2013 NYJC H2 Physics P3 Answer

© NYJC 2013 JC2/Prelim/H2/9646/03 [Turn over Candidate Name Class Tutor Name PHYSICS 9646/03 Paper 3 Longer Structured Questions 18 September 2013 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, class and tutor name on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Section A Answer all questions. Section B Answer any two questions. 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. This document consists of 26 printed pages Nanyang Junior College NANYANG JUNIOR COLLEGE Science Department JC 2 PRELIMINARY EXAMINATION Higher 2 For examiner’s use Section A 1 2 3 4 5 Section B 6 7 8 Total

NYJC JC2/Prelim/H2/9646/03 2 Data speed of light in free space, c = 3.00 × 108 m s–1 permeability of free space, μ0 = 4π × 10–7 H m–1 permittivity of free space, ε0 = 8.85 × 10–12 Fm–1 (1 / (36π)) × 10–9 Fm–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 Formulae uniformly accelerated motion, s = ut + ½at2 v2 = u2 + 2as work done on/by a gas, W = pΔV hydrostatic pressure, p = ρgh gravitational potential,  = –Gm / r displacement of particle in s.h.m. x = x0 sin ωt velocity of particle in s.h.m. v = v0 cos ωt   22 oxx mean kinetic energy of a molecule of an ideal gas E = 3 2 kT resistors in series, R = R1 + R2 + … resistors in parallel, 1/R = 1/R1 + 1/R2 + … electric potential, V = Q / 4πε0r alternating current/voltage, x = x0 sin ωt transmission coefficient, T  exp(–2kd) where k = 12 0.693 t   2 2 8 m U E h   radioactive decay, x = x0 exp (–λt) decay constant λ = 21 693.0 t

3 © NYJC 2013 JC2/Prelim/H2/9646/03 [Turn over For Examiner’s Use Section A Answer all the questions in this section. 1 Three similarly sized balls A, B, and C, of masses 0.40 kg, 0.20 kg, and 0.10 kg respectively, are connected by strings such that their centre -to-centre distances are as shown in Fig. 1.1 below. The setup is swung in a horizontal circle on a frictionless table about O. The balls and strings maintain a straight line, with the outermost ball having a speed of 6.0 m s–1. Fig. 1.1: Top View Calculate (a) the angular velocity ω of C. ω = .............................. rad s–1 [1] (b) the tangential speed of ball B. tangential speed = .............................. m s–1 [2] (c) the tensions in (i) string BC and tension in BC = .............................. N [2] ω O A B C 1.5 m 1.0 m 0.5 m rad s-1 [B1] Since the balls and strings maintain a straight line, the angular velocity of ball B must be the same as that of ball C. [C1] ( ) m s-1 [B1] Considering the free body of ball C, TBC provides for the centripetal force for circular motion of C ( )( ) ( ) [M1: correct substitution] N [A1] Examiner’s Comments Common mistakes included the substitution of incorrect mass or radius of circular motion. Some candidates failed to interpret that the circular motion was on a horizontal table and hence the weight of the balls will not have any effect on the centripetal a cceleration. Weaker candidates were not able to establish a correct relationship between the forces acting on C and the centripetal acceleration of C.

4 © NYJC 2013 JC2/Prelim/H2/9646/03 For Examiner’s Use (ii) string AB. tension in AB = .............................. N [3] 2 (a) State the First Law of Thermodynamics. …………………………………………………………………………………………………… …………………………………………………………………………………………………. [1] (b) The variation with volume of pressure in the internal combustion engine of a car at maximum power output is shown in Fig. 2.1. The engine goes through 4 distinct stages A to D as shown. Fig. 2.1 Complete the rest of the table below to show how the First Law of Thermodynamics applies to the gas in the engine between each of the stages. [3] Process ΔU / J Q / J W / J A→B –1640 0 –1640 B→C –720 –720 0 C→D 760 0 760 D→A 1600 1600 0 Considering the free body of ball B, TAB - TBC provides for the centripetal force for circular motion of B [M1] ( )( ) ( ) [M1: for correct substitution] N [A1] Examiner’s Comments An appropriate free-body needs to be considered and the relationship between the forces and the centripetal acceleration needs to be clearly presented. In some scripts, the presentation of the answers seems to suggest that the candidates were adding/ subtracting 2 centripetal (resultant) forces instead. [The First Law of Thermodynamics states that] the increase/change in the internal energy of a system is the sum of the work done on the system and the heat supplied to the system. Underlined concepts must be mentioned. Bolded words should not be confused, e.g. “internal energy” vs “increase in internal energy”, “work done on” vs “work done by”, “heat supplied to” vs “heat supplied by”. Students must demonstrate understanding of: ΔU = Q + W [1] ΣΔU = 0 [1] WBC, WDA = 0 [1]

5 © NYJC 2013 JC2/Prelim/H2/9646/03 [Turn over For Examiner’s Use (c) (i) Calculate the net work done by the gas per cycle when the engine goes through stages A to D. work done = .............................. J [1] (ii) The car, travelling at a velocity of 30 m s–1 on a level road, experiences a total resistive force of 1.0 kN. The engine operates at a rate of 50 cycles per second. 1. Calculate the rate of net work done by the engine. rate of work done = .............................. W [1] 2. Calculate the coefficient P, given by seful power delivered to car ate of net work done by engine coefficient P = .............................. [2] 3 (a) (i) Explain what is meant by a longitudinal wave. ……………………………………………………………………………………………… ……………………………………………………………………………………………… …………………………………………………………………………………………... [1] Work done on gas = (–1640 + 760) J = –880 J Work done by gas = 880 J Must demonstrate understanding of difference between work done on gas and work done by gas, in their use of numbers or in written explanation. Common misconceptions include taking absolute of W.D., or just removing the sign without explanation. Work done by gas per second = 880×50 = 44 kJ Therefore rate of net work done = 44 kW = 4.4 × 104 W [1] Engine power = 44 kW at 30 m s–1, useful power (to overcome friction) = Fv = 1000×30 = 30 kW [1] P = 30/44 = 0.68 (accept 3 s.f.: 0.682) [1] e.c.f. allowed if value of coefficient is reasonable, i.e. <=1 and positive. The direction of propagation of the wave is parallel to the direction of vibration of the particles. [1]

6 © NYJC 2013 JC2/Prelim/H2/9646/03 For Examiner’s Use (ii) With the aid of a diagram, explain the formation of compression and rarefraction points along a longitudinal wave. …………………………………………………………………………………………………… …………………………………………………………………………………………………… ……………………….………………………………………………………………………… [2] (b) A constant-frequency siren vibrates with displacement y, where y = A sin 200t. This sound causes vibrations of the diaphragm of an ear drum in an observer 500 m away. The speed of sound is 335 m