Cambridge A Level Physics 9702 — 2016 May/June Paper 3 · Variant 2

1 In this experiment, you will investigate the motion of a suspended card shape. (a) Set up the apparatus as shown in Fig. 1.1. Suspend the card from the pin held in the split cork. Ensure that the pin is parallel to the bench. Suspend the plumb-line from the pin. pin A card B i plumb-line bench Fig. 1.1 (b) (i) Measure and record the angle i between the edge of arm B and the plumb-line, as shown in Fig. 1.1. i = ....................................................... [1] (ii) Remove the plumb-line from the pin. (iii) Displace arm B approximately 2 cm to one side and release it so that the card oscillates. (iv) Take measurements to find the period T of the oscillations. Record T. T = ..................................................... s [2] (c) (i) Decrease the length of arm B by cutting approximately 3 cm off its end. (ii) Replace the plumb-line and repeat (b). i = ........................................................ T = ...................................................... s (d) Continue to decrease the length of arm B. For each length of arm B, repeat (b) until you have six sets of values for i and T. You may include your values from (b) and (c). 1 Include values for in your table. tan i [9] 1 (e) (i) Plot a graph of T on the y-axis against on the x-axis. [3] tan i (ii) Draw the straight line of best fit. [1] (iii) Determine the gradient and y-intercept of this line. gradient = ....................................................... y-intercept = ....................................................... [2] (f) The quantities T and i are related by the equation p T = + q tan i where p and q are constants. Use your answers from (e)(iii) to determine the values of p and q. Give appropriate units. p = ........................................................ q = ........................................................ [2] [Total: 20] Please turn over for Question 2. You may not need to use all of the materials provided.

Mark scheme: 1 (b) (i) Value for θ in range 20° to 30° to nearest degree, with unit. [1] (iv) Value for T in range 0.50 s to 1.50 s. [1] Evidence of repeat readings. At least two measurements of nT, with n ≥ 3. [1] (d) Six sets of values for θ and T with correct trend scores 4 marks, five sets scores 3 marks etc. No θ values over 90°. [4] Help from Supervisor –1. Range: [1] θ values must include 30° or less and 70° or more. Column headings: [1] Each column heading must contain a quantity and an appropriate unit. The presentation of quantity and unit must conform to accepted scientific convention e.g. θ / °, θ (°) or θ (deg) etc. 1/ tan θ must have no unit. Consistency: [1] All raw values of time must be given to the nearest 0.1 s, or all to the nearest 0.01 s. Significant figures: [1] Every value of 1/ tan θ must be given to 2 or 3 s.f. Calculation: [1] Values of 1/ tan θ calculated correctly to the number of s.f. given by the candidate. (e) (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 must be plotted. Diameter of plotted points must be ≤ half a small square (no “blobs”). Plotted points must be accurate to half a small square. Quality: [1] All points in the table (at least 5) must be plotted for this mark to be awarded. All points must be no more than ±0.02 s (in the y (T) direction) of 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 plot only if clearly indicated by the candidate. Line must not be kinked or thicker than half a small square. (iii) Gradient: [1] Sign of gradient must match graph drawn. The hypotenuse of the triangle used must be greater than half the length of the drawn line. The method of calculation must be correct. Both read-offs must be accurate to half a small square in both x and y directions. y-intercept: [1] Either: Correct read-off from a point on the line and substituted into y = mx + c. Read-offs must be accurate to half a small square in both x and y directions. Or: Intercept read off directly from the graph (accurate to half a small square). (f) Value of p = candidate's gradient and value of q = candidate's intercept. [1] Do not allow fractions. Correct units for p and q (both should have the unit s). [1]

More questions on Simple harmonic oscillations

2 In this experiment, you will investigate the force exerted by a flow of water. You are provided with two plastic water bottles labelled A and B, each with a hole in the base. (a) (i) Measure and record the distance h between the two lines marked on bottle A, as shown in Fig. 2.1. bottle A h lines d Fig. 2.1 h = ................................................. cm [1] (ii) Measure and record the diameter d of the bottle, as shown in Fig. 2.1. d = ................................................. cm [1] (b) Estimate the percentage uncertainty in your value of d. percentage uncertainty = ...................................................... [1] (c) (i) With the unused stand, clamp the bottle securely by its neck above the tray, as shown in Fig. 2.2. The base of the bottle should be approximately 20 cm above the bench. clamp bottle water level boss stand hole stream of water ≈20 cm tray bench Fig. 2.2 Fill the bottle with water. As the water flows through the hole into the tray, measure and record the time t for the water level to fall from the upper line to the lower line. t = ....................................................... [2] (ii) Calculate the flow rate R of the water using 2 r d h R = . 4 t R = ....................................................... [1] (iii) When the water stops flowing, empty the water from the tray into one of the jugs provided. (d) (i) Refill the bottle with water and position the stand holding the wooden strip so that the stream of water falls on the end of the strip, as shown in Fig. 2.3. stand holding wooden strip water level clamp boss stream of water wooden strip mark stand x1 Fig. 2.3 (ii) When the water level is between the two lines on the bottle, measure and record the height x1 above the tray of the mark on the wooden strip, as shown in Fig. 2.3. x1 = ....................................................... [1] (iii) Move the bottle so that the stream of water is missing the wooden strip, and measure and record the height x2 above the tray of the mark on the wooden strip. x2 = ....................................................... (iv) When the water stops flowing, empty the water from the tray into one of the jugs

Mark scheme: 2 (a) (i) h to nearest mm and in range 2.5 cm to 3.5 cm. [1] (ii) Raw values for d to nearest mm. [1] (b) Absolute uncertainty in d in range 2 mm to 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] (c) (i) Value for t in range 20.0 s to 90.0 s, with unit. [1] Evidence of repeat measurements of t. [1] (ii) Correct calculation of R to the s.f. used by the candidate (must be 2 or more s.f.). [1] (d) (ii) Value for x1 to nearest mm, with unit. [1] (e) Second values of h and d and t. [1] Second values of x1 and x2. [1] Quality: (x2 – x1) greater for shorter t. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Sensible comment relating to the calculated values of k, testing against a criterion specified by the candidate. [1] (g) (i) Limitations [4] (ii) Improvements [4] Do not credit A Two readings are not enough Take more readings and plot “Repeat readings” on its to draw a conclusion graph/ own/few readings/only obtain more k values and one reading/take more compare readings and find average k B Parallax error when Measure on bench between measuring d two set squares/ use (vernier) calipers/ use string to find circumference then calculate d C Bottle distorts when Collect water lost between measuring d/ marks and measure volume d varies along bottle/ base of bottle not flat D Difficult to judge/see/operate Use video with timer in Reaction time stopwatch when water level view/ Light gates reaches mark use frame counting/ use coloured water E Wooden strip moves Use video with scale in view continuously when water is falling on it F Difficult to measure height Use set square on bench/ Only short time to because rule not vertical/rule clamp rule measure x touches strip G Water soaks into wooden Use waterproof strip Use new strip/ strip/ dry the strip water stays on wooden strip H R not constant between lines Move lines closer to top/ have lines closer together

More questions on Physical quantities