NJC H2 Physics Prelim P3 Ans

[Turn over NATIONAL JUNIOR COLLEGE SENIOR HIGH 2 PRELIMINARY EXAM Higher 2 CANDIDATE NAME SUBJECT CLASS REGISTRATION NUMBER PHYSICS Paper 3 Longer Structured Questions Candidate answers on the Question Paper. No Additional Materials are required. 9749/03 25 Aug 2023 2 hours READ THESE INSTRUCTION FIRST Write your subject class, registration number and name on all the work you hand in. Write in dark blue or black pen on both sides of the paper. You may use a 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. Section A Answers all questions. Section B Answer one question only. You are advised to spend one and a half hours on Section A and half an hour on Section B. At the end of the examination, fasten all your work securely together. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use Section A 1 / 7 2 / 10 3 / 9 4 / 10 5 / 8 6 / 6 7 / 10 Section B 8 / 20 9 / 20 Total (80m) This document contains 28 printed pages and 0 blank pages.

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4 Section A 1 A bungee jumper of mass 60 kg is attached to an elastic rope which starts to stretch after a short time of free fall. The gravitational potential energy of the bungee jumper is 0 J when she has fallen through 40 m to the lowest point. (a) gravitational potential energy / kJ elastic potential energy / kJ kinetic energy / kJ top 0 0 half-way 2.6 bottom 0 Fig. 1.1 Fill up the missing energies at the top, bottom and half-way positions in Fig 1.1. Drag forces can be considered negligible. [2] gravitational potential energy / kJ elastic potential energy / kJ kinetic energy / kJ top 24 (23.5) 0 0 half-way 12 (11.8) 2.6 9.2 (9.17) (accept 9.4) bottom 0 24 (23.5) 0 Fig. 1.1 Fill up the missing energies at the top, bottom and half-way positions in Fig 1.1. Drag forces can be considered negligible. [2] GPE (using mgh) [B1], EPE and KE at half -way and bottom positions (using conservation of energy) [B1] Comments: Most students are able to answer this part. Some students seemed to forget that the total energy is the same regardless of the position. (b) Show that the unstretched length of the elastic rope is 10 m. [2]

5 [Turn over Let the spring constant of the elastic rope be k and unstretched length be x At half-way position, 2.6 = 1 2 𝑘(20 − 𝑥)2 At bottom position, 23.5 = 1 2 𝑘(40 − 𝑥)2 [B1 for equations] 2.6 23.5 = (20−𝑥)2 (40−𝑥)2 [M1] √ 2.6 23.5 = 20−𝑥 40−𝑥 𝑥 = 10 𝑚 [A0] Comments: Many students are not able to form up the 2 equations. (c) Determine at what extension will the kinetic energy of the bungee jumper be the highest. extension = m [3] Initially, when the bungee jumper jumps, her weight is greater than the tension in the elastic rope. When the tension increases until it is equal to the weight, she stops accelerating and reaches her highest velocity and kinetic energy. 𝑚𝑔 = 𝑘𝑒 where e is the extension when her speed is the highest [B1] 1 2 𝑘𝑥2 = 1 2 𝑘(30)2 = 23500 𝑘 = 52.2 [C1] 𝑒 = 60×9.81 52.2 = 11.3 𝑚 [A1] Comments: Most students are unable to identify the location of max velocity as the location where there is no resultant force. [Total: 7] 2 Fig. 2.1 shows a small conducting sphere suspended from a long insulating thread between two metal plates M and M' that are 0.0500 m apart. The plates are connected to a  35.0 10 V battery. The sphere has a radius of 0.0025 m and a mass of 1.0 g.

6 Fig. 2.1 The sphere is given an initial displacement such that the sphere touches M. It then moves rapidly to M', touches it, and returns rapidly to M again. This process repeats itself. (a) State and explain why an initial displacement to touch one of the plates is necessary for the process to start. …………………………………………………………………………………………. …………………………………………………………………………………………. ………………………………………………………………………………………….. [2] When sphere is at the centre, the attractive force between sphere and M and Sphere and M’ is equal and opposite. There is translational equilibrium. The sphere does not have a resultant acceleration to move to M or M’ [B1] A displacement to M will result in sphere being positively charged, repelling M and attracted toward M’ thus resulting in an acceleration towards M. This velocity will keep increasing as sphere move towards M. Constant electric Force/Field = constant acceleration [B1] Comments: Most students did not explain why without d isplacement, the oscillation cannot occur, and why with touching one of the plates, the oscillations occurs. (b) When the sphere touches either plate, it acquires a potential that is equal to the potential difference between the plates. The electrical potential on the surface of a charged conducting sphere can be determined by assuming that all its charges are accumulated at the centre of the sphere. Show that the charge on the sphere when it touches M is 50 o . [1] support M M' long insulating thread 0.0500 m

7 [Turn over    = = = 3 4 5.0 10 4 (0.0025) 50 (proved) o o o QV r Q Q Comments: Most students are able to prove this part. (c) If the electric field between the plates is uniform, calculate the magnitude of the electrostatic force acting on the sphere. force = N [1] ( ) −− = = =   =  3 12 4 5.0 1050 8.85 10 1.39 10 N0.0500 VF QE Q d Comments: Most students are able to answer this part. (d) As a long thread is used, the motion of the sphere is nearly horizontal and is due to electrostatic force only. Determine the time taken for the sphere to move from M to M'. time taken = s [3]

8 − −− − = = =  =+ − =  = 4 12 2 12 1.39 10 1.39 10 ms0.0010 1 2 10.0500 0.0050 (1.39 10 )2 0.805 s Fa m s ut at t t Comments: Most students did not take into account the dimension of the moving sphere and its effect on the total displacement possible. (e) When the battery is removed from Fig. 2.1, the plates remain equally but oppositely charged. The sphere is totally discharged and given an initial displacement to enable it to reach one of the plates. State and explain how the time taken to move from one plate to the other will change. …………………………………………………………………………………………………………….. …………………………………………………………………………………………………………….. …………………………………………………………………………………………………………….. …………………………………………………………………………………………………………….. ………………………………………………………………………………………………………… [3] • The electric field or potential difference between the plates decreases with each impact. OR Charge on each plate reduces with each impact. OR The amount of charge deposited on the sphere decreases with each impact. • The electrostatic force acting on the sphere decreases with each impact. • The time taken increases. Comments: Many students did not realise what is happening and there is a transfer of electrons. Some students talk about Gravitational force which is always equal to tension and does not affect the oscillations – student did not appreciate the reason why the string is long. [Total: 10] 3 (a) A student wanted to light a lamp, but only had available a 12 V battery of negligible internal resistance. In order to red