Work, Energy, and Power: Practice Questions & Explanations

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.

A pendulum demonstrates the conservation of mechanical energy. Energy converts between gravitational potential energy (PE = mgh) and kinetic energy (KE = ½mv²). At the highest points (the extremes of the swing): the pendulum is momentarily stopped, velocity = 0, so KE = 0. All energy is potential. At the lowest point: pendulum is at its fastest, maximum KE. All energy has converted to kinetic (height is at minimum). At intermediate points: some kinetic, some potential. Total mechanical energy (KE + PE) is constant in an ideal frictionless pendulum. In reality, air resistance and pivot friction gradually convert mechanical energy to thermal energy, causing the swing amplitude to decrease over time (damping) until the pendulum stops. Pendulum period: T = 2π√(L/g), where L is length and g is gravity. Period depends ONLY on length and gravity — NOT on mass or amplitude (for small angles). Longer pendulum = slower swing. Used in: grandfather clocks (controlled timing), Foucault pendulum (demonstrates Earth's rotation), seismographs (modified versions detect earthquakes). Similar energy transformations: (1) ROLLER COASTER — height to speed; gravity does the work going down, speed climbs back to nearly equal height (some energy lost to friction); (2) BOUNCING BALL — gravitational PE → kinetic → elastic PE (compression) → kinetic → gravitational; energy lost each bounce as heat/sound; (3) SPRING — elastic PE ↔ kinetic in oscillation; (4) PROJECTILE — KE ↔ gravitational PE at peak height. Conservation principle: in absence of non-conservative forces (friction, air resistance), total mechanical energy is conserved.

Kinetic energy KE = ½mv². Calculate both: CAR: ½ × 1000 × 10² = 500 × 100 = 50,000 J. MOTORCYCLE: ½ × 500 × 20² = 250 × 400 = 100,000 J. Motorcycle has twice the KE despite half the mass — because velocity is SQUARED in the formula. Implications: (1) DOUBLING SPEED quadruples KE (and stopping distance for same deceleration); (2) Same KE can come from very different mass-speed combinations; (3) Energy-of-motion explanations: faster moving objects do more damage in collisions; cars hitting things at highway speeds release dramatically more energy than at city speeds; (4) Engineering: vehicles need brakes proportional to KE not mass; aircraft must shed huge KE during landing (a 200,000 kg aircraft at 80 m/s has KE = ½ × 200,000 × 6400 = 640,000,000 J or 640 MJ — equivalent to several gallons of gasoline burning). Kinetic energy types: TRANSLATIONAL (linear motion, ½mv²), ROTATIONAL (½Iω², where I is moment of inertia and ω is angular velocity), VIBRATIONAL (in atomic-scale motion = thermal energy). Energy units: Joule (SI) = kg·m²/s²; calorie (food); BTU (heat); kWh (electricity); foot-pound; erg. Energy conversion: 1 cal ≈ 4.18 J; 1 BTU ≈ 1055 J; 1 kWh = 3.6 × 10⁶ J. Energy in collisions: at impact, KE converts to deformation, heat, sound, and other forms; safety design (crumple zones, airbags) extends collision time to spread KE conversion over more time = less peak force. ASVAB MC tests this conceptually — usually doesn't require complex calculation but does test that velocity affects KE more strongly than mass.

Power = Work / Time. Work = Force × Distance = (mg) × h = 100 × 10 × 5 = 5000 J (joules). Power = 5000 J / 10 s = 500 W (watts). Power units: WATT = Joule per second (SI standard); 1 kW = 1000 W; 1 MW = 1,000,000 W; HORSEPOWER (hp) = 746 W (or 550 ft-lb/s); 1 hp ≈ 0.75 kW. Common comparisons: human walking power ≈ 100 W; cyclist sustained ≈ 200 W; cyclist sprint ≈ 1000-2000 W; horse sustained ≈ 750 W (defining 1 hp); car engine ≈ 100,000-300,000 W (135-400 hp); jet engine takeoff ≈ 50-100 million W; nuclear power plant ≈ 1-3 billion W (1-3 GW). Power = Force × Velocity for constant force scenarios: a car pulling 1000 N of force at 20 m/s = 20,000 W = 20 kW (assuming constant velocity, all motor power overcomes drag and friction). Electrical power: P = IV = I²R = V²/R, where I = current, V = voltage, R = resistance. Energy = Power × Time. Common energy units: 1 kWh = 1000 W × 3600 s = 3,600,000 J = 3.6 MJ; electric bill quoted in kWh. A 100 W bulb running 10 hours uses 1 kWh of energy. Efficiency: useful power output / total power input; expressed as percentage; always less than 100% due to losses (heat, sound, friction). Engines typically 20-40% efficient; electric motors 70-95%; LEDs 30-50%. ASVAB MC may ask for power in basic scenarios (Work/Time), efficiency calculations, or unit conversions. The motor in the question above outputs 500 W (about 2/3 of one horsepower) to lift 100 kg vertically 5 meters in 10 seconds.

In physics, work is done when a force causes an object to move in the direction of that force; work equals force multiplied by the distance moved in the force's direction (W = F × d). If you push on a wall and it doesn't move, you exert force but do no mechanical work because there is no displacement. Lifting a box, pushing a cart, or pulling a rope all involve work because the object moves in the direction of the applied force. Understanding that work requires both a force and movement in that force's direction is a key work-and-energy concept.

Power is the rate at which work is done — that is, the amount of work divided by the time taken (Power = Work ÷ Time). Two machines might do the same amount of work, but the one that does it faster has more power. For example, two motors that each lift the same load to the same height do equal work, but the faster one is more powerful. Work is measured in joules and power in watts (one watt = one joule per second). Understanding that power measures how quickly work is performed — not just how much — is a standard work-and-energy distinction.