Ukraine 10 клас Physics
Chapters: 5
1. Introduction
Physics as a natural science
- Units and Measurement (Class 11) – To measure means to compare a quantity with a fixed, agreed amount called a unit. Result = number × unit. The world now uses the SI system with 7 base units: metre, kilogram, second, ampere, kelvin, mole and candela. Every other unit (like newton or joule) is a derived unit made by multiplying or dividing base units. Prefixes like kilo (10³) and milli (10⁻³) make very big or very small numbers easy.
2. Mechanics
Kinematics · Circular motion · Dynamics · Gravitation · Friction and drag · Equilibrium of bodies · Conservation laws in mechanics · Fluids at rest and in motion · Mechanical oscillations · Mechanical waves and sound
- Motion in a Straight Line (Class 11) – To describe motion we first choose a frame of reference: an origin, a direction and a clock. Position x changes with time t. Velocity v = dx/dt is the slope of the x–t graph; acceleration a = dv/dt is the slope of the v–t graph, and the area under the v–t graph is the displacement. For constant a: v = u + at, x = ut + ½at², v² = u² + 2as.
- Projectile Motion and Uniform Circular Motion (Class 11) – In a plane, r = r₀ + v₀t + ½at² and v = v₀ + at, applied separately along x and y. A projectile has constant horizontal velocity u cos θ and a vertical velocity that changes by g each second, so its path is a parabola: y = x tan θ − gx²/(2u²cos²θ). T = 2u sin θ/g, H = u² sin²θ/2g, R = u² sin 2θ/g (maximum at 45°). In uniform circular motion speed is constant but the velocity turns, giving a centripetal acceleration a = v²/r = ω²r towards the centre.
- Inertia, First Law, Momentum, Second Law and Impulse – A body keeps its state of rest or uniform motion unless a net external force acts on it (first law). Inertia is this laziness to change, and mass measures it. Momentum p = mv. The rate of change of momentum equals the net force: F = dp/dt, which gives F = ma when mass is constant (second law). Impulse J = F × Δt = Δp; a longer stopping time means a smaller force.
- Newton's Universal Law of Gravitation – Every mass in the universe pulls every other mass. The pull between two point masses m₁ and m₂ a distance r apart is F = G m₁ m₂ / r². It acts along the line joining them. The two bodies pull each other with equal and opposite forces. G = 6.67 × 10⁻¹¹ N m² kg⁻² is the same everywhere, so it is called the universal gravitational constant. When many masses pull one body, the forces add as vectors (superposition).
- Friction: Static, Kinetic and Rolling Friction, Laws and Lubrication – Friction is the force that opposes relative motion (or its start) between surfaces in contact. Static friction adjusts itself up to a maximum, the limiting friction fs,max = μs N. Once sliding starts, kinetic friction fk = μk N acts, and μk < μs. Friction depends on the normal force and the nature of the surfaces, not on the area of contact. Rolling friction is much smaller than sliding friction; lubricants and ball bearings reduce friction.
- Torque, Angular Momentum and Equilibrium of Rigid Bodies – Torque is the turning effect of a force: τ = r × F, size rF sinθ, unit N m. Angular momentum is the turning version of momentum: L = r × p; for a body spinning about a fixed axis L = Iω. Torque changes angular momentum: τ = dL/dt. If the outside torque is zero, L stays constant, so pulling mass in makes a body spin faster. A rigid body is in equilibrium when the total force is zero (no sliding) and the total torque about any point is zero (no turning).
- Third Law, Conservation of Momentum and Equilibrium of Forces – Forces always come in pairs: if A pushes B, B pushes A with an equal and opposite force at the same instant (third law). The pair acts on different bodies. For a system with no net external force, the total linear momentum stays constant, which explains recoil, rockets and collisions. A particle is in equilibrium when all forces on it add to zero; three concurrent forces in equilibrium form a closed triangle.
- Viscosity, Stokes' Law and Bernoulli's Theorem – A moving fluid is like a stack of layers sliding over each other. The friction between layers is viscosity: F = ηA(dv/dx). A small ball falling through a fluid feels a drag F = 6πηrv (Stokes' law); when drag plus buoyancy balance the weight, it falls at a steady terminal velocity. Slow flow is streamline; above a critical velocity (Reynolds number about 2000) it becomes turbulent. For steady streamline flow, Av is constant (continuity) and P + ½ρv² + ρgh is constant (Bernoulli). So fast fluid has low pressure. This explains Torricelli's efflux speed √(2gh), the venturimeter, and the lift on wings and spinning balls.
- Simple Harmonic Motion (SHM) – A motion that repeats after a fixed time is periodic. If the object goes to and fro about a middle point and the force pulling it back is proportional to its distance from the middle (F = −kx), the motion is simple harmonic. Its position is x = A sin(ωt + φ), with ω = 2π/T = 2πf. Speed is largest in the middle, acceleration is largest at the ends, and total energy ½kA² stays constant.
- Progressive Waves: Types, Speed and Equation – A wave carries energy from place to place without carrying the matter along. In a transverse wave the particles move at right angles to the wave; in a longitudinal wave they move along it. Speed v = fλ. On a string v = √(T/μ); for sound in a gas v = √(γP/ρ). A wave moving along +x is y = A sin(kx − ωt), with k = 2π/λ and ω = 2πf.
3. Elements of special relativity
Special relativity
- Special Relativity – Special relativity (Einstein, 1905) rests on two postulates: the laws of physics are the same in all inertial frames, and the speed of light in a vacuum, c ≈ 3.00 × 10⁸ m/s, is the same for every observer. It follows that moving clocks run slow (t = γt₀), moving objects are shorter along their motion (L = L₀/γ), and mass is a form of energy (E = mc²), with γ = 1/√(1 − v²/c²). At everyday speeds γ ≈ 1, so Newton's mechanics works; near c it fails.
4. Molecular physics and thermodynamics
Molecular-kinetic theory · Ideal gas law and isoprocesses · Vapour and humidity · Liquids and solids · Laws of thermodynamics · Heat engines
- Kinetic Theory of Gases: Pressure, Temperature and rms Speed – Kinetic theory explains gas behaviour by picturing a gas as tiny, fast, randomly moving molecules that bounce elastically and do not pull on each other. Each hit on a wall reverses the molecule's velocity and hands the wall momentum 2mvₓ. Adding the hits of all molecules gives the pressure P = ⅓ n m v̄² = ⅓ ρ v̄². Comparing with PV = N k T shows that the average kinetic energy of a molecule is (3/2) k T: temperature is a measure of the average kinetic energy of the molecules. The root mean square speed is v_rms = √(3RT/M) = √(3kT/m), so lighter gases move faster at the same temperature.
- Perfect Gas Equation PV = nRT and Work in Compressing a Gas – A gas is made of countless tiny molecules flying about. Their hits on the walls make pressure. For a low-density gas, three simple laws hold: at fixed temperature, P × V stays constant (Boyle); at fixed pressure, V grows in step with kelvin temperature (Charles); at the same P and T, equal volumes hold equal numbers of molecules (Avogadro). Put together they give the perfect gas equation PV = nRT = N k T. One mole holds Avogadro's number, 6.022 × 10²³, of particles. Pushing a piston in does work on the gas; the work equals the area under the P–V graph, and at fixed temperature W = nRT ln(V₁/V₂).
- Changes of State: Melting, Boiling, Evaporation and More – A substance can change between solid, liquid and gas when we heat it or cool it. Melting, boiling, evaporation and sublimation need heat. Freezing, condensation and deposition give heat out. While the state is changing, the temperature stays the same, because the heat is used to break (or is released by making) the pull between particles. This hidden heat is called latent heat. Evaporation happens at any temperature, only from the surface, and it cools things down. Changes of state are physical changes: no new substance forms and the mass stays the same.
- Mechanical Properties of Solids: Stress, Strain and Elasticity – When you pull, push or twist a solid, it changes shape a little. If it comes back when you let go, it is elastic. Stress is the restoring force per area (F/A). Strain is the fractional change in size (like ΔL/L). Up to the elastic limit, stress is proportional to strain (Hooke's law), and the ratio is a modulus: Young's modulus Y for stretching, bulk modulus B for squeezing all round, shear modulus G for sliding faces. A stretched wire also gets thinner (Poisson's ratio), and it stores energy ½ × stress × strain × volume.
- First Law of Thermodynamics – Internal energy U is the total energy of the molecules inside a system. It changes in only two ways: by heat Q (energy that flows because of a temperature difference) and by work W (energy moved by a force, like a moving piston). First law: ΔQ = ΔU + ΔW. Heat given to a gas partly raises its internal energy and partly lets it do work. Work by a gas at constant pressure is PΔV. For an ideal gas Cp − Cv = R.
- Second Law of Thermodynamics, Heat Engines and Refrigerators – The first law says energy is conserved; the second law says which way heat and energy can go. Heat flows by itself only from hot to cold (Clausius). No engine can turn all the heat it takes into work; some must be thrown into a colder body (Kelvin–Planck). A heat engine takes Q₁ from a hot source, does work W and rejects Q₂: efficiency η = W/Q₁ = 1 − Q₂/Q₁. A refrigerator uses work W to move Q₂ from cold to hot: COP α = Q₂/W. The best possible engine, the Carnot engine, has η = 1 − T₂/T₁.
5. Electric field
Electric field strength · Potential and potential difference · Capacitance and capacitors
- Electric Field and Field Strength – A charge changes the space around it so that any other charge placed there feels a force. This region is the electric field. Its strength at a point is the force on a small positive test charge divided by that charge: E = F/q, measured in N/C (same as V/m). For a point charge, E = kQ/r², with k = 9 × 10⁹ N m²/C². E is a vector: it points away from + charges and towards − charges. Field lines show its direction and, by how close they are, its strength. Fields from several charges add as vectors (superposition).
- Electrostatic Potential and Capacitance – Electrostatic potential V at a point is the work done per unit positive charge to bring it from infinity: V = kq/r for a point charge, and potentials of many charges add as plain numbers. Potential difference V_B − V_A = W_AB/q. Equipotential surfaces join equal-V points; E is perpendicular to them and E = −dV/dr. Potential energy of two charges is U = kq₁q₂/r, and of a dipole in a field U = −pE cosθ. Conductors have free charges (E inside = 0); dielectrics have bound charges that polarise and cut the field to E₀/K. A capacitor stores charge Q = CV. A parallel plate capacitor has C = ε₀A/d, and KC with a dielectric. In series 1/C = 1/C₁ + 1/C₂ + …; in parallel C = C₁ + C₂ + …. Energy stored U = ½CV² = Q²/2C = ½QV.