A-LevelPhysicsOscillations9702/31 · Oct/Nov 2017 · Q120 Marks

In this experiment, you will investigate the motion of a Y-shaped pendulum.

(a)You have been provided with two pieces of string. The longer piece of string has a loop at each end. The shorter piece of string is attached to a bob. Set up the apparatus as shown in Fig. 1.1. Attach the shorter string to the middle of the longer string with a knot. Ensure the two rods of the clamps are at the same height above the bench. Position the stands approximately 35 cm apart. The angle θ is the angle between the two halves of the longer string.
(b)Measure and record θ.[1]
(c)Pull the bob a short distance towards you. Release the bob. The bob will oscillate. Determine the period T of these oscillations.[1]
(d)Vary the distance between the stands and repeat (b) and (c) until you have six sets of values of θ and T. Record your results in a table. Include values of cos (θ/2) and T² in your table.[10]
(e)(i)Plot a graph of T² on the y-axis against cos (θ/2) 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.[2]
(f)It is suggested that the quantities T and θ are related by the equation T² = P cos(θ/2) + Q where P and Q are constants. Using your answers in (e)(iii), determine the values of P and Q. Give appropriate units.[2]

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 (Oct/Nov 2017). The mark or mark type is shown in brackets.

[1] Value of θ in range 80-100° with unit.
[1] Value of T in range 0.80-2.00 s with unit.
[5] Six sets of readings of θ (different values) and time showing the correct trend (T increases as θ decreases) and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc.
[1] Range: θ ≥ 120° and θ ≤ 60°.
[1] Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of the quantity and the unit must conform to accepted scientific convention e.g. T²/s² and θ/°. No unit for cos (θ/2).
[1] Consistency: All raw values of time must be given to the nearest 0.1 s or all to the nearest 0.01 s.
[1] Significant figures: All values of T² must be given to the same number of s.f. as (or one more than) the number of s.f. in raw values of time. If raw times recorded to nearest 0.01 s, allow number of s.f. of T² to be one less than the number of s.f. of the raw times.
[1] Values of cos (θ/2) calculated correctly.
[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 (at least 5) must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within 0.05 on the cos (θ/2) axis (x-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 should be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both the x and y directions. The method of calculation must be correct.
[1] y-intercept: Check correct read-off from a point on the line and substituted into y = mx + c. Read-off must be 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 the 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 correct (s²).