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1 Further Mechanics

Force as the rate of change of momentum: o F = Δ(mv) / Δt

Impulse: o FΔt = Δ(mv) which is

derived from the area under a force-time graph.

Principle of conservation of linear momentum applied to problems in one dimension.

Elastic and inelastic collisions and explosions in terms of momentum.

Motion in a circular path at constant speed implies there is an acceleration and requires a centripetal force.

Angular speed: o ω = v / r = 2πf

Centripetal acceleration: o a = v2 / r = ω2r

Centripetal force:

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o F = mv2 / r = mω2r

Characteristic features of simple harmonic motion.

Condition for SHM: o a = −ω2x (where ω =

2πf) o x = A cos 2πft

o v = ±2πf (A2 − x2)

Graphical representations of SHM linking x, v, a and t.

Velocity as gradient of displacement-time graph.

Maximum speed: o vmax = 2πfA. o Maximum acceleration

= amax = (2πf )2A.

Study of mass-spring system.

o T = 2π(m / k)

Study of simple pendulum.

o T = 2π(l / g)

Variation of Ek, Ep and total energy with displacement, and with time.

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Qualitative treatment of free and forced vibrations.

Resonance and the effects of damping on the sharpness of resonance.

Phase difference between driver and driven displacements.

Examples of these effects in mechanical systems and stationary wave situations.

2 Gravitation

Gravity as a universal attractive force acting between all matter.

Force between point masses: o F = Gm1m2 / r2 where G

is the gravitational constant.

Concept of a force field as a region in which a body experiences a force.

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Representation by gravitational field lines.

g as force per unit mass defined by: o g = F / m

Magnitude of g in a radial field given by: o g = GM / r2

Understanding of the definition of gravitational potential, including zero value at infinity and of gravitational potential difference.

Work done in moving mass m given by: o ΔW = mΔV

Gravitational potential V in a radial field given by: o V = − GM / r

Graphical representations of variations of g and V with r.

V related to g by: o g = - ΔV / Δr

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Orbital period and speed related to radius of circular orbit.

Energy considerations for an orbiting satellite.

Significance of a geosynchronous orbit.

3 Coulomb’s law

Force between point charges in a vacuum: o F = 1 / 4πε0 Q1Q2 / r2

(where ε0 is the permittivity of free space):

o 1 / 4πε0 9 x 109

E as the force per unit charge defined by: o E = F / Q

Representation by electric field lines.

Magnitude of E in a radial field given by: o F = 1 / 4πε0 Q / r2

Magnitude of E in a uniform field given by:

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o E = V / d

Understanding of definition of absolute electric potential, including zero value at infinity, and of electric potential difference.

Work done in moving charge Q given by: o ΔW = Q ΔV

Magnitude of V in a radial field given by: o V = 1 / 4πε0 Q / r

Graphical representations of variations of E and V with r.

Comparing electric and gravitational fields

Similarities include inverse square law fields having many characteristics in common.

Differences include masses always attract but charges may attract or repel.

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4 Capacitance

Definition of capacitance: o C = Q / V

Derivation of E = ½QV and interpretation of area under a graph of charge against pd. o E = ½QV = ½CV2

= Q2 / 2C

Graphical representation of charging and discharging of capacitors through resistors.

Time Constant = RC

Calculation of time constants including their determination from graphical data

Quantitative treatment of capacitor discharge o Q = Q0e-t/RC

Experience of the use of a voltage sensor and datalogger to plot discharge curves for a capacitor.

5 Magnetic Fields

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Force on a current-carrying wire in a magnetic field.

F = BIL when the field is perpendicular to current.

Fleming’s left hand rule.

Magnetic flux density and definition of the tesla.

Force on charged particles moving in a magnetic field.

F = B Q v when the field is perpendicular to velocity.

Circular path of particles; application in devices such as the cyclotron

Magnetic flux defined by: o φ = BA where B is

normal to A.

Flux linkage as Nφ, where N is the number of turns cutting the flux.

Flux and flux linkage passing through a

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rectangular coil rotated in a magnetic field: o Nφ = BAN cos θ where

θ is the angle between the normal to the plane of the coil and the magnetic field.

Simple experimental phenomena.

Faraday's and Lenz's laws.

Magnitude of induced emf = rate of change of flux linkage: o ε = N Δφ / Δt

Applications such as a moving straight conductor.

Emf induced in a coil rotating uniformly in a magnetic field: o ε = BANω sin ωt

The operation of a transformer.

The transformer equation:

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o Ns / Np = Vs / Vp

Transformer efficiency: o IsVs / IpVp

Causes of inefficiency of a transformer.

Transmission of electrical power at high voltage.