DHS 2022 Prelim P2

© DHS 2022 9749/02 [Turn over Name: Centre/Index Number: Class: DUNMAN HIGH SCHOOL Preliminary Examination Year 6 H2 PHYSICS Paper 2 Structured Questions Candidates answer on the Question Paper 9749/02 15 September 2022 2 hours READ THESE INSTRUCTIONS FIRST Write your centre number, index number, name and class at the top of this page. Write in dark blue or black pen. You may use an HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all questions in the spaces provided on the question paper. The use of an approved scientific calculator is expected, where appropriate. You may lose marks if you do not show your working or if you do not use appropriate units. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use 1 10 2 9 3 6 4 6 5 8 6 9 7 10 8 22 Total 80 This document consists of 20 printed pages.

2 © DHS 2022 9749/02 Data speed of light in free space, c = 3.00 × 108 m s−1 permeability of free space, o = 4 × 10−7 H m−1 permittivity of free space, o = 8.85 × 10−12 F m−1 (1/(36)) × 10−9 F m−1 elementary charge, e = 1.60 × 10−19 C the Planck constant, h = 6.63 × 10−34 J s 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 molar gas constant, R = 8.31 J K−1 mol−1 the Avogadro constant, NA = 6.02 × 1023 mol−1 the Boltzmann constant, k = 1.38 × 10−23 J K−1 gravitational constant, G = 6.67 × 10−11 N m2 kg−2 acceleration of free fall, g = 9.81 m s−2

3 © DHS 2022 9749/02 [Turn over Formulae uniformly accelerated motion, s = ut + at2 v2 = u2 + 2as work done on/by a gas, W = pV hydrostatic pressure, p = gh gravitational potential,  = −Gm/r temperature, T/K = T/oC + 273.15 pressure of an ideal gas, p = mean translational kinetic energy of an ideal gas molecule, E = displacement of particle in s.h.m., x = x0 sin t velocity of particle in s.h.m., v = v0 cos t =  electric current, I = Anvq resistors in series, R = R1 + R2 + . . . resistors in parallel, 1/R = 1/R1 + 1/R2 + . . . electric potential, V = alternating current / voltage, x = x0 sin t magnetic flux density due to a long straight wire, B = magnetic flux density due to a flat circular coil, B = magnetic flux density due to a long solenoid, B = radioactive decay, x = x0 exp(−t) decay constant,  = 1 2 21 3 Nm cV  kT2 3 22 xxo − r Q o4 0 2 d I  0 2 N r I 0nI 1 2 ln2 t

4 © DHS 2022 9749/02 Answer all questions in the spaces provided. 1 A golfer strikes a ball so that it leaves the ground with a velocity of 6.0 m s–1 at an angle θ to the horizontal, as illustrated in Fig. 1.1. The magnitude of the initial vertical component, vY, of the velocity is 4.8 m s–1. Assume that air resistance is negligible. (a) Show that the magnitude of the initial horizontal component, vX, of the velocity is 3.6 m s–1. [1] (b) The ball leaves the ground at time t = 0 and reaches its maximum height at t = 0.49 s. On Fig. 1.2, sketch separate lines to show the variation with time t, until the ball returns to the ground, of (i) the vertical component, vY, of the velocity (label this line Y), [2] (ii) the horizontal component, vX, of the velocity (label this line X). [2] Fig. 1.1 (not to scale) vY vx

5 © DHS 2022 9749/02 [Turn over (c) Calculate the maximum height reached by the ball. maximum height = ........................... m [2] (d) For the movement of the ball from the ground to its maximum height, determine the ratio kinetic energy at maximum height change in gravitational potential energy . ratio = ........................... [2] Fig. 1.2 t / s

6 © DHS 2022 9749/02 (e) In practice, air resistance is not negligible. State and explain how the actual time taken for the ball to reach maximum height is affected compared to the time calculated when air resistance is assumed to be negligible. …...………………………………………………………………………………………………….. …...………………………………………………………………………………………………. [1] [Total: 10] 2 (a) The variation with extension x of the tension F in a spring is shown in Fig. 2.1. Calculate the energy stored in the spring for an extension of 4.0 cm. Explain your working. energy = ………………………………… J [3] Fig. 2.1

7 © DHS 2022 9749/02 [Turn over (b) The spring in (a) is used to join two frictionless trolleys A and B, of mass M1 and M2 respectively, as shown in Fig. 2.2. The trolleys rest on a horizontal surface and are held apart so that the spring is extended. The trolleys are then released at the same time. (i) Explain why, as the extension of the spring is reduced, the momentum of trolley A is equal in magnitude but opposite in direction to the momentum of trolley B. …...…………………………………………………………………………………………. …...…………………………………………………………………………………………. …...…………………………………………………………………………………………. …...……………………………………………………………………………………… [2] (ii) At the instant when the extension of the spring is zero, trolley A has speed V1 and trolley B has speed V2. Write down 1. an equation, based on momentum, to relate V1 and V2, …………………………………………………………………………………...... [1] 2. an equation to relate the initial energy E stored in the spring to the final energies of the trolleys. …………………………………………………………………………………...... [1] Fig. 2.2

8 © DHS 2022 9749/02 (iii) 1. Show that the kinetic energy EK of an object of mass m is related to its momentum p by the expression 2 2 K pE m= . [1] 2. Trolley A has a bigger mass than trolley B. Use the expression in (iii)1. to deduce which trolley, A or B, has the larger kinetic energy at the instant when the extension of the spring is zero. ..………………………………………………………………………………………. ..…………………………………………………………………………………… [1] [Total: 9] 3 Two progressive sound waves Y and Z meet at a fixed point P. The variation with time t of the displacement x of each wave at point P is shown in Fig. 3.1. (a) Determine the phase difference between the waves. phase difference = ……………………o [1] Fig. 3.1

9 © DHS 2022 9749/02 [Turn over (b) The two waves superpose at P. Use Fig. 3.1 to determine the resultant displacement at time t = 0.75 ms. resultant displacement = ……………………µm [1] (c) The intensity of wave Y at point P is I. Determine, in terms of I, the intensity of wave Z. intensity = …………………… [2] (d) The speed of wave Z is 330 m s−1. Determine the wavelength of wave Z. wavelength = …………………… m [2] [Total: 6]

10 © DHS 2022 9749/02 4 (a) The circuit in Fig. 4.1 contains a battery of electromotive force (e.m.f.) E and negligible internal resistance connected to four resistors R1, R2, R3 and R4, each of resistance R. The current in R3 is 0.30 A and the potential difference across R4 is 2.4 V. (i) Show that R is equal to 4.0 Ω. [2] (ii) Determine the e.m.f. E of the battery.