ASVAB Mechanical Comprehension — Gears, Pulleys and Drive Systems

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.

On a frictionless incline, the component of weight parallel to the incline pulls the object downward along the slope. This component = W × sin(θ), where W = weight and θ = incline angle. For 100 lbs at 30°: parallel force = 100 × sin(30°) = 100 × 0.5 = 50 lbs. To prevent sliding, an equal opposing force is needed (50 lbs up the incline). Incline plane physics: (1) FORCE PARALLEL to incline (driving sliding) = W × sin(θ); (2) FORCE PERPENDICULAR to incline (pressing into surface) = W × cos(θ). At 0° (flat ground): sin=0, parallel force=0, no sliding tendency; perpendicular = full weight. At 90° (vertical): sin=1, parallel = full weight (object in free fall); perpendicular = 0. Common angles to memorize: sin(30°)=0.5, sin(45°)≈0.707, sin(60°)≈0.866, sin(90°)=1; cos same values in reverse order. Inclined plane is a simple machine: mechanical advantage = length of incline / height = 1/sin(θ). A 30° ramp has MA = 1/0.5 = 2 (half the force to lift the same load to the same height, but you push twice as far). Common ASVAB MC inclined plane questions: force to hold/lift on incline, MA of ramp, work done sliding up incline. With friction, additional force = friction coefficient × W × cos(θ).

Galileo's principle (verified famously on the moon by Apollo 15's David Scott dropping a hammer and a feather): in a vacuum, all objects fall with the same acceleration regardless of mass. Acceleration due to gravity on Earth: g = 9.8 m/s² (≈ 32 ft/s²). This is because gravitational force on an object (weight = mg) is proportional to mass, but acceleration = force/mass — the mass cancels: a = F/m = (mg)/m = g. So both objects accelerate at g. In AIR (real world), air resistance affects falling objects, and heavier/denser objects do fall faster (a feather falls slower than a rock because air resistance is more significant relative to feather's weight). Terminal velocity occurs when air resistance equals weight — the object falls at constant velocity. Free fall equations: (1) velocity at time t: v = gt (starting from rest); (2) distance fallen in time t: d = ½gt²; (3) velocity after falling distance d: v = √(2gd). Examples: object falls 1 second → velocity 9.8 m/s, distance 4.9 m; falls 3 seconds → velocity 29.4 m/s, distance 44.1 m. Projectile motion: horizontal motion is independent of vertical motion. An object dropped from a height and one fired horizontally from the same height hit the ground at the same time (assuming flat ground and no air resistance). ASVAB MC tests fundamental physics concepts; precise calculation less common than conceptual understanding.

Pascal's principle: pressure applied to a confined fluid is transmitted equally throughout the fluid. Pressure = Force / Area. In a hydraulic system, pressure is the same in both pistons; force differs based on area. P = F/A is constant: F₁/A₁ = F₂/A₂. Calculation: F₁/A₁ = 100/2 = 50 psi. F₂ = P × A₂ = 50 × 20 = 1000 lbs. The larger piston multiplies force by the area ratio (10:1 in this case). Trade-off: distance moved is reduced by the same ratio. If small piston moves 10 inches, large piston moves 1 inch (volume is conserved: A₁ × d₁ = A₂ × d₂). Work in = work out (ignoring friction): 100 lbs × 10 in = 1000 lbs × 1 in = 1000 in-lbs. Real-world applications: hydraulic brakes (small force at pedal → large force at brake pad), hydraulic lifts (small pump pressure → lift heavy vehicles), hydraulic presses, excavator arms. Mechanical advantage of hydraulic system = A₂/A₁ (area ratio). Pneumatic systems work similarly but with compressed gas (less common in ASVAB). Fluid properties relevant to ASVAB MC: density, pressure increases with depth (P = ρgh in a fluid column), buoyancy (Archimedes' principle: buoyant force = weight of fluid displaced), incompressibility of liquids (vs compressibility of gases).

Archimedes' principle (3rd century BC): a body fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of the fluid it displaces. An object floats when the buoyant force equals its weight. A solid block of steel has density ~7,850 kg/m³, much denser than water (1,000 kg/m³); it sinks. But a steel SHIP is mostly hollow — its overall average density (steel + air inside + cargo) is LESS than water. As the ship sits in water, it displaces water; the buoyant force pushes up. The ship sinks deeper until enough water is displaced for the buoyant force to equal the ship's total weight. Then it floats in equilibrium. Loading more cargo: ship displaces more water (sits lower), buoyant force increases, equilibrium maintained until maximum capacity. Plimsoll line (load line): marking on ships indicating the maximum safe loading depth. Variables affecting buoyancy: (1) Fluid density — same object floats higher in dense water (salt water) than in fresh water; ships displace less salt water for the same buoyant force (which is why ships have different load lines for fresh and salt water); (2) Object density — less dense objects float higher or float entirely; (3) Object shape — shape affects how much fluid is displaced (a flat steel sheet sinks; the same steel formed into a bowl shape floats). Submarines control buoyancy by changing internal volume (ballast tanks fill with water to sink, empty to rise). Hot air balloons use the same principle in air (warm air less dense than cold air → buoyancy). Hydrometers measure fluid density by how deep they sink.

For a symmetric load on a symmetrically supported beam, each support carries half the load. 200 lbs / 2 = 100 lbs at each support. (Note: this assumes the beam's own weight is negligible; if the beam itself weighs 50 lbs, then each support holds 100 + 25 = 125 lbs.) For ASYMMETRIC loads, use the lever/torque principle: torque around one support = torque around the other. If a 200-lb weight is placed 1/4 of the way from support A to support B: support A holds 3/4 × 200 = 150 lbs (because A is farther from the weight in terms of which side bears more — actually closer to the weight bears more). Wait, the rule: the support CLOSER to the load bears MORE. If load is 1/4 from A: distance from A = 1/4 of beam length, distance from B = 3/4. Force at B × 3/4 = Force at A × 1/4. With total weight 200 lbs: F_A = 200 × (3/4) = 150 lbs (at the closer support A), F_B = 200 × (1/4) = 50 lbs (at the farther support B). Verify: F_A + F_B = 200 ✓; torques balance ✓. Beam questions on ASVAB MC: (1) Identify which support bears more weight (the one closer to the load); (2) Calculate the load on each support; (3) Handle cantilever beams (only one support); (4) Add the beam's own weight when given. Cantilever beams: full load and reaction force at the single support; bending moment increases with distance from support. Structural support principles: triangular shapes are strongest; arches transfer load to abutments; suspension cables work in tension; columns work in compression.

Work = Force × Distance (when force and distance are in the same direction). Here: 50 lbs × 4 ft = 200 ft-lbs of work. Units: in US customary, ft-lbs; in SI, Joules (1 J = 1 N·m); 1 ft-lb ≈ 1.356 J. Work principles: (1) Only force IN THE DIRECTION OF MOTION does work. Carrying a box horizontally at constant height: gravity acts vertically; horizontal motion is perpendicular to gravity; no work is done against gravity (though work is done against friction); (2) Lifting AGAINST gravity: work = weight × height; (3) Sliding against friction: work = friction force × distance; (4) If force varies, work = area under force-distance graph. Energy: kinetic (motion) = ½mv²; gravitational potential = mgh; both measured in same units as work. Conservation of energy: total energy in a closed system is constant; transforms between forms. Power: rate of doing work = Work / Time. Units: Watts (J/s) or horsepower (1 hp = 550 ft-lbs/sec = 746 W). Example: lifting 50 lbs 4 ft in 2 seconds = 200 ft-lbs / 2 sec = 100 ft-lbs/sec = 100/550 hp ≈ 0.18 hp. Higher power = same work faster, OR more work in same time. Mechanical advantage doesn't reduce work — it spreads force over distance: lifting 100 lbs 1 ft (100 ft-lbs work) using a 2:1 lever requires 50 lbs over 2 ft (50 × 2 = 100 ft-lbs) — same work, less force needed.

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.