Date | November 2018 | Marks available | 1 | Reference code | 18N.3.SL.TZ0.1 |
Level | Standard level | Paper | Paper 3 | Time zone | 0 - no time zone |
Command term | Draw | Question number | 1 | Adapted from | N/A |
Question
In an investigation to measure the acceleration of free fall a rod is suspended horizontally by two vertical strings of equal length. The strings are a distance d apart.
When the rod is displaced by a small angle and then released, simple harmonic oscillations take place in a horizontal plane.
The theoretical prediction for the period of oscillation T is given by the following equation
where c is a known numerical constant.
In one experiment d was varied. The graph shows the plotted values of T against . Error bars are negligibly small.
State the unit of c.
A student records the time for 20 oscillations of the rod. Explain how this procedure leads to a more precise measurement of the time for one oscillation T.
Draw the line of best fit for these data.
Suggest whether the data are consistent with the theoretical prediction.
The numerical value of the constant c in SI units is 1.67. Determine g, using the graph.
Markscheme
✔
Accept other power of tens multiples of , eg: .
measured uncertainties «for one oscillation and for 20 oscillations» are the same/similar/OWTTE
OR
% uncertainty is less for 20 oscillations than for one ✔
dividing «by 20» / finding mean reduces the random error ✔
Straight line touching at least 3 points drawn across the range ✔
It is not required to extend the line to pass through the origin.
theory predicts proportional relation «, slope = Td = = constant » ✔
the graph is «straight» line through the origin ✔
correctly determines gradient using points where ΔT≥1.5s
OR
correctly selects a single data point with T≥1.5s ✔
manipulation with formula, any new and correct expression to enable g to be determined ✔
Calculation of g ✔
With g in range 8.6 and 10.7 «m s−2» ✔
Allow range 0.51 to 0.57.