5.1.1 - Creating models (A-Level Physics OCR B H557)

#5.1.1a(i)

capacitance as the ratio $C = \dfrac{Q}{V}$

#5.1.1a(ii)

the energy on a capacitor $E = \dfrac{1}{2}QV$

#5.1.1a(iii)

the exponential form of the decay of charge on a capacitor as due to the rate of removal of charge being proportional to the charge remaining $\dfrac{dQ}{dt} = -\dfrac{Q}{RC}$

exponential relationship as shown, explained using constant ratio property

#5.1.1a(iv)

the exponential form of radioactive decay as a random process with a fixed probability, the number of nuclei decaying being proportional to the number remaining $\dfrac{dN}{dt} = -λN$

#5.1.1a(v)

simple harmonic motion of a mass with a restoring force proportional to displacement such that $\dfrac{d^2x}{dt^2} = -\dfrac{k}{m}x$

#5.1.1a(vi)

simple harmonic motion of a system where $a = -ω^2x$ , where $ω = 2πf$ , and two possible solutions are $x = A\sin{ωt}$ and $x = A\cos{ωt}$

#5.1.1a(vii)

kinetic and potential energy changes in simple harmonic motion

example of conservation of energy

#5.1.1a(viii)

free and forced vibrations, damping and resonance.

qualitative treatment only

#5.1.1b

Make appropriate use of:

(i) for a capacitor: the term: time constant τ

(ii) for radioactive decay: the terms: activity, decay constant λ, half-life $T_{1/2}$ , probability, randomness

(iii) for oscillating systems: the terms: simple harmonic motion, period, frequency, free and forced oscillations, resonance, damping

by expressing in words:

(iv) relationships of the form $\dfrac{dx}{dt} = -kx$ , whererate of change is proportional to amount present Learners are expected to be able to transfer relationships from words, formulae and diagrams, converting from any one form to another

by sketching, plotting from data and interpreting:

(v) exponential curves plotted with linear or logarithmic scales *Capacitor charging and discharging curves plotted against linear scales *

(vi) energy of capacitor as area below a Q–V graph

(vii) x–t, v–t and a–t graphs of simple harmonic motion including their relative phases

(viii) amplitude of a resonator against driving frequency.

#5.1.1c(i)

calculating activity and half-life of a radioactive source from data, $T_{1/2} = \dfrac{\ln{2}}{λ}$

#5.1.1c(ii)

solving equations of the form $\dfrac{dN}{dt} = -λN$ by iterative numerical or graphical methods

i $N = N_0e^{-λt}$ as the analytic solution

#5.1.1c(iii)

calculating time constant τ of a capacitor circuit from data; $τ = RC$ ; $Q = Q_0e^{-t/RC}$

#5.1.1c(iv)

solving equations of the form $\dfrac{ΔQ}{Δt} = -\dfrac{Q}{RC}$ discharging $Q = Q_0e^{-t/RC}$ ; charging $Q = Q_0\Big(1 - e^{-t/RC}\Big)$ ; corresponding equations for V and I

#5.1.1c(ix)

solving equations of the form $\dfrac{Δ^2x}{Δt^2} = -\dfrac{k}{m}x$ by iterative numericalor graphical methods

#5.1.1c(v)

$C = \dfrac{Q}{V}$ , $I = \dfrac{ΔQ}{Δt}$ , $E = \dfrac{1}{2} QV = \dfrac{1}{2}CV^2$

#5.1.1c(vi)

$T = 2π\sqrt{\dfrac{m}{k}}$ with $f = \dfrac{1}{T}$ for a mass oscillating on a spring

#5.1.1c(vii)

$T = 2π\sqrt{\dfrac{L}{g}}$ for a simple pendulum

#5.1.1c(viii)

$F = kx$ ; $E = \dfrac{1}{2}kx^2$

#5.1.1c(x)

$x = A\sin{2πft}$ or $x = A\cos{2πft}$

#5.1.1c(xi)

$E_{total} = \dfrac{1}{2}mv^2 + \dfrac{1}{2}kx^2$

#5.1.1d(i)

measuring the period/frequency of simple harmonic oscillations for example mass on a spring or simple pendulum and relating this to parameters such as mass and length

links to 5.1.1a(v), (vi), (vii), b(iii), (iv), c(vi), (vii), (viii), (ix), (x), (xi), PAG10

#5.1.1d(ii)

qualitative observations of forced and damped oscillations for a range of systems

links to 5.1.1a(viii), b(iii), PAG10

#5.1.1d(iii)

investigating the charging and discharging of a capacitor using both meters and data loggers

links to 5.1.1a(iii), b(v), c(iii), c(iv), PAG9

#5.1.1d(iv)

determining the half-life of an isotope such as protactinium.

links to 5.1.1c(i), PAG7

A-Level Physics OCR B H557

5.1.1: Creating models