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Mechanical Aptitude: the syllabus
You cannot prepare for a question type you do not know exists. This is every concept the mechanical aptitude section draws from, taught with worked examples, so nothing on test day is a surprise. Learn a topic, then drill it.
What a lever really does
A lever is a rigid bar that pivots on a fixed point called the fulcrum. You push on one part of the bar (the effort) to move a resistance somewhere else on the bar (the load). The lever does not create force out of nothing. It trades distance for force: if your end of the bar swings five times farther than the load end, the load end pushes five times harder than you do.
Force is measured in newtons (N). One newton is a small push, about the weight of a medium apple resting in your hand. A more useful anchor: gravity pulls on a 10 kg mass with a force of about 100 N, so 100 N feels like holding a 10 kg dumbbell or a full water jug in one hand. When a test question says a firefighter pushes with 100 N, picture leaning on a bar with about that much of your body weight.
The rule that governs every lever is balance of moments: force times distance from the fulcrum must match on both sides. A small force far from the fulcrum can balance a large force close to it. That is the entire secret of the pry bar, and it is why the numbers in lever questions always come down to comparing two distances.
The three classes: find what sits in the middle
Every lever question starts with the same move: identify which of the three parts (fulcrum, load, effort) sits between the other two. First-class levers have the fulcrum in the middle, like a pry bar over a block, a seesaw, or scissors. The effort and load move in opposite directions, and the lever can multiply force, multiply speed, or just reverse direction, depending on where the fulcrum sits.
Second-class levers have the load in the middle, between the fulcrum and the effort. A wheelbarrow is the classic case: the wheel axle is the fulcrum, the debris sits in the tray, and you lift the handles at the far end. Because the effort arm is always longer than the load arm, a second-class lever always multiplies force. Bottle openers and some door-forcing techniques work the same way.
Third-class levers have the effort in the middle, between the fulcrum and the load. Your forearm, a broom, and a pike pole swung with a fixed lower hand all fit here. The effort arm is always shorter than the load arm, so these levers reduce force but multiply speed and reach. That is a feature, not a flaw: it lets a small hand movement sweep a tool head through a big, fast arc.
Effort arm, load arm, and the mechanical advantage formula
The effort arm is the distance from the fulcrum to where you push. The load arm is the distance from the fulcrum to the load. Mechanical advantage (MA) is simply the effort arm divided by the load arm. An MA of 5 means the lever multiplies your force 5 times, and it also means your hand must move 5 times farther than the load. Force multiplied and distance divided, always by the same number.
To find the output force, multiply your effort by the MA. To find the required effort, divide the load by the MA. Keep both distances in the same units before dividing; centimetres with centimetres, metres with metres. Most wrong answers on lever questions come from flipping the ratio, so check the result against common sense: a long handle and a short tip should make the force bigger, never smaller.
Levers on the fireground
Forcible entry is applied lever theory. A pry bar or the fork end of a Halligan set near a door jamb is a first-class lever: the fulcrum is the contact point, the short load arm is the few centimetres between fulcrum and door, and the long handle is your effort arm. This is why crews are taught to set the tool deep and push at the very end of the handle: both moves stretch the effort arm and raise the MA.
A pike pole shows how one tool can be different lever classes depending on grip. Punch straight up through a ceiling and it is a simple pushed rod. Sweep debris with the lower hand fixed and the upper hand driving partway up the shaft, and it becomes a third-class lever: less force at the head, but far more speed and reach. Test writers love this distinction, so practise naming the class from the grip described, not from the tool's name.
Worked example
A firefighter forces a window with a 120 cm pry bar. The fulcrum is set 20 cm from the tip that contacts the frame. The firefighter pushes down on the far end of the handle with 80 N. How much force does the tip apply to the frame, ignoring losses?
- 1. Identify the lever class. The fulcrum sits between the effort (the handle end) and the load (the tip against the frame), so this is a first-class lever.
- 2. Find the two arms. The load arm is 20 cm (fulcrum to tip). The effort arm is the rest of the bar: 120 cm minus 20 cm equals 100 cm.
- 3. Compute the mechanical advantage: effort arm divided by load arm, so 100 divided by 20 equals 5.
- 4. Multiply the effort by the MA: 80 N times 5 equals 400 N at the tip.
- 5. Sanity check the trade-off: the handle end must sweep 5 times farther than the tip moves, which matches the big swing you make with a pry bar for a small movement at the jamb.
About 400 N of force at the tip.
Key facts to know cold
- Mechanical advantage of a lever equals effort arm divided by load arm.
- Classify a lever by what sits in the middle: fulcrum in the middle is first class, load in the middle is second class, effort in the middle is third class.
- Second-class levers (wheelbarrow) always multiply force; third-class levers (pike pole sweep, forearm) always multiply speed and reach at the cost of force.
- Whatever a lever multiplies force by, it divides distance by the same number. No lever multiplies both.
- 100 N is roughly the weight of a 10 kg mass, about a full water jug held in one hand.
- A longer handle or a deeper tool set increases the effort arm, which increases the mechanical advantage.