A-LevelPhysicsOscillations9702/33 · Feb/Mar 2019 · Q120 Marks

In this experiment, you will investigate a pendulum with a mass fixed at each end.

(a)• Assemble the apparatus with the nail passing through the third hole from C, as shown in Fig. 1.1. • Ensure that the nail is held securely in the clamp. • The distance between the nail and C is x, as shown in Fig. 1.1. Measure and record x. x = ..................................................... cm[1]
(b)• Push the bottom of the strip horizontally through a distance of approximately 5cm. Release the strip so that it oscillates. • Determine the period T of these oscillations. T= ..................................................... s[2]
(c)Change x by positioning the nail in a different hole and repeat (b). Repeat until you have six sets of values of x and T. Record your results in a table. Include values of 1/x and T² in your table.[9]
(d)(i)Plot a graph of T² on the y-axis against 1/x on the x-axis.[3]
(d)(ii)Draw the straight line of best fit.[1]
(d)(iii)Determine the gradient and y-intercept of this line. gradient = ................................................................ y-intercept = ............................................................ [2]
(e)It is suggested that the quantities T and x are related by the equation T² = a/x + b where a and b are constants. Use your answers in (d)(iii) to determine the values of a and b. Give appropriate units. a = .......................................................................... b = ..........................................................................[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 (Feb/Mar 2019). The mark or mark type is shown in brackets.

[1] 1(a) value of x to nearest mm and in range 4.5 to 5.5 cm
[1] 1(b) value of T in range 1.50 s to 2.50 s
[1] 1(b) repeat readings – at least two values of at least 5T
[4] 1(c) six sets of readings of x and T with correct trend and without help from supervisor scores 4 marks, five sets scores 3 marks etc.
[1] 1(c) range: Xmin ≥ 2.5cm and Xmax ≤ 13.5 cm
[1] 1(c) column headings: each column heading must contain a quantity and a unit the presentation of quantity and unit must conform to accepted scientific convention. e.g. T²/s²
[1] 1(c) consistency: all values of raw times must be given to the nearest 0.1 s or all values to the nearest 0.01 s
[1] 1(c) significant figures: significant figures for every value of 1 / x same as, or one greater than, the s.f. of x as recorded in table
[1] 1(c) calculation: values of 1/x calculated correctly
[1] 1(d)(i) axes: sensible scales must be used, no awkward scales (e.g. 3:10) 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 which is being plotted scale markings should be no more than 3 large squares apart
[1] 1(d)(i) plotting of points: all observations must be plotted on the grid diameter of plotted points must be < half a small square (no blobs) plots must be accurate to within half a small square in both x and y directions
[1] 1(d)(i) quality: all points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of plots must be no more than ± 0.05cm⁻¹ from a straight line in the 1 / x direction
[1] 1(d)(ii) line of best fit: judged by balance of all points on the grid (at least 5) about the candidate's line. There must be an even distribution of points either side of the line along the full length one anomalous point is allowed only if clearly indicated (i.e. circled or labelled) by the candidate lines must not be kinked or thicker than half a small square
[1] 1(d)(iii) gradient: the hypotenuse of the triangle used must be greater than half the length of the drawn line method of calculation must be correct both read-offs must be accurate to half a small square in both the x and y directions
[1] 1(d)(iii) y-intercept: Either correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with 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 = zero accurate to half a small square in y direction
[1] 1(e) a equal to candidate's gradient, and b equal to candidate's intercept, and values are not written as fractions
[1] 1(e) unit for a is correct and consistent with value unit for b is correct