Forces, Work, and Simple Machines

Format and Why Concepts Beat Calculators

The Mechanical Comprehension Test (MCT) is a computer-adaptive subtest of the Selection Instrument for Flight Training (SIFT) with a 15-minute time limit and a variable number of items (commonly 20-30). Because it is adaptive, correct answers feed you harder questions; there is no single fixed count, and the older "40 questions" claim describes a ceiling, not your actual test. The SIFT scaled score runs 20 to 80, and 40 is the minimum passing score for Army aviation; most aviation programs want 50 or higher to be competitive.

The penalty rule matters: if you leave too many adaptive items unanswered, your score is reduced. Pace at roughly 30-40 seconds per item, answer every question, and lean on relationships rather than long arithmetic.

Force, Mass, Weight, and Work

If you hold a 50-lb box motionless, distance is zero, so work is zero even though you feel strain. Likewise, carrying a box horizontally does little work against gravity because the lifting force is vertical while motion is horizontal.

The Six Simple Machines and Mechanical Advantage

Mechanical advantage (MA) = load / effort = (distance effort moves) / (distance load moves). MA above 1 multiplies force; MA below 1 multiplies speed or distance. A machine never multiplies both force and distance at once.

Levers

Classify a lever by where the fulcrum sits relative to effort and load. Balance follows the lever law:

effort x effort-arm = load x load-arm

Worked example: A 30-lb child sits 4 ft from a seesaw fulcrum. To balance, a 60-lb child must sit at d where 60 x d = 30 x 4 = 120, so d = 2 ft. The heavier child sits closer; the lighter child sits farther.

Pulleys

Count the rope segments that directly support the moving load; that count is the MA.

Lifting a 400-lb engine with a 4-segment tackle needs only 100 lb of effort, but you must pull 4 ft of rope for every 1 ft the engine rises.

Inclined Plane, Wedge, Screw, Wheel-and-Axle

• Inclined plane: MA = ramp length / height. A 12-ft ramp to a 3-ft dock gives MA = 4.
• Wedge: a moving inclined plane (axe, chisel); long and thin equals higher MA.
• Screw: an inclined plane wrapped around a cylinder; finer threads (more turns per inch) raise MA.
• Wheel-and-axle: MA = wheel radius / axle radius (steering wheel, doorknob, screwdriver).

Gears, Friction, and a Fast-Solve Routine

Gears

Two rules answer most gear items:

1. Meshed gears spin in opposite directions. In a chain of three, gears 1 and 3 turn the same way. A belt (not crossed) keeps both pulleys spinning the same direction.
2. Gear ratio = driven teeth / driver teeth. A small driver turning a large driven gear gives more torque but less speed; a large driver turning a small gear gives more speed but less torque.

Worked example: A 10-tooth driver meshes with a 40-tooth gear. Ratio = 40/10 = 4, so the big gear turns at 1/4 the speed with 4x the torque. If the small gear spins at 800 rpm, the large gear spins at 200 rpm.

Friction

Friction always opposes motion and converts kinetic energy into heat. That is why brakes get hot and why a heavier sled is harder to start sliding.

Energy and Conservation

Energy is never created by a machine. Potential energy (PE = m x g x h) converts to kinetic energy (KE = 1/2 x m x v^2) as an object falls. A roller coaster is fastest at the lowest point because PE has fully converted to KE.

Four-Question Solve Routine

When a machine question appears, ask in order:

1. What is the load (the resistance being moved)?
2. Where is the effort applied?
3. Where is the pivot, fulcrum, or support?
4. Is the machine trading force for distance, or distance for force?

Sketch it. A clean diagram with the fulcrum and arms labeled solves most SIFT mechanical items faster than rereading the stem, and it stops you from picking the tempting reversed-ratio answer.