A-LevelPhysicsOscillations9702/33 · Oct/Nov 2017 · Q120 Marks

In this experiment, you will investigate the rotational motion of a mass.

(a)You have been provided with a 10g mass hanger and several 10g slotted masses. Set up the apparatus as shown in [Fig. 1.1]. Adjust the string so that the distance between the bottom of the wooden blocks and the top of the mass hanger is 40.0 cm. The combined mass m of the mass hanger and slotted masses must be 70 g.
(b)(i)Twist the mass through ten complete turns as shown in [Fig. 1.2].
(b)(ii)When the mass is released, it will rotate one way and then rotate the other way. This motion will continue until the mass comes to rest. At this point, the mass will continue to swing slightly with very little rotation. Release the mass. Measure and record the time a taken for the mass to come to rest. a = [1]
(b)(iii)Change the distance between the bottom of the wooden blocks and the top of the mass hanger to 20.0 cm.
(b)(iv)Repeat (b)(i). Release the mass. Measure and record the time b taken for the mass to come to rest. b = [1]
(b)(v)Change the distance between the bottom of the wooden blocks and the top of the mass hanger to 40.0 cm.
(c)Change m and repeat (b) until you have six sets of values of m, a and b. You may include your results from (b). Record your results in a table. Include values of a²/b in your table.[10]
(d)(i)Plot a graph of a²/b on the y-axis against m 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 a, b and m are related by the equation a²/b = Pm + Q where P and Q are constants. Using your answers in (d)(iii), determine the values of P and Q. Give appropriate units. P = Q = [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] (b)(ii) Value of a with unit and in the range 5.00–60.00s.
[1] (b)(iv) Evidence of repeated readings.
[5] (c) Six sets of readings of m (different values), a and b showing the correct trend (as m increases, a and b also increase) and without help from the Supervisor scores 5 marks, five sets scores 4 marks etc.
[1] (c) Range: Values of m must include 10 g and 70 g.
[1] (c) Column headings: Each column heading must contain a quantity and a unit where appropriate. The presentation of the quantity and unit must conform to accepted scientific convention e.g. a²/b/s.
[1] (c) Consistency: All raw values of time must be given to 0.1s or all to 0.01 s.
[1] (c) Significant figures: All values of a²/b 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 significant figures of a² / b to be one less than the number of significant figures of the raw times.
[1] (c) Values of a²/b calculated correctly.
[1] (d)(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] (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"). Points must be plotted to an accuracy of half a small square.
[1] (d)(i) Quality: All points in the table must be plotted on the grid for this mark to be awarded. It must be possible to draw a straight line that is within 10 g on the mass axis (x-axis) of all plotted points.
[1] (d)(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 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] (d)(iii) Gradient: The hypotenuse of the triangle used should be greater than half the length of the drawn line. The 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] (d)(iii) y-intercept: Correct read-off from a point on the line 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] (e) Value of P = candidate's gradient and value of Q = candidate's intercept. The values must not be fractions.
[1] (e) Unit for P correct (sg⁻¹ or skg⁻¹) and unit for Q correct (s).