Zusammenfassung der Ressource
UNIT 4 - Fields and Further Mechanics
- Force and Momentum
- Momentum and Impulse
Anmerkungen:
- Momentum = mv
Force = Δ(mv)/Δt
Impulse = Δ(mv)
- Elastic and Inelastic Collisions
Anmerkungen:
- Elastic - Collision where there is no loss of kinetic energy
Totally Inelastic - Where the colliding objects stick together
Partially Inelastic - There is a loss in kinetic energy
- Motion in a Circle
- Uniform Circular Motion
Anmerkungen:
- v=(2πr)/T
Angular displacement = θ = 2πft
Angular speed = ω = 2πf
= (2π)/T
- Centripetal Acceleration
Anmerkungen:
- a = v²/r = ω²r
Centripetal Force = F = mv²/r = mω²r
- Simple Harmonic Motion
- Oscillations
Anmerkungen:
- Amplitude - Maximum displacement from equilibrium
Time Period - Time for one complete cycle of oscillations
Frequency - Number of cycles per second
Phase Difference = (2π∆t)/T
- Principles
Anmerkungen:
- Simple Harmonic Motion is defined as oscillating motion in which acceleration is proportional and opposite to displacement
a = -(2πf)²x
x = Acos(2πft)
- Applications of SHM
Anmerkungen:
- When:
Adding Extra Mass - The frequency is reduced as it increases the inertia of the system.
Using Weaker Springs - The frequency is reduced as the force at any given displacement will be less so acceleration and speed will be less.
- Energy and SHM
Anmerkungen:
- E = 1/2(mv²)
= 1/2k(A²-x²)
Hence: v = ±(2πf)√(A²-x²)
- Damping
Anmerkungen:
- Light Damping - Amplitude gradually decreases over many oscillations
Critical Damping - Returns to equilibrium in the shortest time possible and then stops
Heavy Damping - The displacement gradually decreases to equilibrium with no oscillation
- Forced Oscillations
Anmerkungen:
- When a periodic force is applied to an oscillating system, the system undergoes forced oscillations. When the periodic force occurs at the same frequency as the natural frequency of the system, maximum displacement is achieved
- Resonance
Anmerkungen:
- A system is in resonance when the applied frequency equals the natural frequency
- Gravitational Fields
- Gravitational Field Strength
Anmerkungen:
- g=f/m
Radial Field - Where the field lines are like spokes on a wheel, always directed to the centre
Uniform Field - Where the field strength is the same in magnitude and direction throughout the field
- Gravitational Potential
Anmerkungen:
- V=W/mPotential Gradient = ΔV/Δr
The gravitational potential at a point is the work done per unit mass to move a small object from infinity to that point
- Potential Gradient
Anmerkungen:
- Equipotentials are lines of constant potential, like contours on a map
The potential gradient at a point in a gravitational field is the change of potential per metre at that point
- Newton's Law of Gravitation
Anmerkungen:
- Planetary Fields
Anmerkungen:
- For a point mass M:
g=F/m=(GM)/r²
For a spherical mass M of radius R:
F = (GMm)/r²
g=(GM)/r²
Gravitational potential near a spherical planet:
V=(-GM)/r
- Satellite Motion
Anmerkungen:
- Speed of a planet: v=(GM)/r
r³/T² = (GM)/4π²
- Electric Fields
- Electric Field Strength
Anmerkungen:
- E=F/Q
Between two parallel plates: E=V/d
- Electric Potential
Anmerkungen:
- V=Ep/Q
The electric field strength is equal to the negative of the potential gradient
- Coulomb's Law
Anmerkungen:
- Point Charges
Anmerkungen:
- Comparison between Electric and Gravitational fields
- Capacitors
- Capacitance
Anmerkungen:
- Energy Stored
Anmerkungen:
- Discharge
Anmerkungen:
- ΔQ/Q = -Δt/CR
Q = Q0e^(-t/RC)
Time Constant = RC
- Magnetic Fields
- Current carrying
conductors in
magnetic fields
Anmerkungen:
- The motor effect takes place when current cuts across a magnetic field, resulting in a force perpendicular to the plane that can be worked out with Fleming's Left Hand Rule. The force is greatest when the wire is at right angles to the magnetic field
F=BIL
- Moving Charges
Anmerkungen:
- Charged Particles in Circular Orbits
Anmerkungen:
- BQv = (mv²)/r
r = (mv)/(BQ)
- Electromagnetic Induction
- Generating Electricity
Anmerkungen:
- An induced emf can be increased by moving the wire faster in a field, by using a stronger magnet, or by making the wire into a coil with more turns.
The direction of motion, field and current can be found using Fleming's Right Hand Rule
- Laws of Electromagnetic Induction
Anmerkungen:
- Coils - At the north end of a coil, current travels anticlockwise and at the south end vice versa
Lenz's Law - The direction of the induced current is always such as to oppose the change that causes the current
Faraday's Law - The induced emf in a circuit is equal to the rate of change of flux linkage through the circuit
EMF = Blv
- Alternating Current Generator
Anmerkungen:
- In an alternating current generator, the amount of emf being produced at any time is reliant on the angle between the coil of wire and the magnetic field
ε = ε0 sin2πft
- Transformers
Anmerkungen:
- Vs/Vp = Ns/Np
A step up transformer has more turns on the secondary coil than on the primary coil and voltage is therefore stepped up. The opposite is true of a step down transformer
Efficiency = (IsVs)/(IpVp) * 100
Electrical Power remains equal