Force and Motion: Practice Questions & Explanations

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.

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.

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.

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.

Weight on Moon = 150 ÷ 6 = 25 lbs. Weight depends on gravity; mass remains constant but weight changes with gravitational force.

Friction converts kinetic energy (motion energy) to thermal energy (heat). When you rub your hands together, friction converts motion to warmth. Friction opposes relative motion between surfaces in contact.

CONSERVATION OF MOMENTUM (perfectly inelastic collision): Total momentum before = Total momentum after. Momentum = mass × velocity. Before: Object A: 2 kg × 6 m/s = 12 kg·m/s; Object B: 4 kg × 0 = 0. Total before: 12 kg·m/s. After: Combined mass = 2 + 4 = 6 kg. 6 kg × v = 12 kg·m/s. v = 12 ÷ 6 = 2 m/s. Note: kinetic energy is NOT conserved in inelastic collisions (some becomes heat/sound/deformation). Momentum IS always conserved in all collisions.

FRICTION is the force that resists the sliding motion between the box and the floor, preventing it from moving when pushed gently. ASVAB Mechanical Comprehension tests forces. FRICTION opposes motion between surfaces in contact; STATIC friction holds an object still until enough force overcomes it; KINETIC friction acts on a moving object. Other forces: GRAVITY (pulls down); TENSION (pull through a rope/cable); NORMAL force (surface pushing up). Friction resisting the push is the relevant force here — a commonly tested concept.

The box remains STATIONARY because the equal, opposite forces are BALANCED — the NET FORCE is zero. ASVAB Mechanical Comprehension tests force balance. When forces are balanced (equal and opposite), there is no net force, so there's no change in motion (Newton's first law — an object stays at rest). If one person pushed harder, there would be a net force and the box would accelerate toward the weaker side. Understanding balanced vs unbalanced forces and net force is commonly tested.

Friction is a force that opposes the motion (or attempted motion) of two surfaces that are in contact with each other. It acts in the direction opposite to movement and depends on the nature of the surfaces and how hard they press together. Friction can be useful (it lets tires grip the road and brakes stop a car) or a hindrance (it wastes energy and causes wear, which lubricants reduce). Rougher surfaces and greater pressing force produce more friction. Recognizing friction as a force opposing motion — and its useful and wasteful effects — is fundamental to the force-and-motion topic.

Inertia is the tendency of an object to resist changes in its state of motion (Newton's first law). An object in motion will continue moving in a straight line at a constant speed unless an unbalanced force acts on it, and an object at rest will stay at rest unless a force moves it. In everyday life, friction and air resistance usually act on moving objects and slow them down, which can make it seem like things stop 'on their own,' but it is actually those forces causing the change. Understanding inertia — objects keep doing what they're doing without a net force — is a key force-and-motion concept.

Ignoring air resistance, all objects fall with the same acceleration due to gravity (about 9.8 m/s²) regardless of their mass, so two objects dropped from the same height at the same time hit the ground at the same moment. This famous principle means a heavy ball and a light ball fall together in a vacuum. In real life, air resistance can slow lighter or less dense objects (like a feather), but the question specifies ignoring air resistance. Understanding that gravity accelerates all masses equally is a classic force-and-motion concept on the Mechanical Comprehension subtest.