Cambridge A Level Physics 9702 — 2024 Oct/Nov Paper 3 · Variant 4

1 In this experiment, you will investigate the flow of water through a nozzle. (a) (i) ● Remove the plunger from the syringe body. ● Assemble the apparatus as shown in Fig. 1.1 with the bottom of the syringe nozzle approximately 15 cm above the bench. syringe body clamp boss syringe nozzle ht hb ≈ 15 cm stand bench Fig. 1.1 (not to scale) ● Measure and record the height ht of the 30 cm3 graduation above the bench, as shown in Fig. 1.1. ht = ............................................................... ● Measure and record the height hb of the 25 cm3 graduation above the bench, as shown in Fig. 1.1. hb = ............................................................... ● Calculate the mean hm of the two values ht and hb. hm = ............................................................... [1] (ii) ● Place the empty beaker below the syringe nozzle. ● Pour water from the other beaker into the syringe body so that the water level is near the top, then watch the water level fall. ● Start the stop‑watch as the water level passes the 30 cm3 graduation, then stop the stop‑watch as the water level passes the 25 cm3 graduation. ● Record the stop‑watch reading T. T = ......................................................... [2] (b) Choose two different graduations that are 5 cm3 apart and measure ht, hb and T. Repeat until you have six sets of values of ht, hb and T. 1 Record your results in a table. Include values of hm and in your table. T [9] 1 (c) (i) Plot a graph of on the y‑axis against hm on the x‑axis. [3] T (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y‑intercept of this line. gradient = ............................................................... y‑intercept = ............................................................... [2] (d) It is suggested that the quantities T and hm are related by the equation 1 = phm + q T where p and q are constants. Using your answers in (c)(iii), determine the values of p and q. Give appropriate units. p = ............................................................... q = ............................................................... [2] [Total: 20]

Mark scheme: Question Answer Marks 1(a)(i) Values of ht and hb with unit and in range 19.0–24.0 cm. 1 1(a)(ii) Value of T in range 1.20–2.60 s. 1 Evidence of repeat measurements of T. 1 1(b) Six sets of readings of ht, hb and T with correct trend (as ht increases, T decreases) and without help from supervisor 4 scores 4 marks, five sets scores 3 marks etc. Range: max ht – min ht ⩾ 5.0 cm. 1 Column headings: 1 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 / T / s–1. Consistency: All values of ht and hb must be given to the nearest mm. 1 Significant figures: 1 Values of 1 / T given to same number of s.f. as (or one more than) number of s.f. in T. Calculation: Values of 1 / T calculated correctly. 1 1(c)(i) Axes: 1 Axes must be labelled with the required quantities. Scales must be chosen so that the plotted points occupy at least half the graph grid in both the x and y directions. Scale markings are no more than 2 cm (one large square) apart. Sensible scales must be used, no awkward scales (e.g.3:10 or fractions). Plotting of points: 1 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 in both x and y directions. Quality: 1 All points in the table must be plotted (at least 5) for this mark to be awarded. It must be possible to draw a straight line that is within  0.05 s–1 (to scale) on the 1 / T axis (normally the y-axis) of all plotted points. General trend of points must be positive. 1(c)(ii) Line of best fit: 1 ‘Best fit’ is judged by the balance of all points on the grid (at least 5 points) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. Lines must not be kinked or thicker than half a square. Some candidates may choose to identify an anomalous point. If they identify one point as anomalous (e.g. by circling or labelling) then this point is to be disregarded when judging the line of best fit. There must be at least five points left after the anomalous point is disregarded. 1(c)(iii) Gradient: 1 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. Method of calculation must be correct, not (x / y). Gradient sign on answer line consistent with graph drawn. y-intercept: 1 Intercept read directly from the graph, with read-off at x = 0, accurate to half a small square in y direction. or 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. 1(d) p equal to candidate’s gradient and q equal to candidate’s intercept. 1 Values must not be written as fractions, roots or given to only one significant figure. Units for p and q correct and consistent with readings, e.g. s–1 cm–1 for p and s–1 for q. 1

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2 In this experiment, you will investigate the conservation of momentum. (a) (i) The apparatus has been partly set up as shown in Fig. 2.1. cork nail boss rod r magnet bench Fig. 2.1 ● Check that the rod can swing freely on the nail. ● The distance between the nail and the centre of the magnet is r. Measure and record r. r = .......................................................... cm ● Record the mass M of the magnet written on the card. M = ............................................................ g [2] (ii) ● Use small pieces of adhesive putty to fix the 30 cm ruler to the bench with the zero of its scale directly below the centre of the magnet, as shown in Fig. 2.2. ● Attach nut A to the bottom of the magnet. Adjust the position of the boss on the stand until the bottom of the nut is approximately 3 mm above the ruler, as shown in Fig. 2.2. cork held in clamp nail through rod nut ruler ≈ 3 mm Fig. 2.2 ● Record the mass m of nut A written on the card. m = ............................................................ g ● Detach the nut from the magnet. ● Move the rod and hold it so that the bottom of the magnet is directly above the 15.0 cm mark on the ruler scale. ● Place the nut on the ruler so that its centre is above the zero on the ruler scale, as shown in Fig. 2.3. 0.0 cm 15.0 cm mark mark Fig. 2.3 ● Release the rod so that the magnet picks up the nut as it passes and then swings back to a position x on the ruler scale, as shown in Fig. 2.4. x cm mark Fig. 2.4 ● Read and record x. x = .......................................................... cm [2]

Mark scheme: 2(a)(i) All raw value(s) for r to nearest mm. 1 Final value of r in range 45.0–49.5 cm. 1 2(a)(ii) Final value of x less than 15.0 cm. 1 Evidence of repeat readings of x. 1 2(a)(iii) Percentage uncertainty based on absolute uncertainty in x in range 0.3–1.0 cm. 1 Correct method of calculation to find percentage uncertainty e.g. (absolute uncertainty / value from (a)(ii))  100. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. 2(a)(iv) Correct calculation of h. 1 2(b) Second value of x. 1 Second value of h. 1 Second x < first x. 1 2(c)(i) Two values of k calculated correctly. 1 The final k values must not be written as fractions or given to one significant figure. 2(c)(ii) Justification for significant figures in k linked to significant figures in (M + m) and h. 1 2(d) Calculation of percentage difference between candidate’s two k values. 1 Comparison of percentage difference with 15% leading to a consistent conclusion. 2(e)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). 4 B Difficulty with r with reason e.g. holding ruler in air / rod moves when hit by ruler / estimating magnet’s centre. C Difficulty with the starting position with reason e.g. parallax / knowing which part of the magnet to use as a reference. D Difficulty with x with reason e.g., parallax / judging when at maximum displacement / at maximum displacement for short time / knowing which part of nut to use as a reference point. E Difficulty with picking up the nut. 1 mark for each point up to a maximum of 4. 2(e)(ii) A Take more readings and plot a graph or take more readings and compare k values (not “repeat readings” on its own). 4 B Clamp ruler / measure magnet’s length and distance to top (or bottom) of magnet / measure to top of magnet and to bottom of magnet and average the length. C Use set square on ruler/a stop to set the starting position. D Record/film/video with ruler in view / use grid behind / trial and error with pointer / use position sensor to side of swing. E Lower the magnet / use a strong(er) magnet / reduce the starting displacement / use a low(er) mass nut / different workable method of increasing adhesion. 1 mark for each point up to a maximum of 4.

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