Gravitation, Work, Energy and Power
Gravitation, work, energy and power links forces to energy accounting, so most questions are one-step calculations with a single trick hidden in the wording.
Gravitation
Universal law: F = Gm₁m₂/r², with G = 6.67 × 10⁻¹¹ N m²/kg². Weight is the gravitational force, W = mg, with g ≈ 9.8 m/s² on Earth and about one-sixth of that on the Moon. Mass is constant; weight changes with g. In free fall all bodies accelerate equally in a vacuum.
Pressure and buoyancy
Pressure = force/area. Liquid pressure depends on depth: P = hρg. Archimedes' principle: upthrust equals the weight of fluid displaced. A body floats when its weight is balanced by the upthrust; relative density = density of substance/density of water. Ice floats with about nine-tenths of its volume submerged.
Work, energy, power
Work = force × displacement in the direction of the force, in joules; W = Fs cos θ, so work is zero when the force is perpendicular to the motion (a coolie carrying a load on level ground). Work against gravity W = mgh. Kinetic energy = ½mv²; potential energy = mgh; mechanical energy is conserved without friction. Power = work/time, in watts; 1 kWh = 3.6 × 10⁶ J.
Simple machines
Lever (effort, load, fulcrum; three classes), pulley (fixed, movable, block and tackle), inclined plane, screw, wheel and axle. Mechanical advantage = load/effort; efficiency = useful work/input × 100%.
Worked example
A 10 kg mass is lifted 2 m at constant speed in 4 s (g = 9.8). Work = mgh = 10 × 9.8 × 2 = 196 J. Power = 196/4 = 49 W.
Traps
Using displacement instead of distance in a round trip; forgetting to convert grams to kilograms; saying mass changes on the Moon; forgetting that work is zero for a force at right angles to motion.