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Flashcards · 7408 · Topic 6

Further mechanics and thermal physics flashcards

19 cards on Topic 6, subtopics 3.6.1 to 3.6.2. Pick a subtopic or study them all.

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3.6.1 Periodic motion

Centripetal acceleration and force
a = v²/r = ω²r, towards the centre. F = mv²/r = mω²r. It is a resultant supplied by real forces, never an extra force.
Condition for simple harmonic motion
Acceleration is proportional to displacement and directed towards the equilibrium position: a = −ω²x.
SHM: maximum speed, maximum acceleration, and speed at displacement x
v_max = ωA (at equilibrium). a_max = ω²A (at the extremes). v = ±ω√(A² − x²).
Periods of a mass-spring system and a simple pendulum
Mass-spring: T = 2π√(m/k). Pendulum (small angles): T = 2π√(l/g), independent of the mass of the bob. Neither depends on amplitude.
SHM energy: where Ek and Ep are greatest, and their period against time
Ek is greatest at x = 0; Ep at x = ±A; the total is constant (undamped). Each energy varies with half the period of the oscillation.
Light, critical and heavy damping
Light: amplitude decays gradually, period about the same. Critical: returns to equilibrium in the shortest time without oscillating. Heavy: returns slowly without oscillating.
Free vs forced vibration, and resonance
Free: no driving force; oscillates at its natural frequency. Forced: oscillates at the driving frequency. Resonance: driving frequency = natural frequency, giving maximum amplitude.
Effect of more damping on a resonance curve
The peak is lower and broader, and occurs at a slightly lower frequency.
Required practical 7: good technique and the graph
Time many oscillations, repeat, and time from the equilibrium position; plot T² against m or l and use the gradient (4π²/k or 4π²/g).

3.6.2 Thermal physics

Internal energy
The sum of the randomly distributed kinetic and potential energies of the particles in a body.
Why does temperature stay constant during a change of state?
The energy supplied changes the potential energies of the particles, not their kinetic energies.
Specific heat capacity and specific latent heat equations
Q = mcΔθ (c: energy per kg per K). Q = ml (l: energy per kg to change state at constant temperature).
Boyle's law, Charles's law and the pressure law (fixed mass of gas)
Boyle: pV constant at constant T. Charles: V ∝ T at constant p. Pressure law: p ∝ T at constant V. T is in kelvin; absolute zero is about −273 °C.
Ideal gas equation, and the link between k, R and N_A
pV = nRT = NkT, with T in kelvin. k = R/N_A.
Kinetic theory assumptions
Many identical molecules in random motion; elastic collisions; negligible molecular volume; no intermolecular forces except during collisions; negligible collision time.
Mean kinetic energy of a gas molecule
½m(c_rms)² = (3/2)kT = (3/2)RT/N_A. At 300 K: 1.5 × 1.38 × 10⁻²³ × 300 = 6.2 × 10⁻²¹ J.
Root mean square speed
c_rms = √(mean of c²). It is not the same as the mean speed.
Brownian motion
The random motion of visible particles (such as smoke) caused by collisions with invisible molecules. Evidence for molecules.
Work done by a gas expanding at constant pressure
W = pΔV, the area under the p–V graph.

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