ASVAB Mechanical Comprehension — Force, Motion, and Fluids

Newton's Second Law: F = ma. Solve for a: a = F/m = 20 N / 5 kg = 4 m/s². Always check units: Newton = kg·m/s², so N/kg = m/s² ✓. Common ASVAB MC F=ma scenarios: (1) Given mass and acceleration, find force; (2) Given force and mass, find acceleration (this question); (3) Given force and acceleration, find mass; (4) With friction or other opposing forces, NET force = ma. Example with friction: if friction force = 5 N opposing the 20 N push, net force = 15 N, acceleration = 15/5 = 3 m/s². Force units: Newton (SI, kg·m/s²) or pound-force (US customary, kg slugs × ft/s²). Mass vs weight: mass is matter (kg); weight is the force of gravity on mass (W = mg, in N). A 5 kg object weighs 5 × 9.8 = 49 N on Earth, 5 × 1.6 = 8 N on the Moon. Pounds: 'lb' often refers to weight (pound-force, lbf) but sometimes mass (pound-mass, lbm); ASVAB usually uses pounds as weight. Conversions: 1 kg ≈ 2.2 lbs; 1 lb ≈ 4.45 N. Friction: static friction prevents motion (up to a maximum); kinetic friction acts on moving objects (usually less than max static). Coefficient of friction (μ) × normal force = friction force. ASVAB MC may include friction conceptually but rarely calculation with μ.

States of matter properties: SOLID — fixed shape and volume; particles vibrate in place; strong intermolecular forces; nearly incompressible. LIQUID — fixed volume, no fixed shape (takes container shape); particles flow past each other; moderate intermolecular forces; nearly incompressible (compressible by only ~5% even under extreme pressure). GAS — no fixed shape OR volume; expands to fill any container; particles move freely with weak interactions; highly compressible (volume changes significantly with pressure). PLASMA — ionized gas, fourth state. Implications for ASVAB MC: (1) HYDRAULIC systems use liquids precisely BECAUSE they're incompressible — pressure transmits efficiently; (2) PNEUMATIC systems use compressed gas, providing spring-like behavior and energy storage; (3) Gas laws: pressure × volume = constant at constant temperature (Boyle's Law); volume increases with temperature (Charles' Law); pressure increases with temperature in fixed volume (Gay-Lussac's Law); combined: PV/T = constant. (4) Fluid (both liquid and gas) physics: pressure increases with depth (P = ρgh); buoyancy works in both; flow rate × area = constant (continuity equation); Bernoulli's principle relates pressure to velocity (faster flow = lower pressure — explains airplane lift, perfume atomizers, carburetors). Density: solids generally densest, liquids next, gases least dense; exceptions exist (mercury liquid denser than many solids; some solids less dense than liquid water like ice — which is why ice floats).

The triangle is the strongest fundamental shape because it's the only polygon that cannot deform without bending or breaking a side. A square or rectangle can collapse into a parallelogram (the angles change while side lengths remain constant). A triangle's three fixed sides constrain its three angles — geometric rigidity. Engineering applications: (1) BRIDGE TRUSSES — networks of triangles (Pratt, Warren, Howe, K-trusses); each triangle transfers load through its members in tension or compression; (2) ROOF TRUSSES — triangular structure supports roof loads efficiently; (3) GEODESIC DOMES — triangulated panels create strong, lightweight curved structures; (4) CRANE BOOMS — triangulated lattice; (5) TOWER CRANES, TRANSMISSION TOWERS — triangulated lattice frame; (6) BICYCLE FRAMES — diamond frame (essentially triangles); (7) AIRCRAFT WINGS — triangulated internal structure. Other strong shapes for specific purposes: (1) ARCHES — convert vertical loads into compression along the curve, transferring to abutments; ancient Roman engineering; modern bridges; (2) DOMES — 3D arches, strong against external pressure; (3) CYLINDERS — strong against internal pressure (gas tanks, pipes); (4) CIRCLES — efficient for distributing radial loads; (5) I-BEAMS — combine flanges (resist bending) with web (resists shear) — common in steel construction. Forces in structures: TENSION (pulling apart, e.g., cables in suspension bridges); COMPRESSION (squeezing together, e.g., columns supporting roofs); SHEAR (sliding parallel surfaces); BENDING (combination of tension and compression in different parts of the member); TORSION (twisting). Engineers select shapes and materials to handle expected loads efficiently.

Conservation of momentum: in any collision (elastic or inelastic), total momentum before = total momentum after, IF no external forces act on the system. Momentum p = mass × velocity. Before collision: p_A = 10 × 5 = 50 kg·m/s; p_B = 5 × 0 = 0; total = 50 kg·m/s. After collision (objects stick = perfectly inelastic): combined mass = 10 + 5 = 15 kg; total momentum still 50 kg·m/s; velocity = momentum / mass = 50/15 = 3.33 m/s. Types of collisions: (1) ELASTIC — kinetic energy AND momentum are conserved; objects bounce off perfectly; idealized — billiard balls approximate this; (2) INELASTIC — momentum conserved, kinetic energy NOT conserved (some becomes heat, sound, deformation); most real collisions; (3) PERFECTLY INELASTIC — objects stick together after collision; momentum conserved, max kinetic energy loss. Newton's third law: every action has an equal and opposite reaction. In a collision, the forces on each object are equal and opposite; force × time on each object causes equal and opposite changes in momentum (impulse-momentum theorem: F·t = Δp). Real-world applications: car safety (airbags, crumple zones extend collision time, reducing peak force); recoil (firearm pushes shooter back; rocket pushes gas back, gas pushes rocket forward); jet propulsion; sports physics (collisions between balls, players). ASVAB MC may include simple momentum conservation problems but more often tests conceptual understanding.

Bernoulli's principle (Daniel Bernoulli, 1738): for a flowing fluid, faster flow = lower pressure. Conversely, slower flow = higher pressure. This is a consequence of conservation of energy in flowing fluids: kinetic energy (motion) + pressure energy + gravitational potential energy = constant. Faster motion → more kinetic energy → less pressure energy. Real-world examples: (1) AIRPLANE LIFT — wings shaped so air moves faster over the top (curved upper surface) than the bottom (flat or less curved); faster top = lower pressure above; slower bottom = higher pressure below; net upward force = lift; (2) CARBURETORS / SPRAY BOTTLES — fast air stream through a venturi (narrowed section) creates low pressure that draws up fuel/liquid; (3) BASEBALL CURVES — spinning ball drags air faster on one side, creating pressure difference and curving the trajectory; (4) ROOFS LIFTED OFF IN STORMS — high winds over roof create low pressure above; interior pressure stays normal; pressure difference can push roof off; (5) SHOWER CURTAIN PULLED INWARD — running water creates low pressure inside the shower; (6) CHIMNEYS — fast wind across the top pulls smoke up. Venturi effect: narrow section in a pipe causes fluid to speed up (continuity equation: A₁v₁ = A₂v₂); speeding up causes pressure to drop (Bernoulli). Pitot tubes measure airspeed by measuring this pressure difference. Despite being central to aerodynamics, Bernoulli's principle is often misunderstood — it applies to ideal flow along streamlines without friction, viscosity, or compressibility effects; real aerodynamics combines Bernoulli with other effects. ASVAB MC tests the basic concept.

A column supporting a load is under COMPRESSION — the force squeezes it from both ends (the load pressing down from above, the foundation pressing up from below). Different structural members experience different primary forces: (1) COMPRESSION — squeezing; columns, pillars, struts, the lower side of beams under load, foundations; (2) TENSION — pulling apart; cables, ropes, suspension bridge cables, the upper side of beams under load, tendons; (3) SHEAR — parallel forces causing sliding; bolts in joints, beams under perpendicular load (vertical shear), scissoring action; (4) BENDING — combination of tension on one side and compression on the other; beams under load (top compressed, bottom in tension); (5) TORSION — twisting force; drive shafts, screws being tightened, hurricanes on towers. Materials chosen for their force characteristics: STEEL — strong in both tension and compression (used widely); CONCRETE — strong in compression, weak in tension (must be reinforced with steel rebar to handle tension); STONE — strong in compression, weak in tension (used in arches that distribute load as compression); WOOD — moderate tension and compression; CABLE — strong in tension only. Reinforced concrete combines concrete (compression strength) with steel rebar (tension strength) — versatile for beams that experience both. Pre-stressed concrete pre-tensions the steel before pouring concrete, increasing tension resistance. Buildings, bridges, and other structures are designed to identify which members experience which forces and choose materials/dimensions accordingly. Columns can fail from EXCESSIVE COMPRESSION (crushing) or BUCKLING (sudden lateral collapse before reaching compressive strength) — long thin columns are more susceptible to buckling.

Pressure in a fluid increases with depth at a predictable rate. P = ρgh, where ρ is fluid density, g is gravity, h is depth. For water: ρ = 1000 kg/m³, g = 9.8 m/s². Pressure increase per meter of depth = 1000 × 9.8 = 9800 Pa per meter ≈ 9.8 kPa/m ≈ 1.4 psi/m. So 33 feet (10 meters) ≈ 14 psi pressure increase, or about 1 atmosphere (atm ≈ 14.7 psi at sea level). Total pressure at depth = atmospheric pressure (at surface) + water pressure (due to depth). At 33 feet depth: total pressure ≈ 2 atm (1 atm air + 1 atm water). At 66 feet: 3 atm. At 99 feet: 4 atm. This affects scuba diving in important ways: (1) GAS COMPRESSION — at 33 feet, lungs and gas spaces compress to half their surface volume per Boyle's Law; at 99 feet, to one-fourth; (2) BREATHING — divers need pressurized gas equal to surrounding water pressure to inflate lungs; modern regulators automatically adjust; (3) NITROGEN ABSORPTION — at higher pressure, more nitrogen dissolves in tissues (Henry's Law); ascending too fast releases nitrogen as bubbles (decompression sickness, 'the bends'); divers ascend slowly with decompression stops on deep dives; (4) OXYGEN TOXICITY — at high pressure, even normal-percentage oxygen becomes toxic (~6 atm); deep divers use special gas mixtures; (5) NITROGEN NARCOSIS — at depth, nitrogen affects the central nervous system; called 'rapture of the deep'; reversible upon ascent. Salt water is slightly denser than fresh water, so pressure increases slightly faster (about 33 feet per atm in salt water, 34 feet per atm in fresh). Atmospheric pressure at sea level: 1 atm = 14.7 psi = 101 kPa. Decreases with altitude (about 0.3 psi per 1000 ft elevation).

Mass and weight are fundamentally different concepts often confused. MASS: amount of matter; intrinsic property; constant regardless of location; SI unit: kilogram (kg); US: slug (rare) or pound-mass (lbm); measured with a BALANCE (compares to known masses). WEIGHT: gravitational force on mass; depends on gravity at the location; SI unit: Newton (N); US: pound-force (lbf); measured with a SCALE (measures force). Relationship: W = mg, where g = gravitational acceleration. On Earth's surface: g ≈ 9.8 m/s² (or 32 ft/s²). A 1 kg object weighs 9.8 N on Earth. A 1 lbm object weighs 1 lbf on Earth (because of how pound-mass is defined). Examples on other planets/moons: 70 kg person — on EARTH: weight = 70 × 9.8 = 686 N (about 154 lb); on MOON (g ≈ 1.6 m/s²): weight = 70 × 1.6 = 112 N (about 25 lb); on MARS (g ≈ 3.7 m/s²): weight = 70 × 3.7 = 259 N (about 58 lb); on JUPITER (g ≈ 24.8 m/s²): weight = 70 × 24.8 = 1736 N (about 390 lb); in deep SPACE (no gravity): weight ≈ 0, but mass still 70 kg. Everyday usage: 'I weigh 150 pounds' technically refers to weight; in physics precision, mass is 150 lbm. Bathroom scales measure weight but display as mass — assuming Earth gravity. Astronauts in orbit appear weightless because they're in free fall around Earth (the same as weightlessness in orbit — actually freefall, not absence of gravity). Mass affects: inertia (resistance to acceleration, F = ma); momentum (p = mv); kinetic energy (KE = ½mv²); gravitational attraction (between all masses). Weight affects: how hard it is to lift something against gravity; reading on a scale; gravitational potential energy in a gravity field.

Bridge types, ranked roughly by typical span: (1) BEAM BRIDGES — simplest, like a board across a stream; load creates bending; relatively short spans (typically <100m); examples: many highway overpasses; (2) ARCH BRIDGES — convert load to compression along the curve, transferring to abutments; spans up to ~500m; examples: Stone Bridge ancient Rome, Sydney Harbour Bridge (steel arch), Pont du Gard (Roman aqueduct); (3) TRUSS BRIDGES — triangulated framework distributes load; spans up to ~600m; examples: many railroad bridges, Pratt and Warren designs; (4) CANTILEVER BRIDGES — beams extending from supports without a beam at the far end; spans up to ~600m; (5) CABLE-STAYED BRIDGES — cables fan directly from towers to the deck; spans up to ~1100m+; cables in tension, towers in compression; examples: Russky Bridge Russia (1104m main span); (6) SUSPENSION BRIDGES — main cables hang from towers, holding hanger cables that suspend the deck; spans up to ~2000m+; examples: Akashi Kaikyō Bridge Japan (1991m), Golden Gate Bridge (1280m). Suspension and cable-stayed bridges use steel cables in tension — steel is extremely strong in tension, very efficient material use. Cables can support enormous loads when only in tension (compared to in compression where they would buckle). The towers and abutments are in compression. The deck experiences bending and shear. Each structure type matches force flows to material strengths. Other factors in bridge design: wind loading (Tacoma Narrows Bridge collapsed in 1940 due to aeroelastic flutter); earthquake (modern bridges designed for seismic loads in earthquake zones); traffic loading (live loads from vehicles); thermal expansion (expansion joints); maintenance access. ASVAB MC tests basic structural understanding and bridge type identification.

PASCAL'S PRINCIPLE: In a closed fluid system, pressure is transmitted equally in all directions. Pressure = Force ÷ Area. Small piston: P = 10N ÷ 2cm² = 5 N/cm². Same pressure at large piston: Force = P × Area = 5 N/cm² × 20 cm² = 100 N. MECHANICAL ADVANTAGE = large area ÷ small area = 20/2 = 10. Input force × MA = Output force: 10N × 10 = 100N. Hydraulic systems are used in: car brakes (small pedal force → large caliper force); hydraulic jacks; heavy machinery. As with all mechanical advantage: the large piston moves 10× less distance than the small piston moves.