Cambridge A Level Physics 9702 — 2017 Feb/March Paper 3 · Variant 3

1 In this experiment, you will investigate forces on a wooden strip in equilibrium. (a) (i) Assemble the apparatus as shown in Fig. 1.1, with the mass resting on the bench. stand boss clamp spring l 2 wooden strip l 1 string loop Y spring mass bench Fig. 1.1 (not to scale) (ii) Adjust the height of the boss and the position of the mass until the wooden strip is parallel to the bench and the springs are vertical. (iii) Measure and record the lengths l 1 and l 2 of the coiled sections of the two springs, as shown in Fig. 1.1. l 1 = ...................................................... l 2 = ...................................................... [1] (b) You are provided with a wire hook and some metal rings. The card shows the mass of the hook and the mass of one ring. (i) Hang the hook and about half the rings from string loop Y. (ii) Repeat (a)(ii) and (a)(iii). l 1 = ...................................................... l 2 = ...................................................... (iii) Using the data from the card, calculate the total mass m hanging from string loop Y. m = ..................................................[1] (c) Change m by altering the number of rings on the hook, and repeat (a)(ii), (a)(iii) and (b)(iii) until you have six sets of values of m, l 1 and l 2. Record your results in a table. Include values of (l 2 – l 1) in your table. [8] (d) (i) Plot a graph of (l 2 – l 1) 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] (e) It is suggested that the quantities l 1, l 2 and m are related by the equation (l 2 – l 1) = am + b where a and b are constants. Use your answers from (d)(iii) to determine the values of a and b. Give appropriate units. a = ...................................................... b = ...................................................... [2] (f) The spring constant k of each spring can be found using the relationship g k = a where g = 9.81 N kg–1. Calculate k. k = ..................................................[2] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1(a)(iii) 1 1(b)(iii) Value of m in range 30 to 70 g, with unit. 1 1(c) Six sets of readings of l 1, l 2 and m with correct trend and without help scores 5 marks, five sets scores 4 marks etc. 5 Range: mmax ⩾ 80.0 g and mmin ⩽ 30.0 g. 1 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. (l2–l1) / mm. 1 Consistency: All values of l1 and l2 must be given to the nearest mm. 1 1(d)(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 which is being plotted. Scale markings should be no more than 3 large squares apart. 1 Plotting of points: All observations 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 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 ±10.0 g in the m direction from a straight line. 1 Question Answer Marks 1(d)(ii) Line of best fit: Judged by balance of all points on the grid (at least 5) about the candidate’s line. There must be an even distribution of points either side of the line along the full length. One anomalous point is allowed 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 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. Both read-offs must be accurate to half a small square in both the x and y directions. 1 y-intercept: Either Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression, with 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 in y direction. 1 1(e) Value of a equal to candidate’s gradient. Value of b equal to candidate’s intercept. The values must not be fractions and must be to at least 2 sig. fig. 1 Unit for a is dimensionally correct. Unit for b is dimensionally correct. 1 1(f) k calculated correctly. 1 k given to 2 or 3 s.f. 1 Total: 20

More questions on Physical quantities

2 In this experiment, you will investigate the friction between string and a plastic pipe. (a) (i) Select the pipe with the larger diameter. (ii) The outside diameter of the pipe is D, as shown in Fig. 2.1. D Fig. 2.1 Take measurements to find D. Record D. D = ........................................... cm [2] (b) (i) Write down the mass m of the newton-meter as written on the card. m = ............................................ kg (ii) Calculate the weight W of the newton-meter using the expression W = m g where g = 9.81 N kg–1. W = ............................................. N [1] (iii) Justify the number of significant figures you have given for your value of W. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] (c) (i) Use the stand, boss and clamp to hold the pipe securely parallel to the bench. Adjust the height of the boss until the pipe is approximately 50 cm above the bench. Assemble the rest of the apparatus as shown in Fig. 2.2, with the string passing over the pipe. boss plastic pipe clamp newton-meter stand hook ≈ 50 cm string mass M bench Fig. 2.2 (ii) Slowly pull down the hook of the newton-meter so that the mass is lifted off the bench and continues to rise. (iii) As the mass is rising steadily, record the reading F from the newton-meter. F = ............................................. N [2] (d) Estimate the percentage uncertainty in your value of F. percentage uncertainty = ..................................................[1] (e) Repeat (a)(ii) and (c) using the smaller diameter plastic pipe. D = ................................................ cm F = .................................................. N [3] (f) (i) It is suggested that the relationship between F, W and D is (F + W )2 = k D where k is a constant. Using your data, calculate two values of k. first value of k = ...................................................... second value of k = ...................................................... [1] (ii) Explain whether your results in (f)(i) support the suggested relationship. .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1]

Mark scheme: 2(a)(ii) All raw values of D to nearest 0.1 cm. 1 Evidence of repeat readings. 1 2(b)(ii) Correct calculation of W. 1 2(b)(iii) Justification for s.f. in W linked to s.f. in m and g. 1 2(c)(iii) Raw values of F to nearest 0.1 N. 1 Evidence of repeat readings of F. 1 2(d) Absolute uncertainty in F of 0.2 to 0.5 N and correct method of calculation to obtain percentage uncertainty. If repeated readings have been taken, then the absolute uncertainty can be half the range (but not zero if values are equal). 1 2(e) D for second pipe. 1 F for second pipe. 1 Quality: Both F > 3 N and < 10 N. 1 2(f)(i) Two values of k calculated correctly. 1 2(f)(ii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. 1 Question Answer Marks 2(g)(i) • Two readings are not enough to draw a valid conclusion. • Difficult to measure diameter with reason, e.g. diameter varies / e.g. ends not square. • Large uncertainty in D. • Difficult to pull hook down steadily. • Difficult to estimate average force during movement / F changes during movement. • Newton-meter collides with mass / observation time too short. • String slides off pipe / slides down pipe. 1 mark for each point up to a maximum of 4. 4 2(g)(ii) • Take more readings and plot a graph / calculate more k values and compare. • Use (vernier) calliper / measure between two blocks / use micrometer. • Improved pulling method to give constant speed, e.g. use a motor / e.g. use a known weight. • Record images (or video) of the reading (or measurement) and play back. • Use longer string with taller stand. • Use two stands / support pipe on rod / use spirit level to ensure pipe is horizontal / use groove around pipe (to guide string). 1 mark for each point up to a maximum of 4. 4 Total: 20

More questions on Physical quantities