Engineering & Physics · Kindergarten–Grade 8 · Quick reference
Engineering & Physics(K–8 · Machines · Structures)
Newton’s laws and simple machines, forces in structures, bridges and buildings, Ohm’s law, circuits, motors and electronics, water and the grid, buoyancy and ships, the four forces of flight, rockets and robots.
1Forces, Motion & Machinesunit 1 · Newton, Archimedes, Galileo
| Law | Says | See it |
|---|---|---|
| 1 · Inertia | a thing keeps doing what it is doing until a force acts | a ball rolls until friction stops it; seat belts |
| 2 · F = ma | force = mass × acceleration; more push, more speed-up; more mass, less | a loaded wagon is harder to start |
| 3 · Action–reaction | every push has an equal push back | a balloon rocket; a rowboat moves back as the oar pushes water |
Push and pull
A force is a push or a pull, measured in newtons (N). Gravity pulls down; friction resists sliding; a net force of zero means balanced (no speed-up). Weight = mass × g (g ≈ 9.8 m/s²). Speed = distance ÷ time; acceleration = change in speed ÷ time.
| Machine | How it helps | Example |
|---|---|---|
| lever | a bar on a fulcrum; long effort arm, big lift | seesaw, crowbar, wheelbarrow |
| pulley | a wheel for a rope; more ropes, less effort | flag pole, crane, Archimedes’ ship |
| wheel and axle | a big wheel turns a small axle | doorknob, bicycle |
| inclined plane | a ramp: longer path, less force | ramp, road up a hill |
| wedge | two ramps that split | axe, knife, nail |
| screw | a ramp wrapped around a post | screw, Archimedes’ water screw, jar lid |
Gears, energy, engines
- Gear ratio = teeth on the driven gear ÷ teeth on the driver: a 10-tooth driving a 30-tooth turns it ⅓ as fast with 3× the turning force. Clocks: pendulum and escapement.
- Energy is the ability to do work: potential (stored: height, a spring) and kinetic (motion). A roller coaster trades one for the other; energy is conserved.
- Momentum = mass × velocity; crumple zones lengthen a crash to lessen the force.
- Engines: steam (Watt), gasoline (intake, compression, power, exhaust), electric motors.
The design process
Ask (criteria, constraints) → Imagine → Plan → Create → Test → Improve. Keep an engineer’s notebook. Failure is data.
2Bridges & Buildingsunits 2–3 · structures
| Force | Means | Who resists it |
|---|---|---|
| compression | squeezing | columns, arches, stone |
| tension | stretching | cables, ropes, steel |
| shear | sliding past | bolts, beams at supports |
| torsion | twisting | shafts; Tacoma Narrows (1940) |
| bending | a beam sags: top squeezed, bottom stretched | I-beams, trusses |
Loads
Dead load (the structure itself), live load (people, traffic, snow), lateral load (wind, earthquake). A safety factor builds in extra strength; a load path carries weight to the ground; redundancy gives a second path.
| Type | How it works | Famous |
|---|---|---|
| beam | a flat span resting on supports; sags under load | log bridge, highway overpasses |
| arch | pushes the load outward into its abutments (compression) | Roman bridges, Pont du Gard |
| truss | triangles share the load as tension and compression | railroad bridges, Forth Bridge (cantilever) |
| suspension | deck hangs from cables over towers to anchorages | Brooklyn Bridge (Roeblings, 1883), Golden Gate |
| cable-stayed | cables run straight from tower to deck | modern river crossings |
Buildings
- Post and lintel (Stonehenge, Greek temples) → arch, vault, dome (Rome: the keystone locks the arch) → flying buttress (Gothic cathedrals take the thrust outside) → steel frame and curtain wall (Chicago, 1885) with Otis’s safety elevator (1854).
- Foundations spread the load; soft ground needs piles or caissons (the Roeblings sank them for Brooklyn).
- Tall buildings fight wind: cross-bracing, a stiff core, setbacks, a tuned mass damper (Taipei 101), base isolation for earthquakes. Codes: fire ratings, exits, sprinklers.
Arch pushes out, cable pulls in
An arch is all compression and needs strong abutments; a suspension bridge is all tension and needs heavy anchorages. Match the material: stone for squeezing, steel for stretching.
3Electricity, Magnets & Electronicsunit 4 · Volta, Ohm, Faraday, Morse
Ohm’s law
Voltage (volts) pushes current (amps) through resistance (ohms). 9 V across 3 Ω → 3 A. Power P = V × I (watts).
V = I × R
Circuits
- A circuit is a complete loop: source (battery) → wire → load (bulb) → back. A switch opens the loop; an open circuit does nothing; a short circuit is a loop with no load (danger).
- Series: one path; the same current everywhere; one bulb out, all out. Parallel: branches; each gets the full voltage; one out, the rest stay lit (house wiring).
- Conductors (copper, aluminum) let charge flow; insulators (rubber, plastic, glass) do not.
- Safety: never put anything in an outlet; water and electricity do not mix; fuses and breakers open when current is too high.
Magnets and motors
- Like poles push apart, unlike poles pull; the earth is a magnet and a compass points north.
- Oersted (1820): a current makes a magnetic field. A coil around iron is an electromagnet; a relay is an electromagnet that works a switch.
- Faraday (1831): a moving magnet makes a current (induction). A generator turns motion into electricity; a motor turns electricity into motion (the commutator keeps it spinning).
- AC (Tesla) travels far through transformers; DC (Edison, batteries) flows one way.
Components
Resistor limits current (color bands) · LED lights one way (long leg +) · diode one-way valve · capacitor stores charge · transistor a switch or amplifier (base, collector, emitter) · integrated circuit thousands of transistors on a chip.
Digital and code
- A bit is 0 or 1; binary counts in twos: 1011 = 8 + 2 + 1 = 11. Logic gates (AND, OR, NOT) with truth tables (Boole, Shannon).
- Morse code (1844): dots and dashes over a telegraph; SOS = ··· ––– ···.
- Program: an algorithm step by step; loops repeat, conditionals choose (if … then), variables store; a bug is a mistake to find.
- Microcontroller (Uno-style board, Raspberry Pi): GPIO pins read sensors and drive motors; sensor → controller → actuator.
- Feedback: a thermostat compares the set point with the reading and turns the heat on or off (closed loop).
Ohm’s triangle
Cover the one you want: V on top, I and R below. V = IR, I = V ÷ R, R = V ÷ I.
4Water, Power & Public Utilitiesunit 5 · the systems behind the tap and the switch
Clean water
- Source: river, lake, well, aquifer; Roman aqueducts ran on a gentle gradient.
- Coagulation: chemicals clump the dirt.
- Settling and filtration through sand.
- Disinfection: chlorine (measured in mg/L) kills germs.
- Water tower: height gives pressure (about 0.43 psi per foot of head); pipes and pumps carry it home.
Wastewater
Sewers carry it to a treatment plant (Bazalgette’s London sewers ended the Great Stink, 1858): screens, settling, bacteria eat the waste, disinfect, return clean water to the river.
Making electricity
- Nearly all power is a spinning generator (Faraday): steam from coal, gas or nuclear heat, falling water (hydro dams), wind turbines; solar panels make DC without spinning.
- Transformers step voltage up for the long transmission lines and down at the substation and the pole.
- The grid runs at 60 Hz; supply must match demand every second; N-1 means it survives any one failure; a cascade caused the 2003 blackout.
- Lineworkers and plant operators keep it running; SCADA screens watch the system.
Roads and telephones
Roman roads: layered stone, cambered to shed water; macadam; asphalt and concrete. Bell’s telephone (1876) turned sound into current; today optical fiber carries light pulses by total internal reflection, and the internet moves packets through data centers.
| Quantity | Unit |
|---|---|
| force | newton (N) |
| work, energy | joule (J); kilowatt-hour on the bill |
| power | watt (W) = J/s; horsepower ≈ 746 W |
| voltage, current, resistance | volt (V), ampere (A), ohm (Ω) |
| pressure | pascal (Pa), psi |
| flow rate | gallons or liters per minute |
| frequency | hertz (Hz), cycles per second |
| speed | m/s, mph; a ship’s knot = 1.15 mph |
Utilities are hidden engineering
Every faucet, outlet and streetlight sits at the end of a long chain of engineers, operators and lineworkers. Say thank you by learning how it works.
5Boats & Shipsunit 6 · Archimedes to the Titanic
Archimedes’ principle
A thing floats when it displaces its own weight of water before it goes under. Steel sinks as a block but floats as a hollow hull: the hull displaces more water than the steel weighs.
buoyant force = weight of the water displaced
Density
density = massvolume. Water is 1 g/cm³; wood floats (about 0.6), stone sinks (about 2.7), a loaded ship’s average density is below 1.
Stability
- The center of gravity (weight) must sit low; the center of buoyancy (the pushed-aside water) must be able to push it back upright.
- Ballast low in the hull lowers the center of gravity; the warship Vasa (1628) was top-heavy and capsized on her first sail. An inclining test checks a ship before launch.
- Watertight compartments and bulkheads limit flooding; the Titanic’s were not tall enough (1912); SOLAS rules followed: lifeboats for all.
Low and wide floats
Weight low, hull wide, and the boat rights itself. Weight high and narrow tips over.
Moving the ship
- Sail: a sail is a wing; a keel keeps the boat from sliding sideways; tacking zigzags into the wind.
- Steam: Fulton’s paddle steamer (1807) → the screw propeller; the steam turbine (Parsons, 1897).
- Drag: skin friction and wave-making drag; a bulbous bow cancels the bow wave; hull speed limits a displacement hull.
- Submarines flood or blow ballast tanks to sink or rise (neutral buoyancy); pressure rises about 1 atmosphere every 10 m; by Boyle’s law the air in the ballast tanks is squeezed to a smaller volume as the pressure rises.
- Liberty ships (1940s) were prefabricated in blocks; cold made their steel brittle: lesson learned.
6Flight, Space & Robotsunits 7–8 · the four forces, sense-think-act
| Force | Direction | Made by |
|---|---|---|
| lift | up | the wing: an airfoil’s curved top (camber) and angle of attack |
| weight | down | gravity on the mass |
| thrust | forward | propeller, jet, rocket |
| drag | backward | air resistance |
How flight was learned
Montgolfier balloons (1783, hot air is less dense) → Cayley’s gliders → Lilienthal → the Wrights’ method: kites, a wind tunnel, data, wing warping, then powered flight at Kitty Hawk, Dec. 17, 1903. Gliders: glide ratio = distance ÷ height lost.
Jets, rockets, orbits
- A propeller is a spinning wing; a jet throws hot gas backward; a rocket carries its own oxygen and works in space (action–reaction). Staging drops empty tanks (Saturn V, Apollo 11, 1969).
- An orbit is falling and missing: fast enough sideways (about 17,500 mph low over the earth) that the ground curves away.
- Helicopters: a rotating wing; collective and cyclic controls; the tail rotor fights torque.
- Drones: four rotors, an IMU senses tilt, a feedback (PID) controller keeps it level; FAA rules and the TRUST test for fliers.
Lift needs airflow
No air moving over the wing, no lift. A plane stalls when it is too slow or too steep, not when the engine stops: it can glide.
Robots
- Sense → think → act: sensors (light, touch, distance, temperature) → controller (the program) → actuators (motors, servos). Unimate (1961) to the Mars rovers.
- Open loop runs blind; closed loop uses feedback to correct itself: a line follower reads the floor and steers.
- Autonomous machines decide from sensor data; a servo turns to an angle on command; motors are driven by pulse-width modulation.
- Code it: an algorithm with loops (repeat), conditionals (if the sensor sees black, turn) and variables (speed).
Toy lab
The Frisbee is a spinning wing (gyroscopic stability); LEGO bricks hold by clutch power and precise tolerance; a Rubik’s cube hides a core mechanism; a wind-up toy stores energy in a mainspring; a Slinky shows waves; a gyroscope precesses. Tear a toy down and draw how it works.