Cambridge A Level Physics 9702 — 2014 Oct/Nov Paper 3 · Variant 3

1 In this experiment, you will investigate the motion of a ball and rod. (a) Press the ball of modelling clay onto the end of the wooden rod, as shown in Fig. 1.1. wooden rod ball hook Fig. 1.1 (b) (i) Set up the apparatus as shown in Fig. 1.2 with the nail through the hook in the wooden rod. hook nail boss wooden rod L stand ball bench Fig. 1.2 (ii) Measure and record the distance L between the nail and the centre of the ball. L = ...................................................... (c) Move the bottom of the rod to the left. Release the rod and watch the movement. The rod will move to the right and then to the left again, completing a swing as shown in Fig. 1.3. one complete swing Fig. 1.3 Measure and record the time for at least 10 swings. Record enough readings to determine an accurate value for the time T taken for one complete swing. T = ................................................. [2] (d) Decrease L by moving the ball along the rod, and repeat (b)(ii) and (c) until you have six sets of values of L and T. Include values of T 2L and L2 in your table. [10] (e) (i) Plot a graph of T 2L on the y-axis against L2 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 T and L are related by the equation T 2L = AL2 + B where A and B are constants. Use your answers in (e)(iii) to determine the values of A and B. Give appropriate units. A = ...................................................... B = ...................................................... [2] You may not need to use all of the materials provided.

Mark scheme: 1 (c) Value of T in range 1.0 s – 2.0 s with unit. [1] Evidence of repeated timings. [1] (d) Six sets of readings of L and time (different values) scores 5 marks, five sets scores 4 marks etc. [5] Help from Supervisor –1. Range: [1] Lmax Lmin ≥ 30.0 cm. Column headings: [1] Each column heading must contain a quantity and a unit. The unit must conform to accepted scientific convention e.g. T2L / s2 m, L2 / m2. Accept separating mark as a solidus, brackets or ‘in’ but not commas. Consistency: [1] All values of raw L must be given to the nearest mm. Significant figures: [1] All values of L2 must be given to the same s.f. as (or one more than) the s.f. in L. Calculation: [1] Values of T2L calculated correctly. (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: [1] All observations in the table must be plotted on the graph grid. Diameter of plotted points must be ≤ half a small square (no “blobs”). Plotted points must be accurate to within half a small square. Quality: [1] All points in the table must be plotted on the grid for this mark to be awarded. Judge by scatter of all points about a straight line. All points must be within ± 0.025 m2 (250 cm2) in the L2 direction from a straight line. (ii) Line of best fit: [1] Judge by balance of all points on the grid (at least 5) 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 by candidate (i.e. circled or labelled). Lines must not be kinked or thicker than half a small square. (iii) Gradient: [1] Sign of gradient must match the graph. The hypotenuse of the triangle must be greater than half the length of the drawn line. Both read-offs must be accurate to half a small square in both x and y directions. The method of calculation must be correct. y-intercept: [1] Either: Correct read-offs 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: Correct read-off of the intercept directly from the graph. (f) Value of A = candidate’s gradient. Value of B = candidate’s intercept. [1] Allow correct rounding unless to 1 s.f. Unit for A (s2 m–1 or s2 cm–1 or s2 mm–1) and B (s2 m or s2 cm or s2 mm). [1] [Total: 20]

More questions on Physical quantities

2 In this experiment, you will investigate how the rebound height of a ball from an inclined board depends on the angle of the board. (a) (i) You have been provided with a ball and a board. Place the board on the bench. Hold the ball above the board as shown in Fig. 2.1. Move the ball until the height h1 of the bottom of the ball above the board is 40 cm. ball before release ball at maximum height after rebound h1 = 40 cm h2 board bench Fig. 2.1 (ii) Release the ball. Measure and record the maximum height h2 of the ball after rebound. h2 = ..................................................[2] (iii) Calculate q, where h q = 2 . h 1 q = ...................................................... (b) (i) Raise the board so that it makes an angle θ with the bench as shown in Fig. 2.2. stand boss clamp board θ bench Fig. 2.2 (ii) Adjust the board until θ is in the range 10° to 12°. Measure and record θ. θ = ..................................................[1] (iii) Calculate cos2 (2θ ). cos2 (2θ ) = cos (2θ ) × cos 6 (2θ )@ cos2 (2θ ) = .................................................[1] (iv) Justify the number of significant figures that you have given for your value of cos2 (2θ ). .................................................................................................................................. .................................................................................................................................. ..............................................................................................................................[1] (c) (i) Place the large container on its side with its open face towards the board as shown in Fig. 2.3. container 40 cm h A Fig. 2.3 (ii) Hold the ball 40 cm above the board. (iii) Release the ball. Watch it bounce at A and follow a curved path before bouncing into the container. Measure and record the maximum height h of the ball after rebound, as shown in Fig. 2.3. h = ..................................................[1] (iv) Estimate the percentage uncertainty in your value of h.

Mark scheme: 2 (a) (ii) Value of h2 with unit, in the range 20.0 cm ≤ h2 ≤ 35.0 cm. [1] Evidence of repeat readings. [1] (b) (ii) Value of θ = 10°, 11° or 12° with unit. [1] (iii) Correct calculation of cos2(2θ). [1] (iv) Correct justification of s.f. in cos2(2θ) linked to s.f. in value of θ. [1] (c) (iii) Value of h with consistent unit. [1] (iv) Absolute uncertainty in h in range 5 mm – 20 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 get percentage uncertainty. [1] (d) (i) Second value of θ. [1] (ii) Second value of h. [1] Second value of h ˂ first value of h. [1] (e) (i) Correct calculation of two values of k. [1] (ii) Valid comment consistent with the calculated values of k, testing against a stated criterion. [1] (f) (i) Limitations (4 max.) (ii) Improvements (4 max.) Do not credit A Two readings not enough to draw Take many readings (for repeat readings / a conclusion different angles) and plot a few readings / graph. “too few readings” / Take more readings and “two readings” / compare values of k “not enough readings” B Large uncertainty in θ Make θ larger / use trigonometry Parallax error in angle with detail measurement Use larger protractor More accurate protractor “Angle too small” Zero line not on edge C Difficult to release the ball without Clamp ball prior to release / use Electromagnet applying a force / difficult to drop at a card gate or stop gate / use Robotic arm 40 cm with reason e.g. hands marker at 40 cm / valid method of shaking. release D Difficult to measure / judge Use a video with a scale / trial Use camera position of h with timing reason and improvement with marker Ignore high speed/slow e.g. ball stops at maximum height motion camera for a short time E Difficult to measure / judge Use a set square on Judging centre of position of h with positioning bench / plumb-line / (graduated) ball / marking line on reason grid behind / clamp a ruler ball / vertical lines / lines e.g. because of parallax horizontally / use a second rule error / ruler not vertical / no lower with detail of position. horizontal reference line. F Rebound height is variable / ball Detailed method to ensure ball Ball falls off the board. veers off course / ball moves does not veer off course. sideways. [Total: 20]

More questions on Physical quantities