RI 2023 Y5 H2 Phy Promo Sect B

© Raffles Institution 9749 Name: ( ) CT Group: 24S0 RAFFLES INSTITUTION 2023 YEAR 5 PROMOTIONAL EXAMINATION 2 October 2023 H2 PHYSICS RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES Section B INSTRUCTIONS TO CANDIDATES Write your name, index number and CT Group. Write your answers to Section B in the spaces provided on the question paper. You are advised to write all your workings and answers clearly. Marks may be deducted for unclear workings. For Examiner’s Use Section A MCQ / 15 Section B 1 / 10 2 / 10 3 / 10 4 / 8 5 / 12 Section C 6 / 15 7 / 15 Deductions Total / 95 This document consists of 14 printed pages.

2 © Raffles Institution 9749 [Turn over Section B (50 marks) 1 A ball is kicked with an initial velocity u at an angle of 32.0° from the ground towards a vertical wall. The ball hits the top of the wall after a time of 1.40 s. The path of the ball, assuming negligible air resistance, is shown in Fig. 1.1. The horizontal distance between the initial position of the ball and the base of the wall is 20.0 m. Fig. 1.1 (not to scale) (a) Calculate the horizontal component of u. horizontal component of u = 1m s− [1] (b) Calculate the vertical component of u. vertical component of u = 1m s− [1] (c) Calculate the time for the ball to reach its maximum height above the ground. time = s [2] u 20.0 m path of ball wall ground ball

3 © Raffles Institution 9749 [Turn over (d) (i) The ball is kicked at time 0 st = . On Fig. 1 .2, sketch the variation with time t of the vertical component v y of the velocity of the ball until it hits the wall at 1.40 st = . Include in your sketch, the values of the initial vertical velocity, the time at maximum height and the final vertical velocity of the ball when it hits the top of the wall. Take direction upwards as positive. Fig. 1.2 [2] (ii) Explain how the graph in Fig. 1.2 may be used to determine the height of the wall. [1] (e) In practice, air resistance is not negligible. Describe qualitatively the effect, if any, of air resistance on the component of the velocity of the ball in (i) the horizontal direction, [1] (ii) the vertical direction. [2] vy / t / s 0 1.40 0

4 © Raffles Institution 9749 [Turn over 2 (a) A circular track is fixed horizontally on a smooth table. A spring, fixed at one end to a stand, is used to project a small ball along the frictionless track. Fig. 2.1. shows the top view of the setup. The spring is compressed and the ball is placed next to it. When the spring is released, the ball goes round the track in a horizontal circle with uniform speed. Fig. 2.1 (top view) Explain how the kinetic energy of the ball can remain constant while a resultant force acts on the ball as it goes round the track. [2] (b) The circular track is now placed upright such that it forms a vertical circle of diameter 0.60 m. Point P is at the top of the track. Fig. 2.2 shows the front view of the setup. The spring of force constant 180 N m− is compressed again and the ball of mass 45 g is placed next to it. The spring is then released and the ball is projected horizontally onto the track. Fig. 2.2 (front view) stand ball table surface 0.60 m P stand ball tabletop

5 © Raffles Institution 9749 [Turn over (i) 1. Determine the minimum speed of the ball at point P such that it just completes the vertical circle without falling off the track. Explain your working. speed = 1m s− [3] 2. Calculate the initial compression of the spring for the ball to have the minimum speed at point P as determined in (b)(i)1. compression = m [2] (ii) If the ball is replaced with one of a greater mass, state and explain how this will affect your answers 1. in (b)(i)1., [1] 2. in (b)(i)2. [1]

6 © Raffles Institution 9749 [Turn over (iii) The initial compression of the spring is reduced and the ball leaves the track at point Q as shown in Fig. 2.3. On Fig. 2.3, draw the path of the ball after it leaves the track at point Q. Fig. 2.3 (front view) [1] 0.60 m P stand ball tabletop Q

7 © Raffles Institution 9749 [Turn over 3 (a) A satellite of mass m orbits the Earth of mass M in a circular path as shown in Fig 3.1. The Earth and the satellite may be considered to be point masses with their masses concentrated at their centres. The satellite has speed v and the radius of its orbit about the Earth is r. Fig. 3.1 (i) Show that the potential energy Ep and kinetic energy Ek of the satellite are related by the expression pk 2EE= − . Explain your working. [2] satellite mass m Earth mass M v r

8 © Raffles Institution 9749 [Turn over (ii) The radius of the Earth is RE. The kinetic energy of the satellite at E4rR= is E. On Fig. 3.2, sketch the variation with orbital radius r, from ErR= to E4rR= , of the satellite’s 1. gravitational potential energy (label this graph Ep), 2. kinetic energy (label this graph Ek), 3. total energy (label this graph ET). Fig. 3.2 [3] RE 2RE 3RE 4RE 4E 2E −2E − 4E 6E − 6E − 8E −10E −12E energy 0 r 0

9 © Raffles Institution 9749 [Turn over (b) Launched on 24 November 1998 , the International Space Station (ISS) serves as a cutting-edge facility dedicated to fostering collaborative scientific research. It r evolves around the Earth in a circular orbit within the outermost layer of the Earth’s atmosphere, at a height of 408 km above the Earth’s surface. The Earth has radius RE of 66.37 10 m× and mass M of 245.98 10 kg× . (i) Determine, with appropriate c