(VJC) 2024 H2 Prelim P2

VICTORIA JUNIOR COLLEGE 2024 JC2 PRELIMINARY EXAMINATION Higher 2 Name : __________________________ CT group : ________________ PHYSICS Paper 2 Structured Questions Candidates answer on the Question Paper. No Additional Materials are required. 9749/02 11 September 2024 WEDNESDAY 8 am to 10 am (2 hours) READ THESE INSTRUCTIONS FIRST Write your name and Civics Group in the spaces provided at the top of this page. 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. DO NOT WRITE ON ANY BARCODES. The use of an approved scientific calculator is expected, where appropriate. Answer all questions. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s use Question Mark 1 2 3 4 5 6 7 g Units s.f. Total / 80 This document consists of 28 printed pages

2 Data speed of light in free space c = 3.00 × 108 m s-1 permeability of free space µo = 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 mol-1 K-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 Formulae uniformly accelerated motion s = ut + (½) at2 v2 = u2 + 2as work done on/by a gas W = pV hydrostatic pressure p = gh gravitational potential GM r =− temperature o/ K / C 273.15TT =+ pressure of an ideal gas 21 3 Nmpc V= mean translational kinetic energy of an ideal gas molecule 3 2E kT= displacement of particle in s.h.m. x = xo sin  t velocity of particle in s.h.m. 0 cos tvv = 22 0x x=  − electric current I = Anvq resistors in series R = R1 + R2 + … resistors in parallel 1/R = 1/R1 + 1/R2+ … electric potential 04 QV r= alternating current/voltage x = xo sin  t Magnetic flux density due to a long straight wire 0 2B d I = Magnetic flux density due to a flat circular coil 0 2 NIB r = Magnetic flux density due to a long solenoid 0B nI= radioactive decay x = xoexp(-t) decay constant 1/2 ln2 t =

4 Answer all the questions in the spaces provided. 1(a) Define the terms moment of a force and torque of a couple . For each of the terms, draw a labelled sketch to illustrate the meaning of the terms. [4] Moment of a force: ………………………………………………………………………………………………… ………………………………………………………………………………………………… Torque of a couple: ………………………………………………………………………………………………… …………………………………………………………………………………………………

5 (b) A 1500 kg truck is positioned on an incline that makes an angle of 4 0° with the horizontal, as shown in Fig. 1.1. The truck is held in place by a frictionless and massless pulley system connected to a counterweight of mass m. The smaller pulley at the top of the incline has a radius r, and the larger pulley has a radius of 3r. The two pulleys at the top are attached together so that they turn together as one. The incline is frictionless. (i) On Fig. 1.2, label all the forces exerted on the truck and the pulley attached to the back of the truck clearly. You do not need to include the internal forces acting between the pulley and the truck. [2] Fig. 1.1 3r 1500 kg truck Fig. 1.2 r  = 40°

6 (ii) Determine the mass m of the counterweight needed to balance the 1500 kg truck on the incline. [4] Mass m = …………………………

7 2 Fig. 2.1 shows an object at rest at the top of a straight slope which makes a fixed angle with the horizontal at a distance h above the ground. The object is released and slides down the slope from A to B with negligible friction. Assume that the potential energy is zero at B. (a) Sketch a graph in Fig 2.2 below, showing: The variation of potential energy along the slope. Label this as P. The variation of kinetic energy of the object along the slope. Label this as K. [2] (b) Sketch another graph in Fig 2.2, showing the variation of kinetic energy along the slope when there is a constant frictional force between the object and the surface. Label this F. Explain your graph. [3] ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Energy/ J h / m Fig. 2.2 Fig. 2.1 h

8 3 The kinetic theory of gases deals with how molecular movement causes pressure to be exerted by a gas. The pressure of a gas is due to the elastic collision of the gas molecules with the walls of a container. A single molecule of mass m is travelling with speed u directly towards a wall of a cubical box of sides L is as shown in Fig 3.1. (a) Express the following in terms of L, m and u. Momentum to the right before collision with wall = mu Momentum immediately after an elastic collision = …………… Time between collisions with the same wall = …………… Number of collisions with this wall per unit time = …………… Rate of change of momentum of the molecule = …………… Average force on the wall due to the molecule = …………… [5] (b) The pressure p of an ideal gas which contains N molecules with different speeds in a container of volume V is given by 21pV = Nm < c3 where <c2> is the mean square speed of the molecules. (i) State the assumption regarding the type of collision between gas molecules. [1] ………………………………………………………………………………………………… L u Fig 3.1

9 (ii) The deduction of the relationship stated in (a) does not involve collisions between the gas molecules. In practice, gas molecules will collide with one another. Using your answer in (b)(i), explain why the collision among the molecules do not have an impact on the pressure. [2] ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… (c) Using the expression in (b) and the ideal gas equation, show that the average kinetic energy of an ideal gas molecule is proportional to the thermodynamic temperature T. [2]

10 (d) The first law of thermodynamics when applied to an ideal gas can be expressed as ΔU = Q + W where ΔU is the increase in internal energy, Q is the heat supplied to the gas and W is work done on the gas. (i) The gas undergoes a process from state A to state B in such a way that ΔU is 0 as shown in Fig 3.2. 1. Shade in Fig 3.2 the area that numerically represents the heat exchange between the gas and its surroundings. [1] 2. State and explain the difference in the product of pressure and volume of the gas at both state A and state B. [2] ………………………………………………………………………………………………… ………………………………………………………………………………………………… ………………………………………………………………………………………………… Pressure Volume B A Fig 3.2