Germany Jahrgangsstufe 11 Physics
Chapters: 4
1. Circular motion
Circular motion and gravitation
- 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)].
2. Oscillations and waves
Oscillations and waves
- 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.
3. Independent work on physics topics
Astronomical world views · Introduction to special relativity · Energy supply
- Kepler's Laws of Planetary Motion – Kepler gave three rules for how planets move. 1) Each planet moves on an ellipse with the Sun at one focus. 2) The line from the Sun to the planet sweeps equal areas in equal times, so the planet moves faster when it is near the Sun. 3) The square of the time for one round (T²) is proportional to the cube of the semi-major axis (a³). The second law is really conservation of angular momentum. The third law follows from Newton's law of gravitation.
- 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.
- Minerals and Energy Resources – Minerals are natural substances found in rocks. They are metallic (ferrous or non-ferrous), non-metallic, or energy minerals. Energy comes from conventional sources like coal, petroleum, natural gas and electricity, and from non-conventional sources like sun, wind, nuclear, biogas, tides and heat from the Earth. Both minerals and energy must be conserved.
4. Profile area (science-technology school, 27 h)
Numerical modelling: method of small steps · Photovoltaics in practice · Extra-curricular physics activity · Applied physics projects
- Numerical Methods: Finding Roots and Areas Step by Step – Some equations and areas cannot be found with a neat formula. Numerical methods get as close as we like with simple repeated steps: check a change of sign, halve the interval (bisection), slide down tangents (Newton-Raphson), repeat x = g(x) (fixed-point iteration), add up trapeziums for an area, and walk along a slope in small steps (Euler).
- Solar Energy: From the Sun to Your Plug – The Sun makes energy by nuclear fusion: hydrogen nuclei join to make helium, and a little mass becomes a lot of energy (E = mc²). The hot surface (about 5800 K) radiates mostly visible light (Wien's law), and its total power grows as T⁴ (Stefan's law). About 1361 W reaches each square metre facing the Sun at the top of the atmosphere; about 1000 W/m² reaches the ground on a clear day. Sunlight hitting at a slant spreads over more area, which explains latitude and seasons. Solar cells turn light into electricity: P = intensity × area × efficiency × cos(angle). Solar water heaters turn light into heat.