TJC 2023 H2 Prelim Paper 2

TEMASEK JUNIOR COLLEGE 2023 JC2 Preliminary Examination Higher 2 NAME CG PHYSICS Paper 2 Structured Questions 9749/02 25 August 2023 2 hours For Examiner’s Use READ THESE INSTRUCTIONS FIRST 1 Write your name and civics group in the spaces at the top of this page. 2 Write in dark blue or black pen on both sides of the paper. 3 You may use an HB pencil for any diagrams or graphs. 4 Do not use staples, paper clips, glue or correction fluid. 5 The use of an approved scientific calculator is expected, where appropriate. 6 Answer all questions 7 8 s.f The number of marks is given in brackets [ ] at the end of each question or part question. Total This booklet consists of 21 printed pages

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 2 Data speed of light in free space c = 3.00 x 108 m s-1 permeability of free space o = 4 x 10-7 H m-1 permittivity of free space o = 8.85 x 10-12 F m-1 or (1/(36)) x 10-9 F m-1 elementary charge e = 1.60 x 10-19 C the Planck constant h = 6.63 x 10-34 Js unified atomic mass constant u = 1.66 x 10-27 kg rest mass of electron me = 9.11 x 10-31 kg rest mass of proton mp = 1.67 x 10-27 kg molar gas constant R = 8.31 J K-1 mol-1 the Avogadro constant NA = 6.02 x 1023 mol-1 the Boltzmann constant k = 1.38 x 10-23 J K-1 gravitational constant G = 6.67 x 10-11 N m2 kg-2 acceleration of free fall g = 9.81 m s-2 Formulae uniformly accelerated motion s = ut + ½ at2 v2 = u2 + 2as work done on/by a gas W = p ΔV hydrostatic pressure p = gh gravitational potential  = –Gm/r temperature T/K = T/oC + 273.15 pressure of an ideal gas p = 3 1 V Nm < c2 > mean translational kinetic energy of an ideal gas molecule E = 2 3 kT displacement of particle in s.h.m. x = xosint velocity of particle in s.h.m. v = vocost = )( 22 xxo −  electric current I = Anvq resistors in series R = R1 + R2 + .... resistors in parallel 1/R = 1/R1 + 1/R2 + .... electric potential V = rε4π Q o alternating current/voltage x = xo sint magnetic flux density due to a long straight wire B = 𝜇𝑜𝐼 2𝜋𝑑 magnetic flux density due to a flat circular coil B = 𝜇𝑜𝑁𝐼 2𝑟 magnetic flux density due to a long solenoid B = onI radioactive decay x = x0 exp(−t) decay constant λ = 𝑙𝑛2 𝑡1/2

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 3 [Turn over Answer all the questions in the spaces provided. 1 An experimental setup used to measure the acceleration of free fall is shown in Fig. 1.1. Fig. 1.1 The steel ball is suspended at the top by an electromagnet. The electronic timer starts when the electromagnet is turned off. As the steel ball falls by height h and goes through the light gate, the timer stops and displays the time of fall, t. Only one set of data was collected: h = (0.600 ± 0.001) m t = (354 ± 1) ms (a) Determine the acceleration of free fall with its associated uncertainty. acceleration =  m s-2 [3]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 4 (b) It was later found out that when the electromagnet was turned off, there is a constant delay before the steel ball starts falling. (i) Suggest a cause for this delay. [1] (ii) State and explain whether the type of error caused by this delay is random or systematic. [2] (iii) Suggest how this delay can be determined. [2] [Total: 8]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 5 [Turn over 2 In a nuclear reactor, a fast moving neutron with initial speed u1 makes a head-on elastic collision with a stationary nucleus of carbon-12. The speed of the neutron and the carbon nucleus after the collision are v1 and v2 respectively as shown in Fig. 2.1. (a) Explain what is meant by head-on and elastic. [2] (b) In an elastic collision, the relative speed of separation is equal to the relative speed of approach. Write an equation in terms of the velocities given to illustrate this fact. [1] (c) For the collision, determine the ratio of the speeds 1 1 v u of the neutron. ratio = [3] u1 v1 v2 Before collision After collision Fig 2.1 neutron carbon nucleus neutron carbon nucleus

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 6 (d) Hence determine the fraction of the kinetic energy of the neutron that is transferred to the carbon nucleus. fraction = [2] (e) If the head-on elastic collision is with a stationary neutron instead of carbon-12, explain how would the answers in part (c) and (d) be different. In your explanation, state the new ratio of the speeds and the new fraction of the kinetic energy transferred. [2] [Total: 10]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 7 [Turn over 3 (a) Define work done. [1] (b) A trolley of mass 400 g is moving at a constant speed of 2.5 m s –1 to the right as shown in Fig. 3.1. . A variable force F acts to the left on the trolley as it moves between points P and Q. The variation of F with displacement x from P is shown in Fig. 3.2. The trolley comes to rest at point Q. (i) Calculate the distance PQ. distance = m [2] Fig. 3.1 Fig. 3.2

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 8 (ii) On Fig. 3.3, sketch the variation with x of the work done on trolley by F. Indicate on your sketch the maximum value of the work done by F. (iii) In order to maintain a constant speed of 2.5 m s –1, an electric motor attached to the trolley is switched on. On Fig. 3.4, sketch the variation with x of the power supplied by motor while the trolley moves from point P to Q. No numerical value is required. [Total: 6] x / m work done by F / J 0 Fig. 3.3 power / W x / m 0 Fig. 3.4 [2] [1]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 9 [Turn over 4 (a) Use Newton’s laws of motion to explain why a body moving with uniform speed in a circle must experience a force towards the centre of the circle. [2] (b) A massless spring of force constant k = 78.4 N m-1 is fixed on the left side of a level track. A block of mass m = 0.50 kg is pressed against the spring and compresses it by a distance d as shown in Fig. 4.1. The block is then released from rest and travels toward a circular loop- the-loop of radius R = 1.5 m. Fig. 4.1 The entire track and the loop-the-loop are frictionless except for the section of track between points A and B. The friction between the block and the track along AB is 1.47 N and the length of AB is 2.5 m. (i) Calculate the minimum speed vmin at C such that the mass remains in contact at point C. vmin = m s-1 [2]

DO NOT WRITE IN THIS MARGIN DO NOT WRITE IN THIS MARGIN 10 (ii) Determine the minimum compression d of the spring that enables the block to just complete the vertical circle without falling off the track at C. compression = m [2]