Cambridge A Level Physics 9702 — 2016 Oct/Nov Paper 3 · Variant 5

1 In this experiment, you will investigate the motion of a bottle in water. (a) You have been provided with a bottle with a mass attached, a measuring cylinder, a jug of water and a large cylindrical container of water. (i) Use water from the jug and the measuring cylinder to determine the maximum volume VF of water held by the bottle. Record VF . (1 ml = 1 cm3) VF = ............................................... cm3 [1] (ii) Return any water to the jug. Do not change the volume of water in the large cylindrical cylinder. (b) (i) Add volume V of water to the bottle where V is approximately 100 cm3. (ii) Record V. V = ........................................... cm3 (iii) Screw the cap on the bottle so that no water leaks out of the bottle when the bottle is inverted. (c) (i) Place both rubber bands around the top of the large cylindrical container. (ii) Gently push the bottle into the water in the large cylindrical container until the top is just on the water surface as shown in Fig. 1.1. Keep the bottle in this position using one hand. (iii) Use your other hand to slide one of the rubber bands down so that it is level with the bottom of the mass. bottle rubber bands large cylindrical container mass bench Fig. 1.1 (iv) Release the bottle. The bottle will move upwards and then move downwards. Place the other rubber band so that it is level with the highest position of the bottom of the mass as s hown in Fig. 1.2. You should repeat this several times before you decide on the position of this rubber band. bottle at its highest position rubber bands y Fig. 1.2 The maximum distance moved upwards by the bottle is y as shown in Fig. 1.2. (v) Measure and record y. y = ................................................. cm [1] 2VF(d) (i) Calculate . 3 2VF = .................................................... cm3 3 (ii) Increase V and repeat (b)(ii), (b)(iii), (c)(ii), (c)(iv) and (c)(v) until you have six sets of values of V and y. 2VF Do not use a value of V greater than . 3 [8] (e) (i) Plot a graph of y on the y-axis against V 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] (f) The quantities y and V are related by the equation y = PV + Q where P and Q are constants. Using your answers in (e)(iii), determine the values of P and Q. Give appropriate units. P = .................................................. Q = .................................................. [2] (g) (i) Use your values from (f) to calculate the value of V when y = 0. V = ............................................... cm3 [1] (ii) Explain why it is impossible to repeat the experiment using the value of V calculated in (g)(i). .................................................................................................................................. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1 (a) (i) Value of VF in the range 260.0 cm3 to 400.0 cm3. [1] (c) (v) All values of raw y to the nearest mm and less than 20 cm. [1] (d) (ii) Six sets of readings of V and y (with correct trend and without help from Supervisor) scores 5 marks, five sets scores 4 marks etc. [5] Range: [1] Maximum value of V ⩾ 200 cm3. Column headings: [1] Each column heading must contain a quantity and an appropriate unit. The presentation of the quantity and unit must conform to accepted scientific convention, e.g. y / m or y (cm), V / cm3 , 2VF / 3 / cm3. Consistency: [1] All values of raw V must be given to the nearest cm3. (e) (i) Axes: [1] Sensible scales must be used. Awkward scales (e.g. 3:10, fractions or non- linear) 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 should be no more than three large squares apart. Plotting of points: [1] All observations in the table must be plotted on the grid. Diameter of plotted points must be ⩽ half a small square (no “blobs”). Points must be plotted to an accuracy of half a small square. Quality: [1] All points in the table must be plotted on the grid (at least 5) for this mark to be awarded. All points must be within ± 0.25 cm (to scale) in the y direction 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. There must be at least four points left after disregarding the anomalous point. Line must not be kinked or thicker than half a small square. (iii) Gradient: [1] The hypotenuse of the triangle must be greater than half the length of the drawn line. The method of calculation must be correct. Do not allow ∆x / ∆y. Sign of gradient on answer line must match graph drawn. Both read-offs must be accurate to half a small square in both the x and y directions. y-intercept: [1] Either: Check 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: Check read-off of the intercept directly from the graph (accurate to half a small square. (f) Value of P = candidate’s gradient and value of Q = candidate’s intercept. Do not allow fractions. [1] Units for P (e.g. mm–2, cm–2, m–2 but not e.g. cm / cm3) and Q (e.g. m) correct. [1] (g) (i) V calculated correctly to the number of significant figures given by the candidate. Sign of answer must be consistent with P and Q values in (f). [1] (ii) Valid comment with a comparison of volumes e.g. V is greater than VF. [1]

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2 In this experiment, you will investigate the deflection of a loaded wooden strip. (a) (i) Clamp the wooden strip as shown in Fig. 2.1. G-clamp L wooden strip bench Fig. 2.1 (not to scale) The distance L that the wooden strip extends beyond the edge of the bench should be approximately 80 cm. (ii) Measure and record L. L = ..............................................[1] (iii) Estimate the percentage uncertainty in your value of L. percentage uncertainty = ..............................................[1] (b) (i) Place the 100 g mass on the end of the wooden strip as shown in Fig. 2.2. The vertical distance between the floor and the bottom of the end of the wooden strip is d1. 100 g mass d1 floor Fig. 2.2 (not to scale) (ii) Measure and record d1. d1 = ..............................................[1] (iii) Remove the 100 g mass from the wooden strip. (c) (i) Use ten 10 g masses to evenly distribute a total mass of 100 g along the length of the wooden strip. (ii) The distance between the floor and the bottom of the end of the wooden strip is d2. Measure and record d2. d2 = ..............................................[1] (iii) Calculate (d2 – d1). (d2 – d1) = ..............................................[1] (iv) The mass per unit length M added to the wooden strip is given by m M = L where the total added mass m is 0.100 kg. Calculate M. M = ..............................................[1] (d) Justify the number of significant figures that you have given for your value of M. .......................................................................................................................................... .......................................................................................................................................... ......................................................................................................................................[1]

Mark scheme: 2 (a) (ii) Value of L with unit in range 0.790 m to 0.810 m. [1] (iii) Absolute uncertainty in L either 1 mm or 2 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] (b) (ii) All values of raw d1 with unit to the nearest mm. [1] (c) (ii) d2 > d1 showing scale on rule is used correctly. [1] (iii) Correct calculation of |d2 – d1|. [1] (iv) Correct calculation of M with consistent unit. Do not allow answers to 1 s.f. [1] (d) Justification for s.f. in M linked to s.f. in m and L. [1] (e) Second value of d1. [1] Second value of d2. [1] Quality: Second value of |d2 – d1| < first value of |d2 – d1|. [1] (f) (i) Two values of k calculated correctly. [1] (ii) Valid comment consistent with the calculated values of k, testing against a stated numerical criterion. [1] (g) (i) Limitations [4] (ii) Improvements [4] Do not credit A Two readings not enough to draw Take more readings and plot a Two readings not a conclusion graph/ enough for accurate obtain more k values and results compare Repeat readings Few readings Take more readings and calculate average k B Difference between d2 and d1 is Improved method to measure Laser small/ (d2 – d1) values e.g. travelling Ultrasonic position (d2 – d1) is small/ microscope/larger masses/clamp sensor large % uncertainty in (d2 – d1) vernier calipers above strip Longer strip Change strip Deflection of strip C Difficult to distribute mass evenly/ Improved method of distribution Masses inaccurate gaps between masses vary/ e.g. use marker or scale on masses do not lie in a straight wooden strip/ Stick masses to strip line/ use smaller masses to produce Masses falling masses have slots the same m/ Replace strip with continuous strip of named material metre rule e.g. modelling clay Masses with no slots D Difficult to measure d values with Improved method to measure d Strip oscillates when reason e.g. rule not vertical/ e.g. clamp metre rule/ masses are put on it difficult to hold second rule still place a set square on the floor Use a set square as a pointer/ next to ruler (to ensure rule is Effects of wind parallax error/ vertical)/ Reference to L rule not held stationary use of pointer (to metre rule) E Strip becomes permanently bent Method to overcome deformation Elastic properties of or deformed e.g. check d without masses wood vary before and between readings/ lay weights on strip to flatten Use a new strip

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