| Date | November 2013 | Marks available | 4 | Reference code | 13N.2.SL.TZ0.1 |
| Level | Standard level | Paper | Paper 2 | Time zone | Time zone 0 |
| Command term | Estimate and Explain | Question number | 1 | Adapted from | N/A |
Question
Data analysis question.
A chain is suspended between two vertical supports A and B. The chain is made of a number of identical metal links.
The length l of the chain can be increased by adding extra links. An experiment was undertaken to investigate how the sag d of the midpoint of the chain, measured from the horizontal between A and B, varies with l. The data obtained are shown plotted below. The uncertainties in l are too small to be shown.
Draw a best-fit line for the data points on the graph opposite.
With reference to your answer to (a),
(i) explain why the relationship between d and l is not linear.
(ii) estimate the horizontal distance between the supports A and B.
Before the experiment was carried out, it was hypothesized that d depends on \(\sqrt l \). Determine, using your answer to (a), whether this hypothesis is valid.
Markscheme
smooth curve that goes through all error bars;
Do not allow thick or hairy or doubled lines, or lines where the curvature changes abruptly.
Do not allow lines that touch horizontal ends of error bars but miss the verticals.
(i) (no)
reference to going through all the error bars;
the line is a curve/not straight / straight line would not pass through all the points / equal increments in l give rise to unequal increments in d;
(ii) mentions or shows clear extrapolation to l axis; { (allow from curve or straight line)
read-off to within a square (0.50±0.05m);
Award [1max] if no extrapolation seen on graph.
Answer must match read-off to 2+sig fig.
two data points on line correctly read and more than 0.5 apart on l-axis;
\({d^2} = kl\) or \(d = k\sqrt l \);
two or more correct calculations of k from readings;
comment that two or more values are not equal (even with error bar consideration) therefore hypothesis is not valid;
Award [3 max] if l-axis values differ by less than 0.5.
