usually qualitative or use simple numbers, and they reward a clear mental model of what is pushing, pulling or turning - not memorised formulae alone.
Core rules
- Moments: for a lever in balance, effort × effort arm = load × load arm. The arm is the perpendicular distance from the fulcrum, not the total length of the lever.
- Mechanical advantage = load ÷ effort. For an ideal lever it also equals effort arm ÷ load arm. A longer effort arm reduces the effort needed.
- Pulleys: count the rope sections supporting the movable load, not the number of pulleys. A single fixed pulley changes direction but gives no mechanical advantage.
- Gears: meshing gears turn in opposite directions. The smaller gear turns faster; ratio = teeth on driven gear ÷ teeth on driving gear.
- Pressure = force ÷ area. The same force over a smaller area produces higher pressure; hydraulic systems transmit pressure and can multiply force through different piston areas.
- Friction opposes motion and converts work to heat; it reduces ideal mechanical advantage.
Worked example
A class 1 lever has a 600 N load 0.4 m from the fulcrum. The effort is applied 1.2 m from the fulcrum on the other side. What effort balances the load? Reasoning: moments must balance. Load moment = 600 × 0.4 = 240 N·m. Effort moment = effort × 1.2. So effort = 240 ÷ 1.2 = 200 N. Mechanical advantage = load ÷ effort = 600 ÷ 200 = 3, matching effort arm ÷ load arm = 1.2 ÷ 0.4 = 3. Using the total lever length, 1.6 m, would give 150 N - a distractor built on the wrong distance.
Traps that cost marks
- Using total length instead of the distance from the fulcrum.
- Swapping load and effort arms, which inverts the advantage.
- Counting pulleys rather than supporting rope strands.
- Assuming meshed gears turn the same way.
- Treating pressure and force as interchangeable, or ignoring area.
- Forgetting that friction makes the real effort greater than the ideal calculation.