2021 RI Prelims H2 Phy Paper 2 QP

© Raffles Institution [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2021 Preliminary Examination PHYSICS Higher 2 Paper 2 Structured Questions 9749/02 September 2021 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your index number, name and class in the spaces 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. 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 1 / 9 2 / 8 3 / 8 4 / 10 5 / 8 6 / 9 7 / 8 8 / 20 Deduction Total / 80 This document consists of 22 printed pages.

2 © Raffles Institution Data speed of light in free space c  3.00 × 108 m s1 permeability of free space 0  4   107 H m1 permittivity of free space 0  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 × 10 23 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  21 2ut at 2v  2 2ua s work done on/by a gas W  p V hydrostatic pressure p  ρgh gravitational potential   Gm r temperature T/K  / C 273.15T  pressure of an ideal gas p  21 3 Nm cV mean translational kinetic energy of an ideal gas molecule E  3 2 kT   displacement of particle in s.h.m. x  0 sinx t velocity of particle in s.h.m. v  0 cosvt  22 0x x  electric current I  Anvq resistors in series R  12 ...RR resistors in parallel 1/ R  121 1 ...RR electric potential V  4 Q r alternating current/voltage x  0 sinx t magnetic flux density due to a long straight wire B  0 2 d   I magnetic flux density due to a flat circular coil B  0 2 N r  I magnetic flux density due to a long solenoid B  0n I radioactive decay x  0 expx t decay constant   1 2 ln2 t

3 © Raffles Institution [Turn over Answer all the questions in the spaces provided. 1 (a) Fig 1.1 shows two frictionless trolleys A and B of mass mA and mB moving horizontally towards a wall with the same speed u. The trolleys are not in contact. Fig. 1.1 Upon collision with the wall, trolley A rebounds with speed u and collides elastically with trolley B. (i) State the principle of conservation of momentum. [2] (ii) Taking motion to the right as positive, show that the speed of trolley B, Bv after the collision with trolley A is given by the expression 3 AB B AB mmvu mm   . [3] trolley A trolley B wall u u

4 © Raffles Institution (b) A student performs a similar experiment with a basketball of mass 0.62 kg and a tennis ball of mass 0.059 kg. The student pl aces the tennis ball slightly above the basketball and releases both at the same time from a height above the ground, as shown in Fig. 1.2. Just before the basketball touches the ground, both the basketball and the tennis ball have the same speed of 4.4 m s 1. The basketball bounces off the ground with a speed of 4.4 m s1. Its subsequent impact with the tennis ball causes the tennis ball to move up at a very large speed. (i) Using the expression in (a)(ii), determine the speed of the tennis ball after its collision with the basketball. speed = m s 1 [1] (ii) Besides the assumptions that all collis ions are elastic and air resistance is negligible, state one other assumption that is necessary in order to use the result in (a)(ii) to determine the speed for (b)(i). [1] (iii) The student repeats the experiment, replac ing the tennis ball with another ball of much smaller mass. Deduce the maximum speed the ball can have after its collision with the basketball. maximum speed = m s 1 [2] tennis ball basketball ground Fig. 1.2

5 © Raffles Institution [Turn over 2 Fig. 2.1 shows an airplane of mass 1.5  105 kg, flying horizontally at a constant velocity. The airplane has four engines, two located on each wing, which produce a combined forward thrust of 8.0  105 N. The other forces acting on the airplane are drag force, the combined lift of both wings and its weight. The horizontal separation of the lines of action of lift and weight is 0.75 m. (a) Define the moment of a force about a point. [1] (b) Determine the vertical separation of the lines of action of thrust and drag. vertical separation = m [3] (c) The airplane starts to accelerate forward. Using Newton’s First Law of Motion, state and explain the direction of the fr ictional force acting on a box that is placed on the airplane floor. [2] 0.75 m thrust weight drag lift engine wing rudder Fig. 2.1 engine

6 © Raffles Institution (d) The engines of the airplane are located 10 m and 20 m perpendicularly from the midline of the airplane’s body. In a training session, both engines on the right wing are shut down, leaving only the two engines on the left wing working. Each of these engines produce a forward thrust of 2.0  105 N. As a result, the airplane rotates in the horizontal plane. To counter this rotation, the rudder at the tail of the aircraft can be adjusted. Fig. 2.2 shows the adjustment of the rudder to an angle such that a force P acts on the rudder at a point 30 m from centre of gravity C.G. along the midline of the airplane. P acts at an angle of 60 to the midline and is due to the airflow incident on the rudder. Calculate the value for P that will prevent the aircraft from rotating. P = N [2] C.G. Fig 2.2 P 2.0  10 5 N 10 m 20 m rudder 60 30 m 2.0  10 5 N engines midline

7 © Raffles Institution [Turn over 3 Fig. 3.1 shows a wind turbine with a diameter of 100 m. Wind of density 1.2 kg m3 is incident normally on the blades of the turbine at a speed of 20 m s1. (a) Calculate the volume of air that passes through the area swept out by the turbine blades in one second. volume = m 3 [2] (b) Hence, calculate the mass of air that passes through the area swept out by the turbine blades in one second. mass = kg [1] 20 m s1 Fig. 3.1 100 m

8 © Raffles Institution (c) After passing through the blades, the wind speed decreases to 15 m s1. (i) Determine the rate of loss of kinetic energy of the wind. rate of loss of kinetic energy = W [2] (ii) Using Newton’s second law, determine the force exerted by the turbine blades on the wind. force = N [2] (d) Explain how the answers obtained in (c)(i) and (c)(ii) are related by the equation P = Fv. [1]

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