Fluids, Electricity, and Motion
Key Takeaways
- Pressure = force / area, so the same force on a smaller area produces greater pressure; Pascal's principle lets hydraulics multiply force in proportion to piston-area ratio.
- An object floats when its density is less than the fluid's; buoyant force equals the weight of fluid displaced (Archimedes' principle).
- Ohm's law, V = I x R, ties the three circuit quantities together; with fixed voltage, higher resistance means lower current.
- Series resistances add directly; parallel paths lower total resistance and let current keep flowing if one branch opens.
- Newton's laws govern motion: balanced forces leave motion unchanged, while an unbalanced (net) force produces acceleration a = F / m.
- Bernoulli's principle, faster fluid means lower pressure, explains lift and shows up because the SIFT screens future aviators.
Fluids: Pressure, Hydraulics, and Buoyancy
Pressure
Pressure = force / area (P = F / A), measured in pascals (Pa) or pounds per square inch (psi). The same force on a smaller area produces greater pressure, which is why a sharp knife or a thumbtack point penetrates while a flat hand does not. Snowshoes do the opposite: they spread weight over a large area, cutting pressure so you do not sink.
Hydraulics and Pascal's Principle
Pascal's principle: pressure applied to an enclosed fluid is transmitted undiminished to every part of the fluid. Because pressure is equal on both pistons, force is multiplied in proportion to area:
F1 / A1 = F2 / A2
Worked example: A hydraulic jack has an input piston of 2 sq in and an output piston of 20 sq in. Press with 50 lb and the output force is 50 x (20 / 2) = 500 lb. As with every machine, the trade is distance: the input piston must move 10 times farther than the output piston rises.
Density and Buoyancy
Density = mass / volume. Archimedes' principle states the buoyant force equals the weight of the fluid displaced.
| Condition | Result |
|---|---|
| Object density < fluid density | Floats |
| Object density > fluid density | Sinks |
| Object density = fluid density | Neutrally buoyant, suspended |
| More fluid displaced | Greater buoyant force |
A steel ship floats because its hull shape displaces enough water that the ship's average density (steel plus enclosed air) is below water's. Crush it into a solid block and it sinks. Objects also float higher in denser fluids, which is why you float more easily in salt water than fresh.
Electricity: Circuits and Ohm's Law
Current flows only through a closed (complete) path. Break the loop and current stops.
| Quantity | Symbol | Unit | Meaning |
|---|---|---|---|
| Voltage | V | volt | Electrical push or potential difference |
| Current | I | ampere | Rate of charge flow |
| Resistance | R | ohm | Opposition to current |
Ohm's Law
V = I x R, rearranged as I = V / R and R = V / I. With voltage held constant, raising resistance lowers current. A 12-volt source across a 6-ohm resistor pushes I = 12 / 6 = 2 amps; double the resistance to 12 ohms and current halves to 1 amp.
Series vs. Parallel
| Arrangement | Resistance | Behavior |
|---|---|---|
| Series | R_total = R1 + R2 + ... (adds up) | One path; if any element breaks, all current stops (old holiday lights) |
| Parallel | R_total is less than the smallest branch | Multiple paths; one branch opening leaves the others lit (house wiring) |
Series circuits share one current but split voltage; parallel branches share the full voltage but split current. Conductors (copper, aluminum) carry current easily; insulators (rubber, glass, dry wood) resist it. A dead battery, blown fuse, open switch, or broken wire all open the circuit and stop current.
Worked example: Two 10-ohm resistors in series give R = 20 ohms, so a 20-volt source pushes I = 20 / 20 = 1 amp through both. Wire those same resistors in parallel and total resistance drops to 5 ohms, raising current from the source to 20 / 5 = 4 amps. Adding parallel paths always lowers total resistance and increases the current the source delivers.
Motion: Newton's Laws and Bernoulli for Flight
Newton's Three Laws
- Inertia (First Law): an object at rest stays at rest, and an object in motion stays in motion at constant velocity, unless acted on by an unbalanced force. Balanced forces produce no change in motion.
- F = m x a (Second Law): a net force accelerates a mass; acceleration is a = F / m. Doubling force doubles acceleration; doubling mass halves it. A 100-N net force on a 20-kg cart gives a = 100 / 20 = 5 m/s^2.
- Action-Reaction (Third Law): every force has an equal and opposite reaction. A rotor pushing air down lifts the aircraft up; a rifle pushes the bullet forward and recoils backward.
Acceleration, Gravity, and Projectiles
| Situation | Outcome |
|---|---|
| Unsupported object | Accelerates downward at g approximately 9.8 m/s^2 (32 ft/s^2) |
| Balanced forces (equal up and down) | Constant velocity or rest, no acceleration |
| Two objects dropped (no air resistance) | Hit ground together regardless of mass |
| Terminal velocity | Air drag balances weight, so falling speed stops increasing |
Bernoulli's Principle and Lift
Because the SIFT screens future aviators, Bernoulli's principle appears: where a fluid moves faster, its pressure is lower. Air speeds up over the curved top of a wing or rotor blade, lowering pressure above relative to below and producing lift. The same effect makes a shower curtain pull inward and lets two passing trucks get tugged together.
Review Habit
When you miss a mechanical item in practice, do not memorize the choice. Name the relationship you missed, force, pressure, density, resistance, torque, or motion, and the exact formula behind it. That diagnosis fixes whole families of questions far faster than rereading definitions.
A hydraulic press has a 2-square-inch input piston and a 20-square-inch output piston. Applying 50 lb to the input produces how much output force?
A 12-volt source is connected across a 6-ohm resistor. What current flows?
A steel ship floats while a solid steel bar of the same metal sinks. Why?