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.
Explain whether the data support the hypothesis that v is directly proportional to W.
Theory suggests that the relation between v and W is
v=kW3
where k is a constant.
To test this hypothesis a graph of v13 against W is plotted.
At W=5.5 N the speed is 250±20 μm s–1.
Calculate the uncertainty in v13 for a load of 5.5 N.
(i) Using the graph in (c), determine k without its uncertainty.
(ii) State an appropriate unit for your answer to (d)(i).
Markscheme
(i) both error bars correct (overall length 4 squares) ±12 square;
(ii) smooth curve going through error bars and within half square of other points;
not proportional because not straight/trend cannot go through origin;
fractional error in v=20250(=0.080);
fractional error in v13=0.0803(=0.027); (allow ECF from first marking point)
uncertainty in v13=(0.063×0.027=)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 v13=3√270−3√2302 or 3√250−3√230 or 3√270−3√250;
= 0.168 ;
conversion to 0.00168ms−1;
(i) large triangle > half line used;
read-offs and substitution correct; (allow power of ten error here)
k13=0.012±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;