Cambridge A Level Physics 9702 — 2013 May/June Paper 3 · Variant 5

1 In this experiment, you will investigate how the motion of an oscillating system depends on the mass attached to the system. (a) (i) Set up the apparatus as shown in Fig. 1.1. stands bosses clamps metre rule string loops 20 cm end A end B string loop metre rule mass m bench Fig. 1.1 Slide the two longer loops of string onto a rule and fix this rule in the clamps. Adjust the clamps until the rule is parallel to the bench. Slide the shorter loop onto the second rule and use the longer loops to support this second rule. Both rules should have their markings facing you. The strings should be vertical, 20 cm apart and equal distances from the centre of the second rule. Use the shorter loop of string to suspend a mass m at the 50 cm mark on the second rule, where m = 0.500 kg. (ii) Move the end A of the lower rule towards you and the end B away from you. For Release the rule and watch the movement. Examiner’s End A will move away from you and back towards you, completing a swing. Use 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] (b) Change m and repeat (a)(ii) until you have six sets of values of m and T. For Examiner’s 1 Use Include values of in your table. T 2 [10] 1(c) (i) Plot a graph of on the y-axis against m on the x-axis. [3] T 2 (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 (d) The quantities m and T are related by the equation For Examiner’s 1 Use = Pm + Q T 2 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] You may not need to use all of the materials provided. For Examiner’s Use

Mark scheme: 1 (a) (ii) Value of T in range 0.4 ≤ T ≤ 1.4 s. [1] Evidence of repeats. [1] (b) Six sets of readings of m and t (or T) scores 5 marks, four sets scores 4 marks etc. [5] Help from Supervisor –1. Range of m : ∆m ≥ 0.600 kg [1] Column headings: [1] Each column heading must contain a quantity and a unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. 1/T2/ s–2. Do not allow 1/T2(s)2 Consistency: [1] All values of raw t must all be given to the nearest 0.1 s or 0.01 s. Significant figures: [1] Significant figures for every row of values of 1/T2 same as or one greater than t (or T) as recorded in table. Calculation: [1] Values of 1/T2 calculated correctly (c) (i) Axes: [1] 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. Plotting of points: [1] All observations in the table must be plotted. Diameter of points must be ≤ half a small square (no “blobs”). Work to an accuracy of half a small square. Quality: [1] All points in the table must be plotted (at least 5) for this mark to be awarded. Scatter of points must be less than 0.1 s–2 of 1/T2 from a straight line. (ii) Line of best fit: [1] 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. Line must not be kinked or thicker than half a small square. (iii) Gradient: [1] The hypotenuse of the triangle 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. GCE AS/A LEVEL – May/June 2013 9702 35 y-intercept: [1] Either: 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: Correct read-off of the intercept directly from the graph. (d) Value of P = candidate’s gradient. Value of Q = candidate’s intercept. [1] Unit for P (kg–1 s–2) correct and consistent with value and Q (s–2) [1] [Total: 20]

More questions on Simple harmonic oscillations

2 In this experiment, you will investigate how the force acting on a straight wire in water depends on its length. (a) (i) Measure the length L of the shorter wire as shown in Fig. 2.1. string wire L Fig. 2.1 L = ...................................................[1] (ii) Estimate the percentage uncertainty in your value of L. percentage uncertainty = ...................................................[1] (b) (i) Set up the apparatus using the shorter wire as shown in Fig. 2.2. For Examiner’s Use stand boss and clamp pulley string loop loop open paper clip (to be used as a hook) string wire bench Fig. 2.2 (ii) Gently add paper clips to the hook until the wire moves upwards. (iii) Count and record the number N1 of paper clips you have added in (ii). Do not include the open paper clip which is used as a hook. N1 = ..................................................[1] (c) (i) You have been provided with a tray containing water. For Set up the apparatus so that it is the same as in Fig. 2.2 but with the wire in the Examiner’s water. It may be necessary to adjust the position of the pulley. Use (ii) Gently add paper clips to the hook until the wire rises out of the water. (iii) Count and record the number N2 of paper clips you have added in (ii). N2 = ..................................................[2] (d) Calculate the force F needed to remove the wire from the water using F = (N2 – N1) mg where the mass m of one paper clip is 4.0 × 10−4 kg, and g = 9.8 N kg−1. F = ............................................... N [1]

Mark scheme: 2 (a) (i) Value of L in range 8.0 ≤ L ≤ 12.0 cm with consistent unit to the nearest mm. [1] (ii) Absolute uncertainty 1 ≤ ∆L ≤ 3 mm. If repeated readings have been taken, then the uncertainty can be half the range. Correct method of calculation to get percentage uncertainty. [1] (b) (iii) Value of raw N1 an integer. [1] (c) (iii) Value of N2 ≥ N1. [1] Evidence of repeats for N1 or N2 either here or in (b)(iii). [1] (d) Correct calculation of F. [1] (e) Second value of L. [1] Second values of N2 and N1. [1] Second (average) value of N1 > first (average) value of N1. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Justification of s.f. in k linked to significant figures in L and (N1 – N2) and m. [1] (iii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] GCE AS/A LEVEL – May/June 2013 9702 35 (g) (i) Limitations 4 max. (ii) Improvements 4 max. Do not credit A two readings not enough (to take more readings and plot a repeat draw a conclusion) graph/calculate more k values and readings/few compare readings/only one reading/take more readings and average k B friction at pulley method of reducing friction of pulley with location C wet string added to force/ waterproof/nylon/wire mass of string not accounted for D can only measure to nearest use smaller masses e.g. half newton meter 0.4g / paperclip paperclips, riders, graph paper E change in N are very small reasoned explanation for changing helpers length of wire parallax errors F copper wire is not circular wire shape change liquid/wire flat/straight/exit not parallel to water level [Total: 20]

More questions on Physical quantities