Simple Machines (Levers, Pulleys, Gears): Practice Questions & Explanations

Three classes of levers, distinguished by the positions of fulcrum, effort, and load: (1) FIRST-CLASS: fulcrum is BETWEEN effort and load. Examples: seesaw, scissors, crowbar, pliers, claw hammer pulling nails. Effort and load move in opposite directions. Mechanical advantage can be >1, =1, or <1 depending on lengths. (2) SECOND-CLASS: load is BETWEEN fulcrum and effort. Examples: wheelbarrow, nutcracker, bottle opener, door (hinge=fulcrum, doorknob=effort, weight=load). Always provides mechanical advantage >1 (force multiplier). Effort and load move same direction. (3) THIRD-CLASS: effort is BETWEEN fulcrum and load. Examples: tweezers, fishing rod, broom, human forearm (elbow=fulcrum, biceps=effort, hand/load = third class). Always has mechanical advantage <1 (speed multiplier — gives distance/speed at cost of force). Effort and load move same direction. Mnemonic 'F-L-E' for what's in the MIDDLE: First class = Fulcrum middle; second class = Load middle; third class = Effort middle. Mechanical advantage = effort arm length ÷ load arm length. ASVAB MC frequently asks identification and MA calculation.

Pulley mechanical advantage equals the number of rope segments supporting the load. (1) FIXED PULLEY (single, attached to a fixed point): MA = 1. It changes direction (pulling down to lift up) but does not reduce the force needed. The load and effort move equal distances. Example: a flag-raising pulley. (2) MOVABLE PULLEY (attached to the load itself): MA = 2. Two rope segments support the load, halving the effort needed, but doubling the distance the rope is pulled. (3) COMPOUND PULLEY SYSTEMS (block and tackle): MA = number of supporting rope segments. A 4-pulley system with 4 supporting segments has MA = 4 — one-quarter the force, four times the distance. Trade-off principle (universal in simple machines): mechanical advantage = force multiplied / distance reduced. Force × Distance = Work; ignoring friction, work in = work out. A 4:1 pulley needs 1/4 the force but pulls 4 times the rope. Real-world losses to friction reduce ideal MA. Counting supporting segments: count the rope segments under the movable pulley(s) that actually support the load, not the rope you're pulling on (which is on top). For typical ASVAB problems, draw the system and count.

Gear ratio = (teeth of driven gear) / (teeth of driver gear) = 60/20 = 3:1. When a smaller gear drives a larger gear, the larger gear rotates SLOWER but with more torque. Calculation: gear A (20 teeth, 6 rotations) — total teeth moved = 20 × 6 = 120 teeth. Gear B has 60 teeth, so 120 / 60 = 2 rotations. General principle: teeth pass at the same rate where gears mesh. Rotations of A × teeth of A = rotations of B × teeth of B. Gear systems: (1) SMALL driving LARGE: torque multiplied, speed reduced (used to lift heavy loads slowly); (2) LARGE driving SMALL: speed multiplied, torque reduced (used in bicycles for fast pedaling at high gear); (3) DIRECTION: meshing gears rotate in OPPOSITE directions; an idler gear between them keeps them rotating in the same direction; chain or belt drives between gears keep them rotating in the SAME direction. Gear trains: multiple gears in series — overall ratio is product of individual ratios. Bicycle gears: smaller front × larger back = easier pedaling (climbing); larger front × smaller back = faster speeds (flat ground). Common ASVAB MC questions: gear ratios, rotation counts, rotation direction, torque multiplication.

Screw pitch = distance the screw advances per revolution = 1 / (threads per inch). 10 threads per inch → pitch = 1/10 = 0.1 inch per revolution. A screw is essentially an inclined plane wrapped around a cylinder. Mechanical advantage of a screw = (2π × radius of handle/screw) / pitch. Example: a screw with 10 threads per inch and a wrench handle 6 inches from center: MA = (2π × 6) / 0.1 = 37.7 / 0.1 = 377. The operator pushes the wrench around a 37.7-inch circumference to advance the screw 0.1 inch — huge force multiplication. This is why screws and wedges can split logs, lift cars (jacks), and clamp materials with relatively modest applied force. Bolts and nuts use the same principle. Screws come in many designs: machine screws (uniform threads for nuts), wood screws (tapered for wood), self-tapping screws (cut their own threads), sheet metal screws, etc. Wedges: similar inclined-plane concept used to split or hold (axes, chisels, doorstops). Combined simple machines: most real-world devices use combinations — a bicycle has wheels and axles, gears (modified wheels), levers (pedals and crank arms), and pulleys (chain drive). Car jacks combine a screw with a lever (the handle). Practical ASVAB MC scenarios test recognizing screws in tools and calculating advancement per rotation.

Wheel and axle is a simple machine where two cylinders of different radii are fixed together and rotate together. Mechanical advantage = radius of wheel / radius of axle = 12/3 = 4. Force at axle = 25 × 4 = 100 lbs. The wheel (larger radius) gets the input force; the axle (smaller radius) outputs the higher force. Trade-off: the axle moves a shorter distance — if the wheel rotates once and covers 2π(12) ≈ 75 inches at its edge, the axle rotates once and covers 2π(3) ≈ 19 inches. The same work (Force × Distance) is done by both. Wheel and axle applications: (1) STEERING WHEEL — large wheel turns steering column (axle) — force multiplier; (2) SCREWDRIVER — handle is the wheel, shaft is the axle — force multiplier for turning screws; (3) DOORKNOB — knob is wheel, latch mechanism is axle; (4) PENCIL SHARPENER — handle is wheel; (5) WINDLASS — well winch, anchor windlass; (6) FAUCET HANDLE — handle is wheel, valve stem is axle. Reverse application (speed multiplier instead of force multiplier): bicycle wheel — pedals/crank apply force at small radius (the axle), wheel rim (large radius) moves faster but with less force per unit of pedal force. Gears connecting wheels and axles transmit power efficiently in machines. The lever family (lever, wheel/axle, pulley) all share the principle of trading force for distance through rotational geometry.

The six classical simple machines (Renaissance scientists, building on ancient Greek engineering): (1) LEVER — rigid bar pivoting on a fulcrum; (2) WHEEL AND AXLE — two cylinders of different radii fixed together; (3) PULLEY — wheel with a grooved rim for a rope or cable; (4) INCLINED PLANE — sloped surface; (5) WEDGE — two inclined planes back-to-back, used to split (axes, chisels) or hold (doorstops, nails); (6) SCREW — inclined plane wrapped around a cylinder. A battery is not a simple machine — it's an electrochemical device that stores and provides electrical energy. Simple machines change the direction or magnitude of mechanical force; they don't create energy, only transform mechanical advantage. All complex machines are combinations of simple machines: (1) BICYCLE — wheel and axle (wheels), levers (pedals, crank, handlebars), pulleys/chain (gear system), wedges (rim brakes); (2) SCISSORS — two first-class levers sharing a fulcrum; (3) CAN OPENER — lever (handles), wheel and axle (turning mechanism), wedge (cutting blade); (4) WHEELBARROW — second-class lever; (5) CAR JACK — screw and lever; (6) CRANE — pulleys, levers, wheels. The principles of work, energy, and mechanical advantage learned through simple machines apply to all mechanical systems. ASVAB MC questions on simple machines test identification, calculation of mechanical advantage, and application to real tools.

MESHING gears rotate in OPPOSITE directions. Their teeth interlock at the contact point; as one gear pushes its tooth into the other, that contact point on each gear must move in the same linear direction at that instant — but since they're rotating around different axes, this means opposite rotational directions. Common in: car transmissions (gears alternate direction); clock mechanisms; rotating machinery. To keep two gears rotating in the SAME direction, an IDLER GEAR can be placed between them. The idler reverses direction once (from the driver), then reverses again (to the driven gear), resulting in net same direction. Idlers don't change the gear ratio (their teeth count cancels out) but they: (1) Change rotation direction; (2) Bridge a gap between gears that can't mesh directly; (3) Take up slack or stress in chain drives. CHAIN/BELT drives connect gears (sprockets/pulleys) and keep them rotating in the SAME direction (the chain only goes one way around its loop). REVERSED belts (crossed) make them rotate opposite — used in old machinery but uncommon today. PLANETARY GEAR SYSTEMS: sun gear in center, planet gears around it, ring gear around them; complex rotation relationships; used in automotive automatic transmissions and many other applications. RACK AND PINION: a circular pinion gear meshes with a straight rack; converts rotation to linear motion (or vice versa); used in steering systems (turn wheel rotates pinion which slides rack linking to wheels), elevators, machine tools. ASVAB MC commonly tests gear direction prediction in gear trains.

MA (lever) = effort arm ÷ load arm = 6 ÷ 2 = 3. A mechanical advantage of 3 means 1 pound of effort lifts 3 pounds of load.

MA (wheel and axle) = wheel radius ÷ axle radius = 12 ÷ 3 = 4.

SCREW PITCH: 30 threads per inch means each full rotation advances the screw 1/30 inch. 3 rotations × (1/30 inch per rotation) = 3/30 = 0.10 inches. The screw is a simple machine (inclined plane wrapped around a cylinder) that converts rotational force (torque) into linear force and motion. MORE THREADS PER INCH = finer pitch = more mechanical advantage per turn = less advance per turn. FEWER THREADS PER INCH = coarser pitch = less mechanical advantage = more advance per turn.

An INCLINED PLANE (ramp) reduces the FORCE needed to raise an object by spreading the work over a greater DISTANCE. ASVAB Mechanical Comprehension tests simple machines. Instead of lifting straight up (high force, short distance), you push up the ramp (less force, longer distance) — the work (force × distance) is about the same, but the force is reduced. A LONGER, more gradual ramp requires less force than a short, steep one. This force-distance trade-off (mechanical advantage) applies to all simple machines and is commonly tested.

A SCREW is essentially an INCLINED PLANE wrapped around a cylinder. ASVAB Mechanical Comprehension tests simple machines. The threads of a screw form a spiral inclined plane; turning the screw converts rotational motion into linear motion and provides mechanical advantage (a screw with closer threads requires more turns but less force). The six simple machines: lever, inclined plane, wheel and axle, pulley, wedge, and screw. A WEDGE is two inclined planes back-to-back. Recognizing the screw as a wrapped inclined plane is commonly tested.

A single fixed pulley (attached to a fixed point overhead) changes the direction of the force — letting you pull down to lift a load up — but it does not reduce the amount of force required; you still must pull with a force equal to the load's weight. To gain a mechanical advantage (reduce the force needed), you use a movable pulley or a combination of pulleys (a block and tackle), which trades reduced force for a longer length of rope pulled. Understanding that a fixed pulley redirects force while movable/multiple pulleys multiply it is a frequently tested simple-machine concept.

When a small gear meshes with a larger gear, the smaller gear turns faster but with less torque, while the larger gear turns slower but with more torque. This is because the teeth move at the same rate where they mesh, so the smaller gear must complete more revolutions to keep up. Gears trade speed for torque (turning force) just as levers and pulleys trade force for distance. Meshed gears also turn in opposite directions. Understanding the speed-versus-torque tradeoff in gear pairs — small gear faster/less torque, large gear slower/more torque — is essential mechanical comprehension content.

An inclined plane (ramp) makes raising a heavy object easier by reducing the force needed to move it — but over a longer distance. Instead of lifting the full weight straight up, you push it up the gentler slope with less force, though you must move it farther. The total work (force × distance) is about the same (ignoring friction), but the reduced force is easier to apply. This is the mechanical advantage of a ramp: a longer, gentler ramp requires less force than a short, steep one. The inclined plane is one of the basic simple machines that trade force for distance.

Mechanical advantage is the factor by which a simple machine multiplies the input (effort) force. For example, a mechanical advantage of 4 means the machine outputs four times the force you put in. It is calculated as the output force divided by the input force (or, ideally, the distance the effort moves divided by the distance the load moves). Machines like levers, pulleys, ramps, and gears provide mechanical advantage by trading reduced force for increased distance — they do not create energy. A higher mechanical advantage means less force is needed, but over a greater distance. This concept ties together all the simple machines.