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Date November 2012 Marks available 3 Reference code 12N.2.SL.TZ0.1
Level Standard level Paper Paper 2 Time zone Time zone 0
Command term Calculate, Determine, Draw, Explain, and State Question number 1 Adapted from N/A

Question

Data analysis question.

The movement of glaciers can be modelled by applying a load to a sample of ice.

After the load has been applied, it is observed to move downwards at a constant speed v as the ice deforms. The constant speed v is measured for different loads. The graph shows the variation of v with load W for a number of identical samples of ice.

The data points are plotted below.

The uncertainty in v is ±20 μm s–1 and the uncertainty in W is negligible.

(i) On the graph opposite, draw error bars on the first and last points to show the uncertainty in v.

(ii) On the graph opposite, draw the line of best-fit for the data points.

[2]
a.

Explain whether the data support the hypothesis that v is directly proportional to W.

[1]
b.

Theory suggests that the relation between v and W is

\[v = k{W^3}\]

where k is a constant.

To test this hypothesis a graph of \({v^{\frac{1}{3}}}\) against W is plotted.

At W=5.5 N the speed is 250±20 μm s–1.

Calculate the uncertainty in \({v^{\frac{1}{3}}}\) for a load of 5.5 N.

[3]
c.

(i) Using the graph in (c), determine k without its uncertainty.

(ii) State an appropriate unit for your answer to (d)(i).

[5]
d.

Markscheme

(i) both error bars correct (overall length 4 squares) \( \pm \frac{1}{2}\) square;

(ii) smooth curve going through error bars and within half square of other points;

a.

not proportional because not straight/trend cannot go through origin;

b.

fractional error in \(v = \frac{{20}}{{250}}\left( { = 0.080} \right)\);
fractional error in \({v^{\frac{1}{3}}} = \frac{{0.080}}{3}\left( { = 0.027} \right)\); (allow ECF from first marking point)
uncertainty in \({v^{\frac{1}{3}}} = \left( {0.063 \times 0.027 = } \right)0.00169\); (allow 0.00168−0.00170)
Allow expression of answer as 0.630±0.002 if calculation above seen.
Award [3] for a bald correct answer.

or

recognizes uncertainty in \({v^{\frac{1}{3}}} = \frac{{\sqrt[3]{{270}} - \sqrt[3]{{230}}}}{2}\) or \({\sqrt[3]{{250}} - \sqrt[3]{{230}}}\) or \({\sqrt[3]{{270}} - \sqrt[3]{{250}}}\);
= 0.168 ;
conversion to 0.00168ms−1;

c.

(i) large triangle > half line used;
read-offs and substitution correct; (allow power of ten error here)
\({k^{\frac{1}{3}}} = 0.012 \pm 0.001\); (allow ECF)
k=1.73×10–6 m N–3 s–1; (allow correct power of ten only)
Award [0] for use of a single data point.

(ii) m N–3 s–1 or kg−3 m−2 s5;

d.

Examiners report

[N/A]
a.
[N/A]
b.
[N/A]
c.
[N/A]
d.

Syllabus sections

Core » Topic 1: Measurements and uncertainties » 1.1 – Measurements in physics
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