SRJC H2 PHY P2 SOLUTION

SRJC 2011 9646/Prelim/2011 SERANGOON JUNIOR COLLEGE General Certificate of Education Advanced Level Higher 2 PHYSICS 9646 Preliminary Examination 18 August 2011 Paper 2 Structured Questions 1 hour 45 minutes Candidates answer on the Question Paper. No additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your name, civics group and index number in the spaces at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use a soft pencil for any diagrams, graphs or rough working. Do not use staples, paper clips, highlighters, glue or correction fluid. Answer all questions. At the end of the examination, fasten all your work securely together. The number of marks is given in bracket [ ] at the end of each question or part question. This document consist of 19 printed pages and 1 blank page For Examiner’s Use 1 2 3 4 5 6 7 8 9 10 Total NAME CG INDEX NO.

2 SRJC 2011 9646/Prelim/2011 [Turn Over For Examiner’s Use DATA AND FORMULAE Data speed of light in free space, c = 3.00  108 m s1 permeability of free space, 0 = 4   107 H m1 permittivity of free space, 0 = 8.85  1012 F m1 (1 / (36 ))  109 F m1 elementary charge, e = 1.60  1019 C the Planck constant, h = 6.63  1034 J s unified atomic mass constant, u = 1.66  1027 kg rest mass of electron, me = 9.11  1031 kg rest mass of proton, mp = 1.67  1027 kg molar gas constant, R = 8.31 J K 1 mol1 the Avogadro constant, NA = 6.02  1023 mol1 the Boltzmann constant, k = 1.38  1023 J K1 gravitational constant, G = 6.67  1011 N m2 kg2 acceleration of free fall, g = 9.81 m s 2 Formulae uniformly accelerated motion, s = ut + ½ at 2 v2 = u 2 + 2as work done on/by a gas, W = p V hydrostatic pressure, p = gh gravitational potential,  = – r Gm displacement of particle in s.h.m., x = x 0 sin t velocity of particle in s.h.m., v = v o cost v =  22 0 xxω  resistors in series, R = R 1 + R2 + … resistors in parallel, 1/ R = 1/R1 + 1/R2 + … electric potential, V = Q / 4or alternating current/voltage, x = x 0sin t transmission coefficient, T  exp(2kd) where k = 2 2 h E)m(U8 π radioactive decay, x = x0 exp(t) decay constant,  = 2 1 693.0 t

3 SRJC 2011 9646/Prelim/2011 [Turn Over For Examiner’s Use Answer all questions 1 A SRJC student who intends to major in Physics in university attempted to recall Bernoulli’s equation, widely used in the field of fluid dynamics. Based on his recollection during H3 lectures, he was able to come up with the following equation:   1 2 akp h ρg ρv where p is pressure, h is height,  is density, v is velocity and k is a constant. However, he was unable to recall the value of a. (a) Based on dimensional analysis (ie. comparison of units of terms in the equation), determine the value of a.   avp 21    a mskgmNm 132     aa skgmmkgms   322 [M1] aa skgmskgm   321 By comparing coefficients, a = 2 [A1] a = ........................ [2] (b) Under certain conditions , the equation reduces to  1 2 ak ρv . Calculate the percentage uncertainty in k, given the values of the quantities as listed below. = (1000 ± 2%) kg m-3 v = (20.0 ± 0.2) m s -1 2 21 vk  v v k k  2  [M1] 04.00.20 2.0202.0      Percentage uncertainty = 0.04 x 100% = 4% [A1] percentage uncertainty = ........................ % [2]

4 SRJC 2011 9646/Prelim/2011 For Examiner’s Use 2 (a) Derive, from the definitions of velo city and acceleration, the expression v 2 = u2 + 2as. [2] (b) In an experiment to test the effect of air resistance on different objects, a small stone and a thin piece of st iff cardboard are separatel y projected horizontally from the same vertical height, at the sa me initial speed. The figure below shows the path taken by the stone. The plane of the paper remains parallel to the ground during its journey. (i) Explain, why the horizontal range co vered by the path of the paper is observed to be further than that of the stone. ………………………………………………………………………………………... ………………………………………………………………………………………... ………………………………………………………………………………………... ………………………………………………………………………………………... ………………………………………………………………………………………... ……………………………………………………………………………………..[2] Since there is no air resistance experienced in the horizontal direction, the horizontal velocity of paper and stone are the same [M1]. Due to the surface area of the paper, air resistance is experienced in the vertical direction. Hence duration of flight for paper is longer [M1]. With a longer flight duration for the same horizontal velocity, the horizontal range covered in longer [A0]. horizontal range by stone path of the stone stiff cardboard ground small stone

5 SRJC 2011 9646/Prelim/2011 [Turn Over For Examiner’s Use (ii) Describe and explain, if the final ve locity of the paper before hitting the ground, is higher, lower or the same, than that for the stone. ………………………………………………………………………………………... ………………………………………………………………………………………... ………………………………………………………………………………………... ………………………………………………………………………………………... ………………………………………………………………………………………... ……………………………………………………………………………………..[2] With the same vertical distance covered, the longer flight duration of the paper would mean that its final vertical velocity is lower. [M1] Since the horizontal velocity for both are the same, the final velocity of the paper would be lower. [A1]

6 SRJC 2011 9646/Prelim/2011 For Examiner’s Use 3 (a) State the Principle of Conservation of Linear Momentum. .................................................................................................................................. ……………………………………………………………………………………………... ……………………………………………………………………………………………[1] (b) Box A, of mass 1.5 kg, s lides down a rough slope with an initial velocity of 2.0 m s1. The vertical height of the slope is 2.5 m and the work done against friction by Box A is 5.0 J. (i) Calculate the velocity of Bo x A at the bottom of the slope.       22 1 Loss in GPE = Gain in KE + Work done against friction 11.5 9.81 2.5 1.5 2.0 5 [M1]2 6.81m s [A1] A A v v     velocity of Box A at bottom of slope = ………………… m s 1 [2] (ii) At the bottom of the slope, Box A travels along a smooth surface before colliding elastically with a stationary Box B of mass 3.0 kg. Calculate the final velocities of Box A and Box B immediately after separation. The total momentum for a system of colliding bodies remains constant provided that no external force acts on the system. A B 2.0 m s1 2.5 m rough slope smooth surface

7 SRJC 2011 9646/Prelim/2011 [Turn Over For Examiner’s Use  1 1 By COLM, 1.5 6.81 1.5 3.0 ......(Eqn1) By RSA = RSS 6.81 0 .......(Eqn2) [M1 for Eqn 1 and 2] Solving Eqn 1 and Eqn 2, 2.27 m s [ 1 ] 4.54m s [ 1 ] AB BA A B vv vv vA vA        velocity of Box A = …………………….. m s 1 velocity of Box B = ..……………………. m s 1 [3]

8 SRJC 2011 9646/Prelim/2011 For Examiner’s Use 4 A tank with an L-shaped pipe is to be used as a weighi ng scale. A light airtight frictionless pis