TJC 2023 H2 Prelim Paper 4 Solutions

1 Name: _____________________________________ CG: ___________ Date: _____________ Question 1 Suggested Mark Scheme No Marking Instructions Mark Score (a)(i) d recorded to nearest 0.1 mm with unit (2 dp in cm) 1 (a)(ii) h recorded to nearest 0.1 mm or 1 mm with unit (1dp or 2dp in cm) D recorded to nearest 0.1 mm with unit (2 dp in cm) with evidence of repeat measurement 1 (b)(iii) x calculated correctly to correct s.f. (with substitution) 1 (b)(iv) Correct justification of s.f. in x linked to s.f. in D, d and h (lowest s.f.) 1 (c)(ii) Value of t to correct d.p. with unit (5.0 s ≤ t ≤ 9.0 s) Evidence of repeat timing 1 (c)(iii) Correct calculation of % uncertainty (1 or 2 sf) using sensible value of t (0.2 s ≤ t ≤ 0.5 s). 1 (d) Second value of x calculated correctly Second value of average t with correct dp and unit 1 1 (e)(i) Correct calculations of the two k values with correct unit 1 (e)(ii) Draw conclusion based on stated criterion. (e.g. not obeyed because % difference of k values > 2 times % uncertainty of t in (c)(iii)) 1 (f)(i) Sources of error might include: 1. Difficult to release small container from same position every time as placing fingers in water changes level of water surface making it difficult to maintain the same start point, affecting t 2. As the centre of gravity of the small container and marbles is located at one side of the container it does not always fall vertically and may hit the sides of the cylinder during descent, affecting t 3. Timing is too short making human reaction time a significant uncertainty in timing t 4. Difficult to identify end point as it is difficult to see the small container due to refraction/similar refractive indices of water, cylinder and container/glass curvature, affecting t 5. Bubble / air in container introduces extra buoyancy, affecting t 1 (f)(ii) One improvement each. Relevant points might include: 1. Better method to hold and release cylinder (e.g. use a pincer / make a mark for reference to ensure same water level for each release) 2. Method to attach string symmetrically / ensure symmetrical distribution of masses e.g. use glass beads/sand/modelling clay for even mass distributions 3. Use a longer tube / video the descent and view frame by frame 4. Method to identify end point (e.g. mark at bottom of cylinder/use colour container) 5. Puncture a small hole in the lid to release bubble / air 1 Total 12 Question 2 Suggested Mark Scheme No Marking Instructions Mark Score (a)(ii) x recorded to nearest mm with unit (or 1 dp in cm, 3 dp in m) 1 (b)(ii) V1 and V2.recorded to correct d.p. with unit (3 d.p. in V) with V2 < V1 1 (c) Collected and tabulated 5 sets of data (for x till 90.0 cm) V2 /V1 calculated correctly to correct s.f. 1 1 (d)(i) Linear graph with y-intercept. Appropriate scales – awkward scales (e.g. 3:10) are not allowed and scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Correct labelling of axes with correct units. All observations plotted to an accuracy of half a small square and line of best fit drawn with a fair scatter of points on either side of the line 1 1 (d)(ii) Correct conclusion of the relationship based on student’s result 1 (d)(ii) Line Z with steeper gradient and same y-intercept 1 1 Total 9

2 Question 3 Suggested Mark Scheme No Marking Instructions Mark Score (b)(i) r recorded to nearest mm with unit with unit with evidence of repeat reading 1 (b)(ii) Measure diameter D of the masses in different orientations and calculate the average D. Record readings R1 and R2 of the outer edges of the masses. Then r = ½ (R2 – R1 –D) OR Measure centre to centre (through the gap) of the 2 slotted masses Divide by 2 1 1 (c)(ii) 2.6 s ≤ T ≤ 4.6 s Evidence of repeat timing 1 (d) Collected 6 or more sets of data (r, T). Award 1 mark if assistance was rendered, or collected only 5 sets of data 2 Each column heading contains an appropriate quantity and unit 1 Consistency in no. of d.p. for raw readings (r to nearest mm, T to 0.1 s) 1 Correct calculation of quantities (T3, r2) 1 All calculated values given to appropriate no. of s.f. 1 (e) Linearising equation and deriving gradient / y-intercept of graph 1 Appropriate scales – awkward scales (e.g. 3:10) are not allowed and scales must be chosen so that the plotted points occupy at least half the graph grid in both x and y directions. Correct labelling of axes with correct units 1 All observations plotted to an accuracy of half a small square 1 Line of best fit – with a fair scatter of points on either side of the line 1 Gradient – hypotenuse of the triangle is greater than half the length of the drawn line. Read-offs must be accurate to half a small square 1 Y intercept – read off directly from the graph to half a small square or determined from y = mx + c using a point on the line 1 Value of a and b calculated correctly with correct units, if any 1 (f) Appropriate comment on any anomaly 1 (g) Diagram with workable arrangement: single spring (extension) with pivot at c.g. Do not accept spring compression methods. Appropriate method to measure and determine average extension x and period T Plot T2 against x to show relationship where gradient gives c Correct explanation of difficulty in using spring constant with small k. 1 1 1 1 Total 22

3 Name of student:_______________________________ CG:_____________ Q4 Planning Question Suggested Mark Scheme Score Marks Marking Points A1 A2 Design (2 mark) Labelled diagram showing method to produce air flow in line with turbine. Method of producing “wind” must be labelled. E.g. electric fan, hair dryer, leaf blower Circuit connecting turbine to lamp with ammeter and voltmeter connected correctly. No additional power supplies in the lamp circuit. B1 B2 B3 B4 B5 Procedure (5 marks) Method to measure power P = IV. Use voltmeter to measure V and ammeter to measure I. Allow wattmeter or joule meter and stopwatch. Method to determine angle . Measure angle with protractor or rule for measurements for trigonometry methods. Must be shown correctly on diagram or explained in text. Method to measure wind speed v, e.g. wind speed meter/detector/sensor(with data logger, anemometer. Control of variables Expt A: Keep v constant, vary  Vary angle  by tilting the plane of the wind turbine with respect to the horizontal/vertical. Expt B: Keep  constant, vary v Method to change wind speed v, e.g. change setting, variable power supply/ resistor/ change distance from fan. C1 C2 C3 Safety and Analysis (2 marks) Expt A: For constant l, lg P = m lg cos  + lg (k vn) Plot lg P vs lg cos. Gradient of the straight line is equal to m. Expt B: For constant , lg P = n lg v + lg(k cosm) Plot lg P vs lg v. Gradient of the straight line line is equal to n. Safety consideration (1 mark) Wear goggles to avoid air flow entering eyes Avoid moving blades of fan using safety screen, switch off fan when changing experiment Wear gloves when handling hot lamp D1 D2 D3 D4 D5 D6 D7 D8 D9 Details (Max 2 D marks) Conduct pre-experiment to determine suitable range of  and v to obtain measurable P. Use of large wind speed to gain measurable readings. Use of low resistance lamp or use turbine with low friction. Additional detail on measuring θ or (cos) θ e.g. use a large protractor, projection method. Measuring wind speed at fixed point from turbine. Adjust height of fan so that air flow is horizontally aligned to the turbine. Wait until airflow/turbine/meter readings constant before taking readings. Keep windows shut/air conditioning switched off/use of wind tunnel to avoid draughts. Any other good physics suggestion. 12

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