3.2 Levers, Fulcrums, and Torque

Every lever, from a halligan to a hydrant key, is the same three-part story: effort (where you push or pull), load (what you are moving or holding), and fulcrum (the pivot the bar rotates about). Mechanical Reasoning items hide those three labels in a fireground-looking sketch. Your job is to find them, name the class, then decide what happens to direction and force.

The three classes

Class 1: the fulcrum sits between effort and load. A halligan forked in a door jamb is the clean fireground picture. The fork against the jamb is the fulcrum, the shaft in your hands is the effort, and the door is the load. Push the shaft one way and the load moves the other way. A seesaw, a pair of pliers, and a crowbar used as a pry are the same pattern. A T-handled hydrant key is class 1 in rotation: the stem is the fulcrum axis, one arm is effort, and the spindle resistance is the load.

Class 2: the load sits between effort and fulcrum. A sack truck or wheelbarrow of rolled hose is the usual picture. The wheel is the fulcrum, the hose in the tray is the load, and the handles are the effort. Effort and load move the same way — both rise when you lift the handles. A nutcracker is class 2. So is a wheeled stretcher of charged line if you lift the far end: the wheels are the fulcrum, the line is the load, your lift is the effort.

Class 3: the effort sits between fulcrum and load. A pike pole under a ceiling sheet is the fireground standard. The rear hand on the butt is the fulcrum (it mostly stops the pole from dropping), the front hand on the shaft is the effort, and the hook is the load. Effort and load move the same way, but you pay for the reach with extra effort. Tweezers, a broom, and a human forearm are class 3.

Raising a ladder from the ground is a useful edge case. The butts on the ground are the fulcrum. The ladder's weight acts at its centre of gravity. If you lift between the butts and that centre, you are in class 3. If you walk your hands beyond the centre of gravity, you have moved into class 2. The figure, not a memory of drill-ground technique, decides the class.

Class comparison

Torque is turning effect

Torque is the turning effect of a force about a pivot. For aptitude diagrams, use:

torque = force × perpendicular distance from the pivot to the line of the force

The word that does the work is perpendicular. If a firefighter pushes a hydrant key along a line that is not square to the arm, only the component of the push that is perpendicular to the radius produces torque. A 200 N push on a 0.40 m arm, square to the arm, is 80 N·m. The same 200 N at 0.40 m but 30 degrees off square is smaller, because the perpendicular distance (the moment arm) has shrunk. Figures love a force arrow that is not drawn at 90 degrees.

Mechanical advantage (MA) of a lever, in the ideal frictionless case, is effort-arm length divided by load-arm length. Equivalently, MA = load / effort. If a halligan has 1.20 m from hands to fulcrum and 0.30 m from fulcrum to the door, MA = 4. A 400 N door resistance then needs about 100 N of effort, ignoring losses. Double the effort arm and the required effort halves. Halve the load arm (move the fulcrum closer to the door) and the required effort also halves. Candidates who remember "longer bar is always better" miss the case where the extra length is on the load side.

Worked numbers, hydrant key: two keys, same 150 N effort, same square push. Key A has a 0.25 m arm; key B has a 0.50 m arm. Torque on B is twice the torque on A. If the stem resistance is 60 N·m, key A cannot start the spindle (37.5 N·m) and key B can (75 N·m). The diagram will not usually ask you to name newton-metres. It will ask which key turns, or which firefighter has the easier job.

Worked numbers, pike pole: fulcrum at the rear hand, load 1.80 m from that hand, effort (front hand) 0.60 m from that hand. MA = 0.60 / 1.80 = 1/3. A 90 N panel load needs about 270 N of effort. That is why class 3 feels weak even though it is the right tool for reach.

Keep this list of lever traps:

• Calling every long bar class 1
• Measuring along a slanted force instead of using perpendicular distance
• Forgetting that class 1 reverses direction while class 2 and class 3 do not
• Treating the halligan adz as the load when the figure shows the fork as the pivot
• Importing rust and paint friction when the figure is an ideal lever
• Mixing torque (a turning effect) with the kinetic-energy items that belong in Chapter 4

If a figure shows a spinning wheel that then hits a block, or a falling tool converting height into speed, that is energy and motion, not a lever class. Leave it for Chapter 4.