| Date | May 2016 | Marks available | 2 | Reference code | 16M.3.SL.TZ0.1 |
| Level | Standard level | Paper | Paper 3 | Time zone | Time zone 0 |
| Command term | Calculate | Question number | 1 | Adapted from | N/A |
Question
A student investigates the oscillation of a horizontal rod hanging at the end of a vertical string. The diagram shows the view from above.
The student starts the rod oscillating and measures the largest displacement for each cycle of the oscillation on the scale and the time at which it occurs. The student begins to take measurements a few seconds after releasing the rod.
The graph shows the variation of displacement x with time t since the release of the rod. The uncertainty for t is negligible.
On the graph above, draw the line of best fit for the data.
Calculate the percentage uncertainty for the displacement when t=40s.
The student hypothesizes that the relationship between x and t is \(x = \frac{a}{t}\) where a is a constant.
To test the hypothesis x is plotted against \(\frac{1}{t}\) as shown in the graph.
(i) The data point corresponding to t=15s has not been plotted. Plot this point on the graph above.
(ii) Suggest the range of values of t for which the hypothesis may be assumed to be correct.
Markscheme
smooth curve passing through all error bars
x=2.5 cm±0.2cm AND Δ0x=0.5cm±0.1cm
«\(\frac{{0.5}}{{2.5}}\)=»20%
Accept correctly calculated value from interval 15% to 25%.
(i) plotted point (0.07, 9.0) as shown
Allow any point within the grey square. The error bar is not required.
(ii) ALTERNATIVE 1
t–1 from 0.025 s–1 to 0.04 s–1
giving t from 25 to 40
ALTERNATIVE 2
the data do not support the hypothesis
any relevant support for the suggestion, eg straight line cannot be fitted through the error bars and the origin
Do not allow ECF from MP1 to MP2.
