Russia 10 класс Physics (basic)
Chapters: 8
1. Physics and scientific method
Scientific method
- 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
Kinematics of a point · Uniform and accelerated motion · Circular motion
- 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.
- Centripetal Force, Car on a Level Road and on a Banked Road – A body moving in a circle is always changing direction, so it needs a net force towards the centre: the centripetal force F = mv²/r. It is not a new kind of force; tension, gravity, friction or a part of the normal force supplies it. On a level road only friction supplies it, so vmax = √(μs r g). On a road banked at θ, a part of the normal force helps: with no friction the ideal speed is v₀ = √(r g tanθ), and with friction vmax = √[r g (μs + tanθ)/(1 − μs tanθ)].
3. Mechanics: dynamics
Newton's laws · Gravitation · Elastic force, weight, friction · Rigid body equilibrium
- 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).
4. Mechanics: conservation laws
Momentum · Work, power, energy
- 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.
- Work, Kinetic Energy, Work–Energy Theorem and Power – Work is done when a force moves something along its direction: W = F·s = F s cos θ. For a changing force, work is the area under the F–x graph. A moving body has kinetic energy K = ½mv². The work–energy theorem says: net work done on a body = change in its kinetic energy. Power is how fast work is done: P = W/t = F·v.
5. Molecular physics
Molecular kinetic theory · Temperature · Ideal gas
- 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.
- Thermal Equilibrium and the Zeroth Law – Two bodies in contact swap heat until their temperatures are equal. Then they are in thermal equilibrium and nothing changes any more. Zeroth law: if A and B are each in equilibrium with C, then A and B are in equilibrium with each other. This is why a thermometer works. A gas in equilibrium is described by state variables P, V, T and n, which are linked by an equation of state. For an ideal gas it is PV = nRT.
- 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).
6. Thermodynamics
First law of thermodynamics · Second law and heat engines · Phase changes
- 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.
- Thermal Expansion, Specific Heat, Calorimetry and Latent Heat – Temperature tells how hot a body is; heat is energy that flows because of a temperature difference. Most things expand when heated: ΔL = αLΔT, ΔA = βAΔT, ΔV = γVΔT, with β = 2α and γ = 3α. Water is an exception between 0 °C and 4 °C, where it shrinks on heating, so it is densest at 4 °C. The heat needed to warm a body is Q = mcΔT, where c is the specific heat; gases have two, Cp > Cv, with Cp − Cv = R per mole. In calorimetry, heat lost by hot bodies equals heat gained by cold ones. During melting or boiling the temperature stays constant and heat Q = mL goes into changing the state.
7. Electrodynamics: electrostatics
Charge and Coulomb's law · Electric field · Potential · Capacitors
- Electric Charges and Fields – Charge comes in two kinds, is conserved and comes in whole-number packets of e = 1.6 × 10⁻¹⁹ C. Two point charges push or pull with F = kq₁q₂/r² (k = 9 × 10⁹ N m² C⁻²). Forces and fields from many charges add as vectors (superposition). The field E = F/q₀ of a point charge is kq/r²; field lines show it. A dipole (±q a distance 2a apart) has moment p = q·2a; in a uniform field it feels zero net force but a torque τ = pE sinθ. Electric flux Φ = E·A, and Gauss's law says the flux out of any closed surface is q_enclosed/ε₀, which quickly gives E for a long wire (λ/2πε₀r), a plane sheet (σ/2ε₀) and a thin spherical shell (kq/r² outside, 0 inside).
- 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.
8. Electrodynamics: direct current
Direct current · EMF and full circuit · Current in different media
- Ohm's Law, Resistivity and Effect of Temperature – Using drift velocity, V = IR with R = ml/(ne²τA) = ρl/A. Resistivity ρ = m/(ne²τ) depends only on the material and temperature; conductivity σ = 1/ρ. Ohm's law in vector form is j = σE. Metals, wires and resistors give a straight V–I line (ohmic); bulbs, diodes and devices like GaAs give curved or one-way graphs (non-ohmic). For metals ρ rises with temperature: ρT = ρ0[1 + α(T − T0)]; alloys like nichrome change very little; semiconductors get lower ρ when hot.
- EMF, Internal Resistance, Power and Combination of Cells – A cell does work on charges; the work per coulomb is its emf ε. Inside the cell there is a small internal resistance r. With current I, the terminal voltage is V = ε − Ir and I = ε/(R + r). Electrical power P = VI = I²R = V²/R, and energy W = Pt. Power delivered to R is largest when R = r. Cells in series: εeq = ε1 + ε2, req = r1 + r2. Cells in parallel: εeq = (ε1r2 + ε2r1)/(r1 + r2), 1/req = 1/r1 + 1/r2.
- Semiconductors and the p-n Junction Diode – A semiconductor has a small energy gap (about 1 eV), so a little heat frees some electrons. Pure silicon is intrinsic (electrons = holes). Adding a 5-valence atom makes n-type; a 3-valence atom makes p-type. Joining p and n makes a junction with a depletion layer and a barrier (about 0.7 V for Si). The diode conducts in forward bias, almost not in reverse bias, so it can change AC into one-way DC (rectifier).