Foundations of physical science

01 / UNDERSTAND & APPLY

Quantities, units and scientific models

A measurement needs a quantity, a unit and relevant conditions. The SI base units include metre, kilogram, second, ampere, kelvin, mole and candela; derived units combine them. A newton is kg·m/s², while a joule is a newton-metre. Writing 20 without specifying whether it means metres, seconds or joules does not describe a complete physical result. Unit conversion must preserve the quantity: one kilowatt-hour is 3.6 million joules, not a unit of power.

A scalar such as mass or temperature has magnitude; a vector such as force or velocity also needs direction. Adding vectors requires their directions, not just their numerical sizes. Precision concerns agreement between repeated measurements under comparable conditions; accuracy concerns closeness to the appropriate reference value. A miscalibrated instrument can repeatedly give a tightly grouped but biased result. Extra displayed decimal places do not remove uncertainty or justify unlimited significant digits.

Dimensional consistency is a useful filter. Adding a length to a time is invalid unless a suitable conversion quantity connects them. Yet two formulas can have matching dimensions while only one describes the experiment correctly: dimensions cannot determine every numerical factor, force law or neglected effect. State the model and uncertainties before interpreting an answer. The exact-looking fictional inputs below simplify calculations; they do not imply real measurements are error-free.

02 / UNDERSTAND & APPLY

Motion, forces and momentum

Distance measures path length, while displacement connects initial and final positions with direction. A runner who completes a circuit has travelled a positive distance but has zero net displacement. Average speed uses total distance/time; average velocity uses displacement/time. Acceleration is the rate of change of velocity, so even constant speed can involve acceleration when direction changes, as in circular motion.

For a constant-mass body in an inertial frame, the vector sum of external forces equals mass times acceleration. The net force matters, not the largest force considered alone. Zero resultant force means zero acceleration: the object can remain at rest or keep moving uniformly along a straight line. It does not mean that no forces act. A supported stationary book has downward gravitational force balanced by an upward contact force.

Newton’s third-law pair acts on two different bodies. If a hand pushes a trolley, the trolley pushes the hand in the opposite direction; that reaction is not an additional backwards force on the trolley. When several bodies are included in one system, their mutual forces are internal. Total momentum remains constant if the net external impulse over the interval is negligible. Momentum conservation therefore depends on the selected system and interval, not on a claim that every object maintains its own momentum.

Mass measures inertia and is expressed in kilograms; weight is the gravitational force, approximately mg near a specified location, expressed in newtons. A change in local g changes weight without necessarily changing mass. Gravity also provides the acceleration that bends an orbiting body’s path. An orbiting astronaut’s apparent weightlessness does not mean Earth’s gravitational attraction has disappeared.

03 / UNDERSTAND & APPLY

Work, energy, power and efficiency

Work by a constant force is the force component along displacement multiplied by that displacement. A perpendicular force contributes no work through that component, despite possibly changing motion’s direction. Translational kinetic energy is mv²/2. At fixed mass, doubling speed quadruples kinetic energy and tripling speed multiplies it by nine. Near Earth, a height increase h changes gravitational potential energy by approximately mgh if g can be treated as constant.

Energy can change form without disappearing. Friction may reduce a system’s mechanical energy while increasing internal energy of contacting materials and surroundings. Whether mechanical energy is conserved depends on the system and transfers; total energy accounting is broader. Efficiency compares a specified useful output with the corresponding input, using compatible energy or power boundaries. It is not meaningful to divide a useful energy by an input power without accounting for time.

Power is the rate of energy transfer, measured in watts or joules per second. A 0.6 kW device operated for 25 minutes receives 0.25 kWh, or 0.9 MJ. If 60% becomes the specified useful output, that output is 0.54 MJ. The remaining 0.36 MJ goes to other forms or destinations in the complete account; it is not destroyed. A kWh is an energy quantity even though its name includes watt.

04 / UNDERSTAND & APPLY

Pressure, density and buoyancy

Pressure is normal force per unit area. In a static fluid of approximately constant density, pressure rises by ρgh below a level reference surface, assuming uniform g. Gauge pressure is measured relative to a reference such as atmospheric pressure; absolute pressure includes that reference. For the supplied freshwater model, depths 1.5 m and 4 m give gauge pressures 15 kPa and 40 kPa, a difference of 25 kPa. Container shape does not change this hydrostatic result under the assumptions.

Archimedes’ principle relates buoyant force to the weight of displaced fluid. A floating body displaces enough fluid for buoyancy to balance its weight, subject to stability and other forces. A hollow steel ship can float because its total mass is spread over a large displaced volume; the average density of the vessel including enclosed spaces can be below the water’s density. A material label alone therefore cannot decide whether a constructed object floats.

In an ideal enclosed-fluid model, an imposed pressure change is transmitted throughout the fluid. A larger-area piston can experience a larger force at the same pressure, but ideal work balance requires it to move a correspondingly smaller distance. Hydraulic force multiplication is not energy creation. Real devices also have friction, deformation and leakage; this conceptual comparison is not an instruction to build or operate a pressure system.

05 / UNDERSTAND & APPLY

Temperature, heat transfer and phase change

Temperature describes a thermal state; heat is energy transferred because of a temperature difference. During a single-phase change with approximately constant specific heat, Q=mcΔT. Latent heat instead describes energy associated with a phase change: Q=mL for the stated mass and transition. For the fictional 0.4 kg material, c=2000 J/(kg K) and a 15 K rise require 12 kJ. A separate complete transition with L=100000 J/kg requires 40 kJ; those are different processes.

Conduction transfers energy through interactions within matter, including mobile electrons in metals, without requiring bulk transport of the material. Convection transfers energy through bulk fluid motion. Thermal radiation is electromagnetic transfer and can cross a vacuum. Several mechanisms can operate together: radiation from a warm surface does not establish that convection around it is absent. The direction of net heat transfer between bodies depends on their temperatures and surroundings.

Evaporation occurs at a liquid surface and can take place below the boiling temperature. Preferential escape of more energetic molecules can cool the remaining liquid when replacement energy is insufficient. Boiling involves vapour formation throughout the liquid when vapour pressure matches external pressure. Pure water’s familiar boiling temperature near 100°C assumes approximately standard atmospheric pressure; lower pressure changes that temperature, and dissolved substances can also change phase behaviour.

During an equilibrium phase change of a pure substance at fixed pressure, added energy can change the fraction in each phase while temperature stays constant. The native qualitative heating curve shows warming segments separated by melting and boiling plateaus; it does not provide numerical latent heats or a universal time scale. A mixture, varying pressure, non-equilibrium heating or heat losses need not produce the same ideal shape. Dividing a phase-change input by mc does not prove a temperature rise while the stated phase transition is occurring.

06 / UNDERSTAND & APPLY

Waves, sound and light

For a periodic wave in a specified medium, speed v equals frequency f times wavelength λ. Sound is a mechanical disturbance and requires matter; electromagnetic waves can propagate through vacuum. Greater sound frequency generally corresponds to higher perceived pitch, while amplitude and intensity affect sound level, with perception also depending on frequency and conditions. The wave carries energy; it does not require every medium particle to travel from source to listener.

Radio, microwave, infrared, visible, ultraviolet, X-ray and gamma-ray labels refer to parts of the electromagnetic spectrum. In vacuum they share speed c while differing in frequency and wavelength. Photon energy is hf, so higher frequency means greater energy per photon. Total beam energy also depends on the number of photons. A high-frequency category alone does not tell us the total exposure or justify a safety conclusion.

Reflection angles are measured from the normal to the surface. At a stationary boundary, transmitted light retains its frequency while its phase speed and wavelength can change. In the supplied air approximation, f=5×10^14 Hz gives λ=600 nm. For ordinary glass with index 1.5, speed becomes 2×10^8 m/s and wavelength 400 nm. At normal incidence the direction does not bend, despite these changes. At oblique incidence, refractive indices and angle determine the bending.

For ordinary glass lenses in air, a convex lens brings initially parallel rays toward a focus and a concave lens spreads them. A real image occurs where outgoing rays actually converge and can be intercepted on a screen at that location. A virtual image is located where backward extensions appear to meet. A convex lens can give a real or virtual image depending on object position, so convex does not mean always real. The surrounding medium and lens shape are part of the model.

Total internal reflection requires travel from a higher to a lower refractive index and an incidence angle greater than the critical angle. At smaller angles some light can be transmitted, so every glass-to-air encounter does not produce total internal reflection. Optical fibres use suitable guiding conditions; the principle is more specific than the general statement that light reflects from a boundary.

07 / UNDERSTAND & APPLY

Charge, current and simple circuits

Current is charge passing a location per unit time. Potential difference is energy transferred per unit charge; resistance expresses the current response to that potential difference. V=IR with constant R applies to an ohmic element under the stated conditions, not to every device under all temperatures or voltages. In a steady single series path, charge does not progressively disappear in each resistor: electrical energy is transferred while current remains the same along the path.

Series resistances add because the same current passes through them and their voltage drops add. Parallel branches connect the same two nodes, share voltage and add conductances: 1/Rtotal=1/R 1+1/R 2. For ideal 6 Ω and 3 Ω resistors across 12 V, series resistance is 9 Ω and current 4/3 A; voltage drops are 8 V and 4 V. In parallel, resistance is 2 Ω, branch currents are 2 A and 4 A and source current is 6 A. The native diagrams show these actual connections, not merely boxes near one another.

Electrical power is VI. For an ohmic resistor this becomes I²R or V²/R. The condition held fixed determines a comparison: increasing R at fixed voltage reduces power, while increasing R at fixed current raises it. In the supplied circuits, total power is 16 W in series and 72 W in parallel. The ideal voltage source supplies different currents; we have not assumed constant source power.

Batteries transfer stored chemical energy into electrical energy, and conducting materials provide mobile charge carriers. Insulation separates accessible surfaces from conductors; protective earthing provides an intended fault-current path in appropriate systems; overcurrent and residual-current protection respond to different fault conditions. None makes every arrangement safe. These are functional distinctions for examination reasoning, not directions for wiring, testing live circuits or bypassing protective devices.

08 / UNDERSTAND & APPLY

Magnetic effects and electromagnetic induction

An electric current produces a magnetic field. A magnetic field can exert forces on moving charges or current-carrying conductors, with direction depending on motion/current and field. For an isolated charged particle, the magnetic part of the force is perpendicular to instantaneous velocity and does no work on that particle by itself. A complete motor system can still transfer energy because electric fields, sources and moving conductors belong in its broader account.

A changing magnetic flux through a circuit can induce an electromotive force. Flux can change through field strength, orientation or the relevant area. Lenz’s rule gives a response opposing the change that produced the induction, rather than a rule that the induced field must oppose every existing field. This resistance to the inducing change is consistent with energy conservation: useful generator output requires an energy input.

A motor converts electrical input into mechanical output, while a generator converts mechanical input into electrical output. An ordinary transformer transfers energy between windings through changing magnetic flux. In an ideal alternating-current model, voltage ratio follows turns ratio while currents adjust to conserve power. A continuously steady DC input does not provide the sustained changing flux required for that result; switching transients are a separate phenomenon. No transformer arrangement creates energy.

09 / UNDERSTAND & APPLY

Matter, atoms and periodic patterns

An element is defined by atomic number, the number of protons in each nucleus. A compound contains chemically combined elements in a defined composition, while a mixture combines substances without requiring one fixed chemical formula. Separating a mixture by a suitable physical property differs from chemically decomposing a compound. Atoms contain protons and neutrons in the nucleus and electrons associated with it; only a neutral atom has equal proton and electron counts.

Mass number is the integer total of protons and neutrons. Isotopes of an element have the same proton number but different neutron numbers. Ion formation changes electron count without changing element identity. For Z=12, A=26 and charge +2, the counts are 12 protons, 14 neutrons and 10 electrons. The positive charge reflects two fewer electrons than protons, not the addition of two protons.

An isotope’s actual mass in atomic mass units is not generally identical to its integer mass number. A sample’s average atomic mass weights isotope masses by their abundances. With supplied approximate masses 24 u and 26 u at 75% and 25%, the average is 24.5 u. That noninteger result describes an average, not an atom with half a neutron. Actual calculations require actual isotope masses and the relevant composition.

Electronic structure helps explain periodic patterns. Atomic radius generally increases down a group because additional occupied shells extend the electron distribution. Across a main-group period it generally decreases as increasing effective nuclear attraction draws electrons in the same principal shell inward. Radius depends on its definition and bonding context, and exceptions occur. Similarly, metals tend to conduct and many non-metals do not, but graphite and other structural examples show why labels are not universal property laws.

10 / UNDERSTAND & APPLY

Bonding and chemical change

Ordinary chemical reactions rearrange atoms and bonding. A balanced chemical equation conserves the number of atoms of each element; coefficients change the numbers of formula units, not the identity of the substances. A physical change such as a phase transition can alter arrangement and properties without creating a new chemical substance. A visible change alone is not always sufficient to distinguish the mechanisms.

Ionic bonding describes electrostatic attraction between oppositely charged ions; covalent bonding involves shared electron density; metallic bonding includes delocalised electrons. In a typical metal those mobile electrons carry current. In an ordinary solid ionic crystal, ions are not free to move through the lattice and the simple model predicts poor conduction; molten material or a suitable solution can conduct through mobile ions. Solubility and structure matter. Covalent materials range from molecular substances to extended networks: graphite’s mobile electrons make the claim that all covalent solids insulate false.

Oxidation and reduction occur together: oxidation involves electron loss or an increase in oxidation state, and reduction the reverse. Corrosion is an environmental chemical process, often electrochemical; its rate and form depend on the material, moisture and other conditions. A catalyst supplies an alternative reaction route with a lower activation barrier and is regenerated in the overall process. It accelerates approach to equilibrium without changing the equilibrium constant at fixed temperature. Faster reaction is not the same as a different final equilibrium yield.

11 / UNDERSTAND & APPLY

Solutions, acids, bases and concentration

A solute is dissolved in a solvent, and concentration specifies how much solute is present relative to a stated solution or solvent quantity. Solubility describes an equilibrium limit under specified conditions. A saturated solution is therefore defined relative to temperature, solvent and composition; it is not automatically highly concentrated compared with a different substance. Dissolution can disperse existing particles or involve equilibria and does not by itself prove decomposition into different elements.

Acid and base strength must be separated from concentration. In aqueous acid teaching, strength concerns the extent of proton donation/ionisation in water under the relevant conditions. Base strength concerns acceptance of protons or reaction with water; strong soluble hydroxides supply hydroxide extensively on dissolution, while a weak base such as ammonia reacts only partly with water at equilibrium. Concentration instead concerns amount per volume. A strong acid or base can be dilute, and a concentrated weak acid is not thereby a strong acid.

pH is minus the base-ten logarithm of dimensionless hydrogen-ion activity. Suitable dilute-solution calculations often approximate activity using concentration relative to its standard state. An activity of 10^-3 gives pH 3 and 10^-5 gives pH 5: the first has 100 times the hydrogen-ion activity. This does not independently reveal the total analytical acid concentration or its strength. Neutrality concerns equal hydrogen-ion and hydroxide-ion activities; neutral pH is approximately seven near 25°C, but changes with temperature.

Acid–base neutralisation does not guarantee a final pH of seven. The mixing proportions may leave excess reactant, and ions from a weak acid or weak base can react with water after stoichiometric neutralisation. Thus stoichiometric equivalence, chemical strength and neutrality are distinct concepts. The lesson compares mechanisms and supplied quantities, without suggesting chemical handling or using pH alone to judge personal safety.

12 / UNDERSTAND & APPLY

Radioactivity, half-life and scientific claims

Radioactive decay transforms unstable nuclei. Alpha particles are helium nuclei with charge +2e and a mass of about four atomic mass units, much greater than an electron’s mass. Beta radiation includes electrons with charge −e or positrons with charge +e; each has the electron rest mass. Gamma radiation consists of uncharged photons with zero rest mass. Alpha particles are readily stopped externally, while beta particles are typically more penetrating than alpha particles under comparable shielding conditions. Gamma-photon penetration depends strongly on photon energy and the material encountered; these are qualified comparisons, not universal shielding guarantees. An alpha-emitting material can still be hazardous if it enters the body. Risk depends on radiation type, amount, dose and pathway, not simply whether the source is natural or artificial. No handling procedure is implied.

Half-life is a statistical property of the specified radionuclide under the decay model. After each half-life, the expected number of undecayed parent nuclei halves. It is not the instant when every nucleus is halfway through decay. Starting with 8000 parent nuclei and a three-hour half-life, nine hours gives three halvings: 8000→4000→2000→1000 expected parents. The expected number that has decayed is 7000. Fluctuations occur, and any activity contributed by radioactive daughters requires a separate account.

Fission splits a nucleus into smaller nuclei and other particles; fusion combines light nuclei into a heavier system. Energy release in suitable reactions reflects a lower final mass and increased binding per nucleon, with the mass difference corresponding to energy. Not every imaginable nuclear combination releases energy. Chemical combustion mainly rearranges electrons and bonds rather than changing nuclear identity. These distinctions do not provide reactor operating details, weapons instructions or a claim about current commercial fusion capability.

When eliminating an answer, identify its units, system and hidden condition. Constant speed need not mean zero acceleration; zero net force need not mean rest; lower resistance raises power only under the appropriate fixed-voltage comparison. A numerical answer can be correct within a simplified model while remaining insufficient to forecast a real device or hazard. Evidence and stated assumptions are stronger guides than an impressive scientific label.