2024 RI Prelim H1 Phy Paper 2 Questions

This document consists of 24 printed pages. © Raffles Institution 8867/02 [Turn over Centre Number Index Number Name Class S3016 RAFFLES INSTITUTION 2024 Preliminary Examination PHYSICS Higher 1 Paper 2 Structured Questions 8867/02 11 September 2024 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 in the spaces provided in this booklet. You may use 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 one question only. Circle the question that you had attempted. You are advised to spend one and half hours on Section A and half an hour on Section B. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use 1 / 8 2 / 9 3 / 5 4 / 8 5 / 5 6 / 8 7 / 9 8 / 8 Circle either number 9 or 10 / 20 Deduction Total / 80

2 © Raffles Institution 8867/02 [Turn over Data speed of light in free space c  8 13.00 10 m s  elementary charge e  191.60 10 C unified atomic mass constant u  271.66 10 kg rest mass of electron me  319.11 10 kg rest mass of proton mp  271.67 10 kg the Avogadro constant NA  23 16.02 10 mol  gravitational constant G  11 2 26.67 10 N m kg  acceleration of free fall g  29.81 m s Formulae uniformly accelerated motion s  21 2ut at 2v  2 2u as resistors in series R  1 2 R R   resistors in parallel 1/R  1 21 1 R R  

3 © Raffles Institution 8867/02 [Turn over Section A Answer ALL questions from this section. 1 A small ball at the bottom of a frictionless slope is projected up the slope with speed u, as shown in Fig. 1.1. The slope has a height of 4.0 m and makes an angle of 30 to the horizontal ground. Fig. 1.1 (a) In one instance, 17.0 m su  . (i) Calculate the maximum distance 0s from the bottom of the slope that the ball reaches. 0s = m [2] (ii) As the ball moves up the slope from the bottom, draw on Fig. 1.2 the variation with distance s travelled by the ball from the bottom of the slope of its 1. kinetic energy (label as EK), 2. potential energy (label as EP). Potential energy at the bottom of the slope is zero. [2] Fig. 1.2 s / m energy 0 0 30 4.0 m u ground ball

4 © Raffles Institution 8867/02 [Turn over (b) In another instance, 114.0 m su  . The ball travels to the top of the slope, leaves the slope and hits the ground. (i) Show that the speed of the ball at the top of the slope is 110.8 m s . [1] (ii) Calculate the horizontal distance travelled by the ball after it leaves the slope. distance = m [3] [Total: 8]

5 © Raffles Institution 8867/02 [Turn over 2 Two identical balls A and B approach each other along the same straight line on a smooth horizontal surface, as shown in Fig 2.1. Fig. 2.1 At time 0 st  , ball A moves towards ball B with a speed of 14.0 m s , while ball B moves towards ball A with a speed of 11.0 m s . Each ball has a mass of 0.50 kg. At time 0.50 st  , the balls undergo a head-on elastic collision and are in contact for a duration of 0.25 s. After the collision, ball A moves with velocity vA and ball B moves with velocity vB. (a) Explain whether both balls could be stationary at the same time during the collision. [2] (b) Show that vB is 14.0 m s . [2] A B

6 © Raffles Institution 8867/02 [Turn over (c) Calculate the magnitude of the average force on ball A during the collision. Explain your working. force = N [3] (d) Fig. 2.2 shows the variation with time t of the momentum pA of ball A and momentum pB of ball B before the collision. On Fig. 2.2, complete the graphs for pA and pB from 0.50 st  to 1.5 st  . Fig. 2.2 [2] [Total: 9] -3 -2 -1 0 1 2 3 momentum / N s t / s pA pB 0 1.0 0.5 1.5

7 © Raffles Institution 8867/02 [Turn over 3 A uniform circular disc of radius R and weight W is in contact with a smooth horizontal ground and the corner of a box of height 2 R , as shown in Fig. 3.1. A horizontal force F acts at the centre O of the disc to keep the disc in equilibrium. Fig. 3.1 (a) Force F is increased until the disc is just about to rotate about the corner of the box. Use the principle of moments to determine the ratio F W . Explain your working. F W = [3] (b) The box is replaced with one of height R. State and explain how the force F acting at the centre O would need to be changed for the disc to rotate about the corner of the box. [2] [Total: 5] F O R box ground disc

8 © Raffles Institution 8867/02 [Turn over 4 A ball of mass m is attached to one end of a light inextensible string of length L. The other end of the string is attached to a fixed point O. (a) The ball is swung around in a vertical circle, as shown in Fig. 4.1. The speeds of the ball at the top and bottom of the vertical circle are vT and vB respectively. Fig. 4.1 (i) Show that for the ball to just complete the vertical circle, Tv gL . Explain your working. [2] (ii) Explain why the ratio B T v v must be greater than 1 for the ball to complete the vertical circle. [1] O vT vB L ball string

9 © Raffles Institution 8867/02 [Turn over (iii) A student wishes to swing the ball in a vertical circle such that B T 3v v  . With appropriate calculations, state and explain if this ratio is achievable. [3] (b) The ball is now swung in a horizontal circle around the fixed point O, as shown in Fig. 4.2. When the ball is swinging around with angular velocity  , the string is at an angle  from the vertical and the tension in the string is T. Fig. 4.2 Determine the tension in the string, in terms of T, when the angular velocity of the ball is doubled. tension = [2] [Total: 8] O ball string

10 © Raffles Institution 8867/02 [Turn over 5 (a) State Newton’s law of gravitation. [1] (b) A satellite is launched from the surface of the Earth so that it orbits about the centre of the Earth. The height of the orbit from the surface of the Earth is 72.1 10 m . (i) Show that the speed v of the satellite in its orbit is given by the expression EGMv r where ME is the mass of the Earth and r is the radius of orbit. Explain your working. [2] (ii) When the satellite of mass 1600 kg reaches the height of its orbit, the increase in gravitational potential energy is 7.67  1010 J. The Earth has a radius of 6400 km and a mass of 24 6.0 10 kg . Calculate the energy required to launch the satellite into orbit. Neglect the effects of the rotation of the Earth. energy = J [2] [Total: 5]