2024 CJC H1.Phy.PRELIM P2 ans

CANDIDATE NAME CLASS 2T PHYSICS 8867/2 Paper 2 Structured Questions 23 August 2024 2 hours Candidates answer on the Question Paper. No additional materials are required. READ THESE INSTRUCTIONS FIRST Write your name and class on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected, where appropriate. Section A Answer all questions. Section B Answer any one question. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. MARK SCHEME This document consists of 27 printed pages and 1 blank page. [Turn over FOR EXAMINER’S USE DIFFICULTY L1 L2 L3 Q1 / 7 Q2 / 7 Q3 / 7 Q4 / 8 Q5 / 8 Q6 / 7 Q7 / 16 Q8 / 20 Q9 / 20 PAPER 2 (WEIGHTAGE: 67%) / 80 PAPER 1 (WEIGHTAGE: 33%) / 30 TOTAL % Catholic Junior College JC2 Preliminary Examination Higher 1

2 Data speed of light in free space, c = 3.00  108 m s1 elementary charge, e = 1.60  1019 C unified atomic mass constant, u = 1.66  1027 kg rest mass of electron, me = 9.11  1031 kg rest mass of proton, mp = 1.67  1027 kg the Avogadro constant, NA = 6.02  1023 mol1 gravitational constant, G = 6.67  1011 N m2 kg2 acceleration of free fall, g = 9.81 m s2 Formulae uniformly accelerated motion, s = ut + 1 2 at2 v2 = u2 + 2as resistors in series, R = R1 + R2 + . . . resistors in parallel, 1/R = 1/R1 + 1/R2 + . . .

3 [Turn over Section A Answer ALL questions in this section. 1 (a) A student writes down the following equation to describe the forces acting on a sphere falling under gravity through a medium of liquid,   2 3 L 46 3rv r g     whereby r is the radius of the sphere, v the velocity, g the acceleration of free fall,  the coefficient of viscosity of the liquid with units: kg m−1 s−1,  and L the densities of the sphere and the liquid respectively. By checking the homogeneity of the equation, deduce whether the equation is correct. [2] L2   2 3 L 46 3rv r g     Units of left hand side: (kg m−1 s−1) (m) (m s−1)2 = (kg m2 s−3) Units of right hand side: (m3) (kg m−3) (m s−2) = (kg m s−2) Since the units on left and right hand sides are not equal, the equation is not correct. M1 A1 (b) The drag force F experienced by a steel sphere of radius r dropping at speed v through a liquid is given by 2 2F Br v  where B is a constant. A student obtained the following set of data for a steel sphere dropping through a fluid. F = (8.0  0.1) mN r = (3.0  0.1) cm  = (1.00  0.01)  103 kg m−3 v = (24  1) cm s−1

4 (i) Random errors are associated with the measurement of the diameter of the steel sphere. 1. Explain what is meant by a random error. ..…………………………………………… .…………………………………... ……. .…... ……………………………………… ……..... ………….…….…….… ....... [1] L1 Random error is an error when the measured readings are scattered about the mean value with no fixed pattern. They have equal probability of having different magnitudes and signs. A1 2. Hence, explain how such a random error can be minimized in this experiment. ...………………………………………………………………………………... ……. .…...……………………………………… ……..... ………….…….…….… ....... [1] L2 Difficult to ascertain the exact diameter of the steel sphere. Measure the diameter along different orientations of the steel sphere and take average. A1 (ii) Using the data given, determine the value of B together with its associated uncertainty. B = …... … … .….. … ±.… …... ...… ..... [3] L3 2 2F Br v  2 2 FB r v      3 2 2 8.0 10 0.030 1000 0.24  = 0.15432 2 2B F r v B F r v                     0.1 0.1 0.01 12 2 0.17250.15432 8.0 3.0 1.00 24                B C1 M1

5 [Turn over 0.15432 0.1725 0.0266   B 0.15 0.03B   A1 [Total: 7] 2 A ball was kicked over a wall of height h as shown with a velocity 16.4 m s-1 at an angle of 50° above the horizontal. At the highest point of the trajectory, the ball managed to just go over the wall. It landed into a pit 2.0 m deep. Fig. 2.1 (a) Calculate the height h of the wall. h = …... …… … …… … …. .… ….. .. m [2] L2 Let vy be the vertical velocity of ball at top of wall, uy be initial velocity and ay be the acceleration of ball. Taking upwards and rightwards as positive, consider the ball at its highest point of its trajectory. 2 2 y y y y 2v u a s      200 16.4sin50 2 9.81 h   h = 8.0445 m = 8.04 m (3 s.f.) M1 A1 (b) Calculate the time of flight of the ball when it just hits the pit. 16.4 m s-1 50° 2.0 m h ball wall pit

6 time = …... ……… …… ….. … …. .… ... s [3] L2 Let sy be the displacement, uy be the initial velocity, ay be the acceleration and t be the time taken for the ball to hit the pit Taking upwards and rightwards as positive, consider the ball just before it hits the pit. 2 y y y 1 2s u t a t      0 2 12.0 16.4sin50 9.81 2t t    29.81 25.12625773 4 0t t          2 25.12625773 25.12625773 4 9.81 4 2 9.81t      = 2.712 s or -0.1504 s t = 2.71 s or -0.150 s (rejected) C1 M1 A1 (c) Calculate the vertical velocity of the ball just before it hits the pit. vertical velocity = …... ……… ….. … …. .… ... m s-1 [2] L2 Let vy be the vertical velocity of ball just before it hits the pit, uy be the initial velocity, ay be the acceleration and sy be the displacement of the ball. Taking upwards and rightwards as positive, consider the ball just before it hits the pit. 2 2 y y y 2v u as       22 0 y 16.4sin50 2 9.81 2.0v     vy = –14.038 m s-1 = 14.0 m s-1 (downwards) (3 s.f.) M1 A1 [Total: 7]

7 [Turn over 3 (a) Three co-planar forces act on a body that is in equilibrium. (i) By drawing a vector diagram, d escribe how a vector diagram can be used to represent these forces. ………………………………………………………………………………………... ……. ………………………………………………………………………………………... ……. ………………………………………………… …….....………….…….…….…....... [2] L2 Correct vector diagram with arrows joining from head to tail. Arrow length represents the magnitude and the direction of the arrow represents the direction of force. B1 B1 (ii) Explain why the vector triangle cannot be used to show that a body is in rotational equilibrium. ………………………………………………………………………………………... ……. ………………………………………………………………………………………... ……. ………………………………………………… ……..... ………….…….…….… ....... [1] L2 The moments about a pivot cannot be found using the vector