2017 RI H2 Physics Prelims P2 QP

This document consists of 20 printed pages. © Raffles Institution 9749/02 [Turn over Centre Number Index Number Name Class 3016 RAFFLES INSTITUTION 2017 Preliminary Examination PHYSICS Higher 2 Paper 2 Structured Questions 9749/02 14 September 2017 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your index number, name and class in the spaces at the top of this page. Write in dark blue or black pen in the spaces provided in this booklet. You may use 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. Answer all questions. The number o f marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use 1 / 10 2 / 10 3 / 10 4 / 10 5 / 10 6 / 10 7 / 20 Deduction Total / 80

2 © Raffles Institution 9749/02 Data speed of light in free space c = 3.00 × 108 m s−1 permeability of free space µ0 = 4 π × 10−7 H m−1 permittivity of free space ε0 = 8.85 × 10−12 F m−1 = (1/(36π)) × 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 21 2s ut at= + 22 2v u as= + work done on / by a gas W = p∆V hydrostatic pressure p = ρgh gravitational potential Gm rφ = − temperature T/K = T/°C + 273.15 pressure of an ideal gas 21 3 Nmpc V= mean translational kinetic energy of an ideal gas molecule 3 2E kT= displacement of particle in s.h.m. 0 sinxx t ω= velocity of particle in s.h.m. 0 cosvv t ω= 22 0xxω= ±− electric current I = Anvq resistors in series R = R1 + R2 + . . . . resistors in parallel 1/R = 1/R1 + 1/R2 + . . . . electric potential V = Q/(4πε0r) alternating current / voltage x = x0 sinωt magnetic flux density due to a long straight wire 0 2B d µ π= I magnetic flux density due to a flat circular coil 0 2 NB r µ= I magnetic flux density due to a long solenoid 0Bn µ= I radioactive decay x = x0 exp(−λt) decay constant 1 2 ln 2 tλ =

3 © Raffles Institution 9749/02 [Turn over 1 A sphere is projected with velocity u from the bottom of a ramp which is inclined at an angle θ to the horizontal as shown in Fig. 1.1. Fig. 1.1 (not to scale) (a) Define acceleration. [1] (b) (i) When u = 9.0 m s–1 and θ = 26°, the sphere leaves the ramp after 0.70 s. Show that the sphere leaves the ramp at a speed of 6.0 m s−1. [1] (ii) Determine the height of the ramp. height = m [2] u θ floor ceiling ramp

4 © Raffles Institution 9749/02 (c) After the sphere leaves the ramp, it continues to travel upwards until it hits the ceiling at an angle of 5.0° to the horizontal as shown in Fig. 1.2. Fig. 1.2 (not to scale) (i) Show that the vertical component of velocity of the sphere just before hitting the ceiling is 0.47 m s−1. [1] (ii) Calculate the vertical displacement of the sphere from the instant it leaves the ramp to the instant it hits the ceiling. vertical displacement = m [2] (iii) State and explain whether the momentum of the sphere is conserved in the collision with the ceiling. [1] ceiling 5.0°

5 © Raffles Institution 9749/02 [Turn over (c) Using answers in (b)(ii) and (c)(ii), sketch on Fig. 1.3 the variation with the horizontal displacement x of the vertical displacement y of the sphere from the instant it is projected up the ramp to the instant it hits the floor. Fig. 1.3 [2] 0 y x

6 © Raffles Institution 9749/02 2 A car travels at 50.0 km h−1 due north for 25.0 minutes, after which it travels at 65.0 km h−1 in the north-east direction for another 30.0 minutes. (a) Distinguish between vector and scalar quantities. [1] (b) (i) Using a scale of 1.0 cm to represent a speed of 10 km h–1, draw a vector diagram to show the change in velocity ∆v of the car. The direction of north is indicated. [2] (ii) Hence, or otherwise, determine the magnitude of the average acceleration of the car if it takes 30.0 seconds to change its velocity. average acceleration = m s−2 [2] N

7 © Raffles Institution 9749/02 [Turn over (c) (i) Calculate the total distance travelled by the car. total distance = km [1] (ii) The uncertainty of each velocity measurement is 0.5 km h −1, and that of each time measurement is 0.5 minute. Determine the actual uncertainty in the total distance travelled. actual uncertainty = km [3] (iii) Hence, express the total distance travelled with its associated uncertainty. total distance = ± km [1]

8 © Raffles Institution 9749/02 3 (a) State the principle of conservation of linear momentum. [2] (b) A block X of mass 2.2 kg travelling at a speed of 6.0 m s−1 on a smooth floor collides head- on and sticks together with a block Y of mass 1.0 kg which is travelling at a speed of 2.0 m s−1 in the opposite direction, as shown in Fig. 3.1. The collision lasts for 0.35 s. Fig. 3.1 (i) Show that the blocks move with a speed of 3.5 m s−1 to the right after the collision. [2] (ii) Determine the magnitude of the average force acting on either block during the collision. average force = N [2] X 6.0 m s−1 Y 2.0 m s−1 floor water 2.2 kg 1.0 kg

9 © Raffles Institution 9749/02 [Turn over (iii) The blocks then slide off the edge of the floor and into a tank of water as shown in Fig 3.1. The density of water is 1000 kg m−3. The blocks have uniform densities and their dimensions are shown in Fig. 3.2. Fig. 3.2 1. The blocks eventually achieved equilibrium when they are submerged at depth h as shown in Fig. 3.3. Fig. 3.3 Explain how the blocks achieved this final position. You may draw a diagram if you wish. [2] 2. Calculate h. h = m [2] h water X Y 0.15 m 0.20 m X Y 0.10 m 0.10 m

10 © Raffles Institution 9749/02 4 (a) Define work. [1] (b) Using your definition in (a), derive an expression for the increase in gravitational potential energy ∆Ep when an object of mass m is raised vertically through a distance ∆ h near the Earth’s surface. The acceleration of free fall near the Earth’s surface is g. [2] (c) Fig. 4.1 shows a block P of mass 1.0 kg and a block Q of mass 3.0 kg connected by a light inextensible cord passing over a frictionless pulley. Block P starts from rest and moves up a rough slope inclined at an angle of 30° to the horizontal, while