Cambridge A Level Physics 9702 — 2016 May/June Paper 3 · Variant 1

1 In this experiment, you will investigate the motion of a loaded wooden strip. (a) (i) Use the modelling clay to attach the slotted masses to the centre of the wooden strip as shown in Fig. 1.1 and Fig. 1.2. [ wooden strip small string loop slotted mass large string loop springs Fig. 1.1 slotted masses modelling clay end of wooden strip Fig. 1.2 (ii) Measure and record the distance x between the end of the wooden strip with the small string loop attached and the centre of the slotted masses as shown in Fig. 1.1. x = ..................................................[1] (b) (i) Set up the apparatus as shown in Fig. 1.3. stand clip clip stand loop of spring bench Fig. 1.3 (ii) Slide the small string loop over the rod of a stand and fix it in place using a clip. Slide the free loop of the spring down the rod of the other stand and fix it in place using the other clip. (iii) Adjust the apparatus until the large string loop and springs are parallel to the bench. (iv) Use G-clamps to secure both stands to the bench. (c) Move the right-hand end of the wooden strip downwards through a distance of approximately 3 cm. Release the wooden strip. The wooden strip will oscillate. Determine the period T of these oscillations. T = ..................................................[1] (d) Change x by moving the slotted masses along the wooden strip. For each value of x, adjust the position of the clips so that the large string loop and springs are parallel to the bench. Repeat (a)(ii) and (c) until you have five sets of values of x and T. Include values of T 2 in your table. [10] (e) (i) Plot a graph of T 2 on the y-axis against x 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) It is suggested that the quantities T and x are related by the equation T 2 = P x + 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] [Total: 20] You may not need to use all of the materials provided.

Mark scheme: 1 (a) (ii) Value of x with consistent unit and in the range 36.0 cm to 39.0 cm. [1] (c) Value of T with unit in range 0.300 s < T < 1.00 s. [1] (d) Five sets of readings of x and time with correct trend scores 5 marks, four sets scores 4 marks etc. [5] Help from Supervisor –1. Range: [1] xmax – xmin ≥ 30 cm. 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. x / m or x (cm), T2 / s2 or T2 (s2). Consistency: [1] All values of x must be given to the nearest mm. Significant figures: [1] Every value of T2 must be given to the same number of s.f. as (or one more than) the number of s.f. in the corresponding raw values of time. Calculation: [1] T2 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 should be no more than three large squares apart. Plotting of points: [1] All observations in the table must be plotted. 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 no more than ±5 cm (to scale) in the x 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 4 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 by the candidate. Lines must not be kinked or thicker than half a 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 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: Correct read-off from a point on the line substituted into y = mx + c or an equivalent expression. Read-offs must be accurate to half a small square in both x and y directions. Or: Intercept read 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. Unit for P correct (e.g. s2 m–1) and unit for Q correct (e.g. s2). [1]

More questions on Simple harmonic oscillations

2 In this experiment, you will investigate the motion of a container on a wooden board. (a) Measure and record the length w of the shorter side of the wooden board, as shown in Fig. 2.1. wooden board Z Fig. 2.1 w = ..............................................m [1] (b) (i) Set up the wooden board as shown in Fig. 2.2. stand boss clamp gripping shorter side of board longer side of wooden board 15 cm e bench Fig. 2.2 The distance between the bottom of the board and the bench should be approximately 15 cm. (ii) Measure and record the angle θ as shown in Fig. 2.2. θ = ..................................................[1] (iii) Estimate the percentage uncertainty in your value of θ. percentage uncertainty = ..................................................[1] (c) (i) Place the container on the wooden board as shown in Fig. 2.3. clamp container lid Fig. 2.3 The container should be aligned with the edges of the board as shown in Fig. 2.3. (ii) Release the container. The container will follow the path shown in Fig. 2.4. \ Fig. 2.4 (iii) Measure and record the distance y, as shown in Fig. 2.4. y = ..............................................m [2] (d) (i) Calculate D using w2 + y2 D = . w D = ..............................................m [1] (ii) Justify the number of significant figures that you have given for your value of D. .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1]

Mark scheme: 2 (a) All values of w to nearest mm, with final value in range 0.200 m to 0.300 m. [1] (b) (ii) Value(s) of θ to the nearest degree. Final value < 45° with unit. [1] (iii) Percentage uncertainty in θ based on an absolute uncertainty in range 1° to 3°. 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) (iii) Value of y in range 0.20 m to 0.50 m. [1] Evidence of repeat readings. [1] (d) (i) Correct calculation of D. [1] (ii) Correct justification for s.f. in D linked to s.f. in w and y. [1] (e) (ii) Second value of θ. [1] Second value of y. [1] Quality: Second value of y > first value of y (if θ2 > θ1). [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 not enough to draw Take more readings and plot a Few readings/ a conclusion graph/ only one reading/ obtain more k values and not accurate result/ compare “repeat readings” on its own B Difficulty with starting position e.g. Improved method for initial Change shape of starting position of container not placement or release container parallel to edge e.g. use of block with detail (aligned with side) C Small range of angles Workable method to increase “No friction” on its possible/cylinder slips when angle friction e.g. sheet of paper on own/ too high/cylinder moves off wrong board/ smoother board/ edge on board sanding board/ use longer board use a rougher board/ roughen edge of container D Difficult to measure y or locate Improved method for measuring Effects of moving position where container moves y e.g. use marker or scale on air/fans/ off edge with reason e.g. moves board/use video and playback “frame by frame” off edge too fast/short time to with scale/ observe moving off edge paint on lid/ calibrate board E Difficulty with set up e.g. board Method to improve stability of G-clamp to bench moves/clamp moves/board not an board e.g. use two clamps/ even height across width/board Blu-Tack to fix board to bench/ not aligned correctly spirit level across board/ support board on long blocks F Difficult to release without Improved method of release e.g. Electromagnetic applying force card gate/block with detail of release removal

More questions on Physical quantities