A1. Data analysis question.
Caroline carried out an experiment to measure the variation with water depth d of the wave speed c of a surface water wave. Her data are shown plotted below.
The uncertainty in the water depth d is too small to be shown. Uncertainties in the measurement of the wave speed c are shown as error bars on the graph except for the data point corresponding to d .
(a) Caroline calculated the wave speed by measuring the time t for the wave to travel 150 cm. The uncertainty in this distance is 2 cm. For the reading at a water depth of 15 cm, the time t is 8.3 s with an uncertainty 0.5s.
- (i) Show that the absolute uncertainty in the wave speed at this time is 1.3 cms–1.
- (ii) On the graph opposite, draw the error bar for the data point corresponding to d=15cm.
(b) Caroline hypothesized that the wave speed c is directly proportional to the water depth d.
- (i) On the graph opposite, draw a line of best-fit for the data.
- (ii) Suggest if the data support this hypothesis.
(c) Another student proposes that c is proportional to d0.5.State a suitable graph that can be plotted to test this proposal.
(d) There is a systematic error in Caroline’s determination of the depth.
- (i) State what is meant by a systematic error.
- (ii) State how the graph in (c) would indicate that there is a systematic error.
A2. This question is about the properties of tungsten.
(a) Tungsten is a conductor used as the filament of an electric lamp. The filament of the lamp is surrounded by glass which is an insulator.Outline, in terms of their atomic structure, the difference between the electrical properties of tungsten and of glass.
(b) A tungsten filament lamp is marked 6.0 V, 15 W.
- (i) Show that the resistance of the lamp at its working voltage is 2.4 Ω.
- (ii) The length of the filament is 0.35 m and the resistivity of tungsten is 5.6×10–7Ωm at its working voltage.Calculate the cross-sectional area of the tungsten filament.
(c) The diagram shows part of a potential divider circuit used to measure the current-potential difference (I–V ) characteristic of the bulb.
Draw the complete circuit showing the correct position of the bulb, ammeter and voltmeter.
A3. (a) A nuclide of deuterium (21H) and a nuclide of tritium(31H) undergo nuclear fusion.
- (i) Each fusion reaction releases 2.8×10–12 J of energy. Calculate the rate, in kgs–1,at which tritium must be fused to produce a power output of 250 MW.
- (ii) State two problems associated with sustaining this fusion reaction in order to produce energy on a commercial scale.
(b) Tritium is a radioactive nuclide with a half-life of 4500 days. It decays to an isotope of helium.Determine the time at which 12.5 % of the tritium remains undecayed.