2021 RI Promo Sect C QP

© Raffles Institution 9749   Name: ( ) CT Group: 22S0 RAFFLES INSTITUTION 2021 YEAR 5 PROMOTIONAL EXAMINATION 30 September 2021 H2 PHYSICS RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFL ES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES INSTITUTION RAFFLES Section C INSTRUCTIONS TO CANDIDATES Write your name, index number and CT Group. Write your answers to Section C in the spaces provided on the question paper. For Examiner’s Use Section C 6 / 15 7 / 15 This document consists of 10 printed pages.

2 © Raffles Institution 9749 [Turn over     Section C (30 marks) 6 (a) (i) Define gravitational potential at a point. [1] (ii) Explain why gravitational potential in a gravitational field is negative. [2] (b) The variation with distance r of the gravitational potential  from the centre of a planet is shown in Fig. 6.1. Fig. 6.1 r / 108 m / 108 J kg–1 -10.0 -8.0 -6.0 -4.0 -2.0 0.0 0.0 2.0 4.0 6.0 8.0 10.0 12.0

3 © Raffles Institution 9749 [Turn over     (i) Using Fig. 6.1, show that the mass of the planet is 271.9 10 kg . [1] (ii) Fig. 6.2 shows the planet and two points, X and Y, in its gravitational field. Points X and Y are 88.0 10 m and 82.0 10 m from the centre of the planet respectively. Fig. 6.2 1. Determine the orbital speed of an object that is orbiting the planet with a radius of 82.0 10 m . Explain your working. orbital speed = 1m s [3] X Y planet

4 © Raffles Institution 9749 [Turn over     2. As a space stone approaches the planet, it passes through point X with a speed of 413.5 10 m s  and continues to pass through point Y. The direction in which the space stone passes through point Y is parallel to a tangent to the planet’s surface as shown in Fig. 6.3. Fig. 6.3 Explain why the space stone will not move in a circular orbit around the planet when it reaches point Y. Support your explanation with appropriate calculations and with reference to your answer in (b)(ii)1. [4] X Y path of space stone planet

5 © Raffles Institution 9749 [Turn over     3. If the mass of the space stone is 51.5 10 kg , calculate the total energy of the space stone. total energy = J [2] 4. Deduce if the space stone will escape the gravitational field of the planet after it passes through point Y. State your reason. [2]

6 © Raffles Institution 9749 [Turn over     7 A hyperloop is a potential super speed transportation system that consists of a system of tubes with vacuum interiors that makes it very ener gy efficient. People can travel in a hovering pod inside these vacuum tubes at speeds close to the speed of sound in air. Fig. 7.1 shows what a hovering pod in a hyperloop may look like. A proposed route runs from Los Angeles to S an Francisco Bay. It takes about half an hour to cover this 500 km route. This is considerably shorter than current rail or air times. Fi g. 7.1 Groups of engineers from different compani es have conceptualised the idea and worked on prototypes of the hyperloops. The first stage of testing is to use computer simulations and compare it with experiments to see whether ther e are differences in the theoretical and actual results. (a) In one computer simulation, the pod in the hyperloop starts from rest, accelerates uniformly before travelling at a constant speed, then finally decelerates uniformly to rest. Theoretical values of the distance s travelled by the pod at various times t are obtained. Fig. 7.2 shows the values of s for part of the journey from 0.0 mint  to 3.0 mint  . t / min s / m t / min s / m 0.0 0.000 1.6 13 310 0.2 209 1.8 16 440 0.4 835 2.0 19 570 0.6 1 879 2.2 22 700 0.8 3 341 2.4 25 830 1.0 5 220 2.6 28 960 1.2 7 517 2.8 32 090 1.4 10 230 3.0 35 220 Fig. 7.2 (i) Using kinematics equation(s) and relevant data from Fig. 7.2, show that the acceleration of the pod during the initial part of the journey is 22.9 m s . [1]

7 © Raffles Institution 9749 [Turn over     (ii) Estimate the time taken for the pod to accelerate to its constant speed. Explain your working. time taken = min [3] (iii) The technology of the hyperloop can actual ly accelerate the pod at accelerations much greater than 22.9 m s . Suggest a reason for not doing so despite potentially saving transport time. [1] (b) The engineers also studied the motion of objects that are dropped in the pod while it travels in the hyperloop. This study serves to inform them whether the high speed at which the pod travels may cause potential danger to passengers when objects are dropped in front of or behind them. Fig. 7.3 shows a pod within a hyperloop tube travelling to the right at constant speed when a passenger in the pod releases a box from rest. Fig. 7.4 shows the pod and passenger a while later when the box hits the floor of the pod. direction of motion box Fig. 7.3 Fig. 7.4 hyperloop tube pod

8 © Raffles Institution 9749 [Turn over     (i) 1. On Fig. 7.4, draw the position of the box when it hits the floor of the pod. [1] 2. Draw the path of the box from the moment the box is released in Fig. 7.3 to the moment the box hits the floor in Fig. 7.4, as seen by an observer outside the pod. [1] (ii) The pod now decelerates uniformly. The passenger repeats the experiment again by releasing the box just before the pod starts to decelerate and observes the motion of the box until it hits the floor. Describe the motion of the box as obs erved by the passenger in the pod and compare the position of the box where it hits the floor with the position you have drawn in (b)(i)1. [2] (c) (i) In an experiment, a scaled-down prototype of the hyperloop is made with a straight tube that contains air. The engineers used this to study the effects of resistive forces on the motion of the pod travelling in such a hyperloop. The known specifications of the prototype are such that the variation with the pod’s speed v of the total resistive force F R experienced by the pod is