A-LevelPhysicsForces, density and pressure9702/31 · Oct/Nov 2020 · Q120 Marks

In this experiment, you will investigate the equilibrium of a plastic cup.

(a)You have been provided with a cup attached to a string loop. A mass is attached to the cup as shown in Fig. 1.1. [Figure 1.1] Set up the apparatus as shown in Fig. 1.2. [Figure 1.2] The horizontal distance between the edges of the cup is p, as shown in Fig. 1.2. Measure and record p. p =[1]
(b)Pour approximately 12cm³ of water into the measuring cylinder. The mass of 1 cm³ of water is 1g. Determine the mass of water in the measuring cylinder. mass = g Gently pour this water from the measuring cylinder into the cup. Record the total mass m of water in the cup. m = g Measure and record p. p =[1]
(c)Using the measuring cylinder, add water to the cup to increase m. Measure and record p. Repeat until you have six sets of values of m and p. Record your results in a table. Include values of √m and √p in your table.[10]
(d)(i)Plot a graph of √p 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 p and m are related by the equation √p = A√m + B where A and B are constants. Using your answers in (d)(iii), 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 (Oct/Nov 2020). The mark or mark type is shown in brackets.

[1] 1(a) Value(s) of p in the range 9.0–15.0 cm with unit.
[1] 1(b) Value of m in the range 10.0-14.0 g.
[5] 1(c) Six sets of readings of m (different values) and p with correct trend and without help from the Supervisor scores 5 marks, five sets scores 4 marks, etc.
[1] 1(c) Range: Δm ≥ 80 g.
[1] 1(c) Column headings: Each column heading must contain a quantity, a unit and a separating mark where appropriate. The presentation of quantity and unit must conform to accepted scientific convention, e.g. m/g, √p / m².
[1] 1(c) Consistency: All values of p must be given to the nearest mm.
[1] 1(c) Significant figures: All values of √m must be given to the same number of significant figures as, or one greater than, the number of s.f. of the m values as recorded in table.
[1] 1(c) Calculation: Values of √p are correct.
[1] 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] 1(d)(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. Points must be plotted to an accuracy of half a small square.
[1] 1(d)(i) Quality: All points in the table must be plotted on the grid. Trend of points must be correct. It must be possible to draw a straight line that is within ±0.1 on the √p axis of all plotted points.
[1] 1(d)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate's line (at least 5 points). 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] 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, e.g. not Δx/Δy. Gradient sign on answer line matches graph drawn. Both read-offs must be accurate to half a small square in both the x and y directions.
[1] 1(d)(iii) 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 = zero, accurate to half a small square.
[1] 1(e) Value of A = candidate's gradient and value of B = candidate's intercept. The values must not be fractions.
[1] 1(e) Unit for A correct (e.g. cm0.5 g−0.5 or cm½ g−½) and unit for B correct (e.g. cm0.5 or cm½).