RVHS H2 Physics P4 Soln

Mark Scheme Question Answer Marks 1(a)(i) current recorded to correct 1 d.p. in mA (setting of digital ammeter) 1 (ii) 1 I recorded in the same s.f. as recorded in the corresponding I. 1 (iii) percentage uncertainty calculated correctly using appropriate method and given to 1 or 2 s.f. E.g. I = 70.4 mA, 1 𝐼 = 14.2 A-1 Using Δ(1 𝐼) 1/𝐼 = Δ𝐼 𝐼 , so percentage uncertainty = ±2 70.4 × 100% = ±2.8% 𝑜𝑟 ± 𝟑% Alternative or max 1 𝐼 = 1 68.4 = 14.6 A-1 taking difference with 1 𝐼 = 14.2 A-1 So absolute uncertainty can be estimated as ±0.4 A-1, so percentage uncertainty = ±0.4 𝟏𝟒.𝟐 × 100% = ±2.8% 𝑜𝑟 ± 𝟑% M1 A1 (b) gradient = 𝑅 𝐸 intercept = 𝑟 𝐸 1 (c)(i) correctly plotting of points with acceptable best fit line drawn 1 (ii) correct method to calculate gradient 1 correct method to calculate intercept 1 (iii) 𝑅 𝑟 obtained by 𝑔𝑟𝑎𝑑𝑖𝑒𝑛𝑡 𝑖𝑛𝑡𝑒𝑟𝑐𝑒𝑝𝑡 1 (iv) line parallel to original line and shifted upwards (or to the left) 1

Question Answer Marks 2(a) • L = 98.5 ± 0.1 cm 1 (b) • y2 lesser than y1 • y, y2 and y1 are all recorded to the nearest 0.1 cm • Repeated measurements 1 (c) Tabulation • Collected 5 sets of data for m, y1 and y2. • Correct trend (0 marks for 4 sets and fewer) 1 Column Heading • Each column heading must contain a quantity and a unit: y/cm, m/g • No split table 1 Raw data (i.e x and I): Precision of recording • All values of y1 and y2. to nearest mm & • All values of m to nearest g 1 Calculated quantity: Accuracy of calculation All values of y calculated correctly with the correct d.p 1 (d) Graph: Scale, Size & Axes • Sensible scales, no awkward scales (eg 3 units into 10 small squares) • Plotted pts occupy at least ½ the graph grid in both x & y directions • Axes labelled with the quantity & unit {ECF for wrong units in (c)} Successive scale markings: no more than 20 small squares apart. 1 Plotting of Points • ALL observations in table must be plotted • accurate to within half a small square. • Thickness of plots (ie the crosses, ‘x’)  half a small square 1 Best fit line & Anomaly • Minimum number of 4 non-anomalous points. • Line drawn with approx. equal number of points on either side of line (anomalous points not considered). • Line not be kinked/disjointed or thicker than half a small square • Anomalous plot clearly indicated (eg by a circle or labelled.) • Allow 1 anomalous plot only. 1

• {Rule of thumb: A plot is considered anomalous if it is > 4 mm from line of best fit.} Determination of Gradient  Recorded the 4 coordinates for gradient calculation correctly  Hypotenuse of triangle > half length of line drawn  No obscurity of the 2 points used for gradient calculation. {Hence triangle must not be drawn too near a data plot.} 1 Determination of y-intercept Vertical intercept calculated using a point on the line {not from the table} & value of gradient. {Allow reading off the y- intercept if x-axis starts from zero & there is no ‘bunching of plots’} 1 m/g y1/cm y2/cm y/cm 60 90.0 84.0 87.0 80 70.0 65.0 67.5 100 51.0 44.0 47.5 110 40.2 34.5 37.4 120 34.0 24.0 29.0 130 24.0 13.0 18.5 y = -0.9769x + 145.5 0 10 20 30 40 50 60 70 80 90 100 0 20 40 60 80 100 120 140 Series1 Linear (Series1)

Question Answer Marks 3(a)(ii) value of d to nearest 0.01 mm and final value in range 1.50 − 1.70 mm show repeated readings 1 3(a)(iii) value of 𝜃 to nearest degree and final value in range 55o−65o 1 3(a)(iv) Δ𝜃 range from ±3o to ±5o percentage uncertainty given to 1 or 2 s.f. 1 3(a)(v) correct calculation of sin2(θ/2) using values from (a)(iii) substitution of values in your working is needed correct significant figures no units 1 3(b)(i) Value of e to nearest 0.1 cm and final value in range 0.8 − 1.6 cm. Δ𝑒 range from ± 0.2 cm to ± 0.5 cm percentage uncertainty given to 1 or 2 s.f. clear working and substitutions correct significant figures correct units 2 3(b)(iii) value of t in range 15.00 − 20.00 s show repeated readings All t values to nearest 0.01 s 1 3(c) value of 𝜃 to nearest degree and final value in range 25o−35o correct calculation of sin2(θ/2) value of t in range 7.00 − 9.00 s show repeated readings for values of t All t values to nearest 0.01 s correct significant figures correct units 2 3(d)(i) Two values of k calculated correctly. correct significant figures correct units 2 3(d)(ii) Testing against percentage uncertainty in (a)(iv) and (b)(i) with appropriate conclusion. Do not accept arbituary criterion such as 10% or 20% 1

3(d)(iii) spring constant of spring / length of wire / mass of wire / angle θ between the straight part of the wire 1 3(e) • Setup according to Fig. 3.2 and conduct oscillations according to Fig. 3.3. Appropriate procedures with mention of variation of masses and collect corresponding values of t. Conduct at least 6 sets of data for masses and t. • Identify masses attached to end of wire as independent variable, time as dependent variable. Angle of bend, length of wire, spring constant, etc as controlled variable. • Identify stopwatch to record timing and protractor to measure angle. (optional: mass balance to measure calibrated masses). • Plot a graph of time against mass to determine constant gradient of the graph and zero y-intercept. • Light masses may result in unstable oscillating behaviour of the wire / Heavy masses may fall off the wire during oscillating (or not able to conduct experiment since the spring is deformed due to heavy masses) 5 3(f)(i) values of t (no mass) is less values of t (with mass) Use a table to present the results. Repeats: At least two values of t ≥ 10 s All t values to nearest 0.01 s correct significant figures correct units 3 3(f)(ii) When masses are attached to the end of the wire, the centre of gravity shifted lower/away from the pivot point. Since period is proportional to the distance between the pivot and the centre of gravity for a simple oscillating object about the vertical plane, the period increases when masses are added. 1

Qn Answer Marks 4 Diagram labelled diagram with • retort stand to hold capillary tube; • h labelled; container resting on bench. (Include rule if mentioned in procedure) 1 Defining the problem Part 1 r is the independent variable and h is the dependent variable or vary r measure h. and density of liquid to be kept constant. 1 Part 2 𝜌 is the independent variable and h is the dependent variable or vary r measure h. and r to be kept constant. 1 Methods to data collection Measure inner diameter d using travelling vernier microscope or allow estimate diameter d by measuring external d using micrometer screw gauge or vernier caliper and r = d/2 1 Measure volume of water using measuring cylinder Measure mass of water using electronic balance. Calculate density using mass / volume (accept measure density using hydrometer) 1 Measure h using tail of vernier caliper or metre rule clamped vertically. 1 Method of varying density of liquid. E.g. changing different types of liquid or add solute into solvent. Need to give examples of solute used. 1 Method of analysis Part 1 Plot lg ℎ 𝑣𝑠 lg 𝑟; 𝑝= gradient 1 Part 2 Plot Plot lg ℎ 𝑣𝑠 lg 𝜌; 𝑞 = gradient 1

Additional detail including safety considerations max 3 • Method of ensure capillary tube and instruments used to measure h is vertical. E.g. use of plumbline or use set square 1 • Ways to check if cross-section of capillary tube is constant. E.g. pass a fixed volume of coloured liquid through tube. Check if length of coloured liquid is constant. 1 • check that the temperature is constant throughout experiment to prevent expansion or contraction of capillary tube. 1 • M