Cambridge A Level Physics 9702 — 2020 May/June Paper 3 · Variant 3

1 In this experiment, you will investigate the equilibrium of a metre rule. (a) You have been provided with a metre rule with a string attached to it. ● Set up the apparatus as shown in Fig. 1.1. pulley attached to stand string L ≈ 60 cm metre rule mass m A B string loop pivot stand 100 g mass wooden block bench Fig. 1.1 ● Add masses to the mass hanger so that mass m is 80 g. ● Adjust the pivot so that it is 5 mm from end B of the rule. The distance between the string at end A and the pivot is L. ● Measure and record L. L = ............................................................... ● Adjust the string loop supporting the 100 g mass so that it is approximately 60 cm from end A. ● Hold the rule at end A so that the rule is approximately horizontal. ● Adjust the position of the string loop to find the position where end A is just about to move upwards when the rule is released. The distance between the string at end A and the string loop is y1 as shown in Fig. 1.2. y1 A Fig. 1.2 ● Measure and record y1. y1 = ............................................................... ● Adjust the position of the string loop to find the position where end A is just about to move downwards when the rule is released. The distance between the string at end A and the string loop is y2. ● Measure and record y2. y2 = ............................................................... ● Calculate y where y1 + y2 y = . 2 y = ............................................................... [3] (b) Increase m. Measure the new values of y1 and y2. Repeat until you have five sets of values of m, y1 and y2. Record your results in a table. Include values of y in your table. [8] (c) (i) Plot a graph of y on the y-axis against m on the x-axis. [3] (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 y and m are related by the equation y = Am + B where A and B are constants. Using your answers in (c)(iii), determine the values of A and B. Give appropriate units. A = ............................................................... B = ............................................................... [2] (e) Theory suggests that RA B = L – 2 where R is the mass of the metre rule. Determine a value for R. Give your answer to three significant figures. R = ......................................................... [1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a) Value of L in the range 0.987–0.993 m. 1 Value of y1 > y2. 1 Correct calculation of y. 1 1(b) Five sets of readings of m and y (different values) showing the correct trend and without help from the Supervisor scores 5 marks, four sets scores 4 marks etc. 5 Range: Must include values of m ⩽ 100 g and m ⩾ 140 g. 1 Column headings: Each column heading must contain a quantity, a unit and a separating mark where appropriate. The presentation of the quantity and unit must conform to accepted scientific convention e.g. y / cm. 1 Consistency: All raw values of y1 and y2 must be given to the nearest mm only. 1 1(c)(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 that is being plotted. Scale markings should be no more than three large squares apart. 1 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 Quality: All observations in the table (at least 4) must be plotted on the grid. Trend of points on graph must be correct. It must be possible to draw a straight line that is within ± 2.0 cm (to scale) on the y / cm axis (normally y-axis) of all plotted points. 1 Question Answer Marks 1(c)(ii) Line of best fit: Judge by balance of all points on the grid about the candidate’s line (at least 4 points). There must be an even distribution of points either side of the line along the full length. If there are 5 or more points, allow one anomalous point only if clearly indicated by the candidate. Line must not be kinked or thicker than half a small square. 1 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. 1 y-intercept: Correct read-off from a point on the line and 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. 1 1(d) Value of A = candidate’s gradient and value of B = candidate’s intercept. The values must not be fractions. 1 Units for A (e.g. cm g–1) and B (m, cm or mm) correct. 1 1(e) Calculation of R correct [= 2(L – B) / A] and given to three significant figures. 1

More questions on Equilibrium of forces

2 In this experiment, you will investigate the result of a collision between two cylinders. (a) ● The wooden cylinder labelled A has diameter D. Measure and record D. D = ............................................................... ● The wooden cylinder labelled B has diameter d. Measure and record d. d = ............................................................... [2] (b) (i) You have been provided with a wooden strip with a line drawn on one face. ● Use the stand, boss and clamp to set up the wooden strip in the position shown in Fig. 2.1. The end near the line should touch the bench and the other end should be approximately 5 cm above the bench. wooden strip line ≈ 5 cm bench Fig. 2.1 ● Place cylinder B approximately 30 cm from the end of the strip. L cylinder B Fig. 2.2 ● The distance between the end of the strip and B is L, as shown in Fig. 2.2. Measure and record L. L = ......................................................... [1] (ii) ● Place cylinder A on the line on the strip as shown in Fig. 2.3. cylinder A Fig. 2.3 ● Release A. ● A will roll down the strip and along the bench until it collides with B. B will roll and then come to rest as shown in Fig. 2.4. The distance between B and the end of the strip is l, as shown in Fig. 2.4. l Fig. 2.4 Measure and record l . l = ......................................................... [2] (iii) Estimate the percentage uncertainty in your value of l . Show your working. percentage uncertainty = ......................................................... [1] (iv) Calculate (l – L)2. (l – L)2 = ......................................................... [1] (c) ● Measure and record the diameter D of cylinder C. D = ............................................................... ● Using cylinder C instead of cylinder A on the wooden strip, repeat (b)(i), (b)(ii) and (b)(iv). L = ............................................................... l = ............................................................... (l – L)2 = ............................................................... [3]

Mark scheme: 2(a) Value of D in the range 2.300─2.500 cm with unit and to the nearest 0.01 cm or 0.001 cm. 1 Value of d in the range 1.100–1.300 cm with unit and to the nearest 0.01 cm or 0.001 cm. 1 2(b)(i) Value of L in the range 29–31 cm with unit and to the nearest 0.1 cm. 1 2(b)(ii) Final value of l in the range 40–80 cm with unit. Raw readings to the nearest mm. 1 Evidence of repeats. 1 2(b)(iii) Percentage uncertainty in l based on an absolute uncertainty of 2–5 mm. If repeated readings have been taken, then the uncertainty can be half the range (but not zero) if the working is clearly shown. Correct method of calculation to obtain percentage uncertainty. 1 2(b)(iv) Correct calculation of (l – L)2. 1 2(c) Second value of D. 1 Second values of L and l. 1 Quality: Second value of l < first value of l. 1 2(d)(i) Two values of k calculated correctly. 1 2(d)(ii) Valid comment consistent with calculated values of k, testing against a criterion stated by the candidate. 1 Question Answer Marks 2(e)(i) A Two readings are not enough to draw a (valid) conclusion (not “not enough for accurate results”, “few readings”). B Problem in placing cylinder A on the line (e.g. because cylinder covers line when placed). C Narrow strip so A (or C) not centrally placed at release. D A (or C) not hitting B ‘full on’. E Large step at bottom of strip causes deviation. F Uneven friction of surface of bench. G Difficult to measure L (or l) with a reason e.g. parallax/rule not touching edge of ramp. 1 mark for each point up to a maximum of 4. 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). B Improved method of releasing A (or C) from the same height each time e.g. a stop. C Use wider strip. D Improved method of guiding A (or C) after rolling down strip e.g. place apparatus in a channel. E Use a thinner strip/bevelled edge. F Provide smoother/more even surface for A (or C) to roll horizontally. G Improved method to measure L (or l) e.g. place apparatus on a grid of 1 mm graph paper/use set square. 1 mark for each point up to a maximum of 4. 4

More questions on Physical quantities