Cambridge A Level Physics 9702 — 2012 Oct/Nov Paper 3 · Variant 1

1 In this experiment, you will investigate how the extension of a spring depends on the load applied to it. (a) Set up the apparatus as shown in Fig. 1.1 where the mass m is 200 g. stand wooden rod wooden rod wooden strip with hooks boss spring mass m e G-clamp block 90 protractor bench front view side view Fig. 1.1 Use the Blu-Tack to attach the protractor to the edge of the block along the 90° line. Use the ruler to ensure that the wooden rod is directly above the edge of the block as shown. Clamp the block to the bench with the G-clamp. The boss should be clamped tightly to the stand to prevent the rod from rotating. (b) (i) Adjust the height of the boss so that the spring is perpendicular to the wooden strip. For Use the set square to check that the strip and spring are perpendicular to each Examiner’s other by placing it gently as shown in Fig. 1.2. Any contact of the set square with Use the strip will cause the apparatus to move. L set square Fig. 1.2 (ii) Measure and record the length L of the coiled part of the spring as shown in Fig. 1.2. L = ..................................................[1] (iii) Measure and record the angle θ between the strip and the vertical line on the protractor as shown in Fig. 1.1. θ = ..................................................[1] (c) Change m and repeat (b) until you have five sets of values of m, L and θ. For For each set of readings the spring and strip should be perpendicular to each Examiner’s other. Use Include values of m sin θ in your table. [10] (d) (i) Plot a graph of L on the y-axis against m sin θ 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] For Examiner’s Use (e) The quantities L, m and θ are related by the equation For Examiner’s L = P m sin θ + Q Use 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] You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (b) (ii) Values of raw L in range 2.0 cm Y L Y 8.0 cm consistent with unit. [1] (iii) Value of θ < 90 ° with unit. No raw value greater than 0.5 ° precision. [1] (c) Five sets of readings of L, m and θ scores 5 marks, four sets scores 4 marks etc. [5] Incorrect trend then –1. Major help from Supervisor –2. Minor help from Supervisor –1. Range: mmin Y 0.100 kg, mmax [ 0.350 kg. [1] Column headings: [1] Each column heading must contain a quantity and a unit where appropriate. The unit must conform to accepted scientific convention e.g. m / kg, m sin θ / kg, θ / °. Consistency: [1] All values of L must be given to the nearest mm. Significant figures: [1] All values of m sin θ must have the same number of significant figures as, or one more than, the least number of significant figures in m and θ. Calculation: [1] Values of m sin θ calculated correctly. (d) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10) are not allowed. 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 must be no more than three large squares apart. Plotting of points: [1] All observations in the table must be plotted on the graph grid. Diameter of plots must be Y half a small square (no blobs). Check that the points are plotted correctly. Work to an accuracy of half a small square in both the x and y directions. Quality: [1] All points in the table must be plotted (at least 4) for this mark to be scored. Judge by the scatter of all the points about a straight line. All points must be within ± 0.01 kg in the m sin θ direction of a straight line. (ii) Line of best fit: [1] Judge by balance of all the points on the grid (at least 4) about the candidate’s line. 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. Line must not be kinked or thicker than half a small square. GCE AS/A LEVEL – October/November 2012 9702 31 (iii) Gradient: [1] The sign of the gradient must match the graph. The hypotenuse of the triangle used must be at least 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. The method of calculation must be correct. y intercept: [1] Either: Check correct read-off from a point on the line and substitution into y = mx + c. Read-off must be accurate to half a small square in both the x and y directions. Or: Check the read-off of the intercept directly from the graph. (e) Value of P = candidate’s gradient. Value of Q = candidate’s intercept. [1] Do not allow a value presented as a fraction. Unit for P (m kg–1 or cm kg–1 or mm kg–1 or m g–1 or cm g–1 or mm g–1) and Q (m or cm or mm) correct and consistent with value. [1] [Total: 20]

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2 In this experiment, you will investigate how the motion of a rule depends on its mass. (a) (i) Tie one of the lengths of string into a loop of circumference approximately 40 cm. (ii) Measure and record the value of the circumference of the loop. circumference = ..................................................[1] (iii) Estimate the percentage uncertainty in your value of the circumference. percentage uncertainty = ..................................................[1] (iv) Tie the other length of string into a loop of the same circumference. Measure and record the value of the circumference of the loop. circumference = ..................................................[1] (b) (i) Set up the apparatus as shown in Fig. 2.1. For Examiner’s stands Use bosses clamps string loops metre rule half-metre rule end A end B 25 cm bench Fig. 2.1 Both rules should have their markings facing you. The strings should be looped over the metre rule and support the half-metre rule. The strings should be vertical, 25 cm apart and equal distances from the centre of the lower rule. (ii) Move the end A of the half-metre rule towards you and the end B away from you. Release the rule and watch the movement. End A of the half-metre rule will move away from you and back towards you, completing a swing. The time taken for one complete swing is T. By timing several of these complete swings, determine an accurate value for T. T = ............................................... s [2] (c) (i) Repeat (b) with the half-metre rule at the top and the metre rule supported by the For strings. Examiner’s Use T = ..................................................[2] (ii) Repeat (b) with the 30 cm ruler supported by the strings. T = ..................................................[1] (d) It is suggested that the relationship between T and the mass m of the supported rule is T = k m where k is a constant assuming the loops are of equal circumference. The value of T also depends on the value of this circumference. (i) Copy the data from the card. Mass of metre rule = ………………….g Mass of half-metre rule = ………………….g Mass of 30 cm ruler = ………………….g

Mark scheme: 2 (a) (ii) Value of circumference in range 30.0 – 50.0 cm to the nearest mm with unit. [1] (iii) Absolute uncertainty in circumference is between 2 mm – 6 mm. [1] If repeated readings have been taken, then the absolute uncertainty can be half the range. Correct method used to calculate the percentage uncertainty. (iv) Value of circumference within 2 cm of first value. [1] (b) (ii) Raw time values to at least 0.1s or 0.01 s, value of 0.5 s < T < 2.0 s. [1] Evidence of repeats. [1] (c) (i) Second value of T. [1] Second value of T > first value of T. [1] (ii) Third value of T. [1] (d) (ii) Correct calculation of two values of k. [1] Correct calculation of third value of k. [1] (iii) Justification of significant figures in k linked to significant figures in time and m (not just “raw readings”) [1] (iv) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS/A LEVEL – October/November 2012 9702 31 (e) (i) Limitations 4 max. (ii) Improvements 4 max. Do not credit A three results not enough take more readings and plot a two results not /not enough results graph enough /repeat readings /few readings B string too wide for markings use thinner string on rule C rules have different use rulers of similar thicknesses/ thicknesses so effective length readings/method to take of loop changes/ thickness into account /different lengths so not a fair /use rulers of the same length test D times are small use longer strings/improved /large uncertainty in time method of timing E difficult to judge start/ end Position/motion sensor facing the position sensor at of/complete oscillation rule end or in middle /video with timer F swings of 30 cm ruler highly damped G difficult to make two loops of method by which this can be the same circumference achieved H large uncertainty in mass method of measuring mass more accurate balance precisely [Total: 20]

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