Mechanical Reasoning
Mechanical Reasoning tests basic physical principles behind fireground tools and systems: levers, pulleys, gears, friction, pressure, and fluid behavior. You do not need engineering mathematics, but you must apply relationships accurately and avoid everyday guesses.
Core concepts
- Lever: mechanical advantage equals effort-arm length divided by load-arm length, measured from the fulcrum. A first-class lever has the fulcrum between load and effort; a second-class lever has the load between; a third-class lever has the effort between and gives a force disadvantage.
- Pulley: a fixed pulley changes direction but has mechanical advantage 1. A movable pulley supported by two rope segments has ideal mechanical advantage 2. Count supporting rope segments, not total pulleys.
- Gears: meshing gears turn in opposite directions. Gear ratio equals driven teeth divided by driving teeth. A larger driven gear turns slower and with more torque.
- Pressure: pressure equals force divided by area. The same force over a smaller area produces higher pressure. Hydrostatic pressure depends on depth and density, not on total volume or container shape. Fresh water rises about 0.433 psi per foot of height.
- Friction: friction opposes motion; rougher surfaces and greater normal force increase it; rollers, lubricants, and smooth surfaces reduce it.
Worked example
A 240-pound load sits 3 feet from a lever's fulcrum. The effort is applied 12 feet from the fulcrum. Ignoring friction and the lever's weight, what effort balances the load? Mechanical advantage = effort arm divided by load arm = 12 divided by 3 = 4. Required effort = 240 divided by 4 = 60 pounds. The common error is to use the total lever length of 15 feet as the effort arm, which would produce a wrong answer of 48 pounds.
Traps that cost marks
- Assuming a fixed pulley multiplies force.
- Using the total bar length instead of the distance from the fulcrum.
- Thinking pressure depends on container volume rather than depth.
- Mixing force in pounds with pressure in psi.
- Forgetting that meshing gears reverse direction.
- Ignoring friction or tool weight when the question says ideal.