A-LevelPhysicsKinematics9702/32 · May/June 2018 · Q120 Marks

In this experiment, you will investigate the motion of a rolling sphere.

(a)(i)Assemble the apparatus as shown in [Figure 1.1]. The top end of the track is a distance d above the bench. The initial value of d should be approximately 5cm. • Place the sphere on the track and hold it gently against the tape, as shown in [Figure 1.2]. • Measure and record the height h of the top of the sphere above the bench. h = [1]
(a)(ii)• Release the sphere. • Measure and record the time t from release for the sphere to reach the target. t= [2]
(b)Change d and repeat (a) until you have six sets of values of h and t. Do not use values of d greater than 10cm. Ensure that the distance from the bottom of the track to the target is always 50.0 cm. Record your results in a table. Include values of 1/t² in your table.[9]
(c)(i)Plot a graph of 1/t² on the y-axis against h on the x-axis.[3]
(c)(ii)Draw the straight line of best fit.[1]
(c)(iii)Determine the gradient and y-intercept of this line. gradient = y-intercept = [2]
(d)It is suggested that the quantities t and h are related by the equation 1/t² = ah + b where a and b are constants. Use your answers in (c)(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 (May/June 2018). The mark or mark type is shown in brackets.

[1] (a)(i) Value of h to nearest mm, with unit.
[1] (a)(ii) Value of t in the range 1.0-5.0s, with unit.
[1] (a)(ii) At least two readings of t.
[4] (b) Six sets of readings of h and t showing the correct trend and without help from the Supervisor scores 4 marks, five sets scores 3 marks etc.
[1] (b) Range: tmax ≥ 2.0s and tmin ≤ 1.5s.
[1] (b) 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. (1 / t²)/s⁻².
[1] (b) Consistency: All raw values of t must be given to 0.01 s or all must be given to 0.1 s.
[1] (b) Significant figures: Significant figures for every value of 1/t² same as, or one greater than, the number of s.f. of t as recorded in table.
[1] (b) Calculation: Values of 1/t² calculated correctly to the number of s.f. given by the candidate.
[1] (c)(i) 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] (c)(i) Plotting of points: All observations in the table 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] (c)(i) Quality: All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be no more than ± 0.05s⁻² from a straight line in the 1/t² direction.
[1] (c)(ii) 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 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] (c)(iii) Gradient: The hypotenuse of the triangle used must be greater than half the length of the drawn line. The method of calculation must be correct. Do not allow Δx/Δy. Both read-offs must be accurate to half a small square in both the x and y directions. Sign of gradient must match graph.
[1] (c)(iii) y-intercept: Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression. 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 y direction.
[1] (d) Value of a equal to candidate's gradient and value of b equal to candidate's intercept.
[1] (d) Unit for a correct (e.g. mm⁻¹s⁻² or cm⁻¹s⁻²) and unit for b is s⁻².