A-LevelPhysicsOscillations9702/33 · May/June 2017 · Q120 Marks

In this experiment, you will investigate the motion of a chain of paper clips.

(a)You have been provided with a chain of fifteen paper clips with a sphere of modelling clay attached to one end of the chain. Measure and record the length L of one paper clip as shown in Fig. 1.1. [Figure 1.1] L =[1]
(b)(i)Set up the apparatus as shown in Fig. 1.2. [Figure 1.2] The chain should be suspended from the nail. The wooden rod should be positioned so that the chain, when hanging vertically, just touches the rod with 6 paper clips below the rod.
(b)(ii)Record the number n of paper clips below the rod. n =
(c)Move the sphere towards you through a distance of approximately 10 cm. Release the sphere. The chain will oscillate and hit the rod during these oscillations. Determine the period T of the oscillations. T =[2]
(d)Change n by moving the wooden rod vertically and repeat (b)(ii) and (c) until you have six sets of values of n and T. Record your results in a table. Include values of √n to three significant figures in your table.[8]
(e)(i)Plot a graph of T on the y-axis against √n on the x-axis.[3]
(e)(ii)Draw the straight line of best fit.[1]
(e)(iii)Determine the gradient and y-intercept of this line. gradient = y-intercept =[2]
(f)It is suggested that the quantities T and n are related by the equation T = P√n + Q where P and Q are constants. Using your answers in (e)(iii), determine the values of P and Q. Give appropriate units. P = Q =[2]
(g)Theory suggests that P = π √(L/g) where g is the acceleration of free fall. Use your values in (a) and (f) to determine a value for g. Give an appropriate unit. g =[1]

This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

[1] Value of L with unit to the nearest mm in the range 2.5–3.5 cm.
[1] Value of T with unit in the range 0.7 s to 1.5s.
[1] Evidence of repeated timings. Must see nT repeated where n ≥ 5.
[4] Six sets of readings of n (different values) and time with correct trend and without help from Supervisor scores 4 marks, five sets scores 3 marks etc.
[1] Range of n ≥ 9.
[1] Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of quantity and unit must conform to accepted scientific convention e.g. T/s. No unit for n or √n.
[1] Consistency: All values of raw time must be given to either 0.1 s or 0.01 s.
[1] Significant figures: All values of √n must be given to 3 significant figures.
[1] Axes: Sensible scales must be used, no awkward scales (e.g. 3:10 or fractions). Scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Scales must be labelled with the quantity that is being plotted. Scale markings should be no more than three large squares apart.
[1] Plotting of points: All observations must be plotted on the grid. Diameter of plotted points must be < half a small square (no "blobs”). Points must be plotted to an accuracy of half a small square.
[1] Quality: All points in the table must be plotted for this mark to be awarded. It must be possible to draw a straight line that is within ± 0.10 on the √n axis of all plotted points.
[1] Line of best fit: Judge by balance of all points on the grid about the candidate's line (at least 5). There must be an even distribution of points either side of the line along the full length. Allow one anomalous point only if clearly indicated (i.e. circled or labelled) by the candidate. There must be at least five points left after the anomalous point is disregarded. Lines must not be kinked or thicker than half a small square.
[1] Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. Method of calculation must be correct. Do not allow ∆x / ∆y. Both read-offs must be accurate to half a small square in both x and y directions.
[1] y-intercept: Correct read-off from a point on the line substituted correctly into y = mx + c or an equivalent expression. Read-off accurate to half a small square in both x and y directions. or Intercept read directly from the graph, with read-off at x = 0, accurate to half a small square in y direction.
[1] Value of P = candidate's gradient and value of Q = candidate's intercept. The values must not be fractions.
[1] Units for P and Q both s.
[1] Correct calculation of g = Lπ²/ P² with consistent unit.