SIR MICHELANGELO REFALO SIXTH FORM

SIR MICHELANGELO REFALO SIXTH FORM Annual Exam 2016 Subject: Physics A Level Time: 3 hours Section A: Answer all questions in this section 1. a) For an object to be in equilibrium, two conditions must be satisfied. What are they? b) What does it mean that an object is in equilibrium? You should explain both translational and rotational equilibrium. c) Two children loop a rope over a tree trunk and hang on to either end. One child has as mass of 40 kg and the other of 50 kg. Assuming no friction between the trunk and rope, find the tension in the rope and the initial acceleration of the two children. d) A uniform ladder of weight 100 N is at rest against a frictionless wall. The ladder makes 70 degrees angle with the horizontal and is 2 m long. i) What is the normal reaction of wall on the ladder ii) If someone standing on a ladder climbs up the ladder, will the tendency that the ladder slips increase? Explain why. (2, 2,5,2,2 marks) 2. a) Show how the law of conservation of momentum proceeds from Newton s Laws of Motion. b) A ball of mass 1kg moving with a speed of 4m/s collides with a stationary ball of mass 4kg. Immediately after collision, the 4 kg ball acquires a speed of 1.6 m/s forwards in the same direction that the first ball was travelling and the 1 kg ball starts moving in the opposite direction with a speed of 2.4 m/s. i) Is momentum conserved in this collision? Is the collision possible? P a g e 1

ii) Is the collision elastic? You are required to show how you arrived at your conclusions in both answers. (4,4,4 marks) 3. Some children are playing on a merry go round in a playground. a) When the merry go round is rotating, a child experiences the tendency to be thrown out on the ground. Explain this using physics. b) Will this tendency be greater if the child is closer to the centre of rotation? Explain. c) Some children are on a stationary merry go round and another child who is on the ground is pushing it to start it moving. Will he find it more difficult if the children are standing near the edge of the merry go round? Explain. d) The merry go round is rotating at a constant rate. Does a child on it have angular acceleration? Does the child have centripetal acceleration? Explain. e) The merry go round is rotating and children who are on it at the edge move towards the centre. Explain if anything changes and give a reason why. (2, 2, 2, 4, 3 marks). 4. a) When studying the topic Gravitation in Physics, the symbol g refers to two quantities. i) Define them. ii) Give their units and show that they have the same base units. b) In the topic Gravitation we also use the symbol G. i) Explain what this stands for? ii) G is a very small number. What is the effect of this on the magnitude of gravitational forces when compared to electrical forces? c) The Sun has a mass of 1. 99x 10 30 kg. Show that if the Sun were of radius 2500 m, it would become a black hole i.e. show that the escape velocity from its surface would be more than the speed of light. (The speed of light is 2.998 x 10 8 m/s.) d) This question is about projectiles. A projectile leaves the ground at an angle of 60 degrees to the horizontal. Its initial kinetic energy is E. Neglecting air-resistance, find in terms of E, its kinetic energy at the highest point of its motion. (2,2,2,1,3,4 marks). P a g e 2

5. The pressure of a gas p = 1 3 ρc2 where ρ is the density of the gas and c 2 is the mean density of the gas. a) State 3 assumptions needed to derive the equation above. b) Starting with the equation above, show that the r.m.s. velocity of gas particles is: c 2 = 3RT where M is the mass of one mole and T is the temperature of the gas. M c) Hence show that the k.e. of each particle is k. e. = 3 2 R T N A d) Given that M oxygen : M hydrogen = 16: 1, determine the ratio of c oxygen: 2 c hydrogen 2 for oxygen particles and hydrogen particles at identical temperatures. (3, 4, 4, 2marks) 6. The inner electrons orbit around an oxygen nucleus at a distance of 3.3 10 11 m from the centre. a) By considering that the electrostatic force between the nucleus (charge = 1.28 10 18 C) and the electron (charge= 1.6 10 18 C) is necessary as centripetal force, calculate (i) the velocity (ii) the angular velocity (iii) the periodic time of the electron. b) Determine the values of the k.e. of the electron and the electrical p.e. of the electron as it orbits at this distance. c) For electrons orbiting at a bigger distance from the nucleus, state whether the following quantities are bigger or smaller: (i) force, (ii)velocity, (iii) angular velocity (iv) k.e. (iv) p.e. (4, 4, 5 marks) 7. Electrons are drifting at a velocity v in a direction opposite to the flow of current. a) Determine the number of electrons that are drifting each second. b) Hence show that the current flow in the wire is equal to nave. c) A current of 6.5A flows in a copper wire that has 1.2 10 29 charge carriers per m 3. If the drift velocity of the electrons is 0.45mm/s, determine the cross sectional area of the wire. P a g e 3

d) Explain how; in spite of such a low drift velocity, an electrical appliance will switch on immediately when the switch is closed. d) Use the Band Theory to explain the difference between conductors, insulators and semiconductors. (2, 2, 2, 1, 6 marks) 8. a) The adjacent capacitor charging/discharging circuit is connected. a) Define the time constant of a capacitance-resistance circuit. b) Find the time constant (i) during the charging process (ii) during the discharging process. c) The switch is kept on the left hand side for a relatively long time such that the capacitor is fully charged. It is then turned to the right hand side so that discharging commences. Find the initial values of (i) charge (ii) current (iii) voltage during the discharging process. d) Find the values of the quantities in (i) after a time of 2s. (3, 2, 3, 5 marks) P a g e 4

Section B: Choose 4 questions out of 7. 9. a) Derive KE from work = Force x distance. Hint: you need to use one of the equations of motion and imagine the object starts from rest. b) Describe an experiment in which you would find Young s Modulus. The write up should include a diagram of the set-up, precautions, method and readings taken and how you arrive at your answer. c) This question is about gravitation. The Lagrange Point in the Earth Moon system is the point between the Earth and the Moon where the gravitational field strength of the Moon is exactly equal and opposite to that of the Earth. It is found closer the Moon; the distance from the Earth to the Lagrange Point is 9 times the distance from the Moon to the Lagrange Point. i) Explain why at the Lagrange point, the gravitational potential is not zero. ii) Find the ratio of the mass of the Earth to that of the Moon using the information given about the ratio of distances. (5, 12, 2, 6 marks) 10. a) A car is rounding a bend of radius r with velocity v. Derive an equation for the banking angle θ that the road has to be banked in order for the car to change direction and follow the circular path of radius r without needing friction. Include a diagram. b) If in real life a car enters this part of the banked road at a speed smaller than v and friction is present between the tyres and the ground, will the direction of friction be upwards or downwards to keep the car moving in the circular path of radius r c) A cylinder is rolling down a slope. The cylinder has a mass of 2 kg and a radius of 10 cm and after the height of its centre of gravity has decreased by 2m, it acquires a speed of 5 m/s. Assuming no kinetic energy is changed to heat, what is the moment of inertia of this cylinder? d) This question is about materials. When talking about materials, a person made the following statements. Say whether each is true or false and explain why. i) If material A is stiffer than B, then A is stronger. ii) If C is ductile, then it is brittle. iii) Strength is related to its Young s Modulus. iv) Stiffness is related to its UTS. (9, 3, 5, 2, 2, 2, 2 marks) P a g e 5

11. a) i) An object is moving with constant speed and changes direction. Say whether this amounts to acceleration and explain why. ii) Derive an equation for the centripetal acceleration experienced by an object moving with constant speed v in a circular orbit of radius r. b) The Olympic Games are near and we shall see pirouetting skaters who will increase their rate of rotation when they change the shape of their body. Explain what they have to do to increase their rate of rotation without having an external torque acting on them and use physics principles to explain why this happens. c) Explain whether the fact that the Earth is spinning on its own axis and that it bulges at the Equator has an effect on the measured g at the Equator when compared to the measured g at the Poles. d) i) State Newton s First Law of Motion. ii) A book is at rest on a table. What is the action/reaction to the weight of the book? iii) Explain using physics principles two reasons why an airbag reduces face injuries in a car crash. (2, 9, 4, 4, 2, 2, 2 marks) 12. a) Derive s = ut + ½at 2 from the velocity time graph shown. b) This question is about gravitation. i) An astronaut in the orbiting International space station floats in it. Explain whether this is due to the fact that his weight is zero. ii) If the astronaut of mass 70 kg is 400 km above the Earth s surface, calculate the total energy (both kinetic and potential) that he has. Mass of Earth = 6 x 10 24 kg. Radius of Earth =6400 km. iii) Your answer to (e) should have a negative value. What does this tell you about the state in which the astronaut is? c) This question is about simple harmonic motion i) Define simple harmonic motion. ii) What readings does one need to take from a displacement time graph for an object performing simple harmonic motion, to be able to plot the velocity time graph of the same motion. iii) A mass m is on top of a platform which is vibrating at 10 Hz. The amplitude of the vibrations is slowly increased. At one point the mass loses contact with the platform. At P a g e 6

which point in the vibration does this happen? What is the amplitude of the platform at which the mass just loses contact with the platform? (5, 2, 8, 2, 2, 2,4 marks). 13. a) A 1.8kg block of aluminium (c = 850Jkg 1 K 1 )at a temperature of 110 is lowered into 0.9kg of water (c = 4200Jkg 1 K 1 ) that is at a temperature of 15. If 24kJ is lost to the surroundings, find the temperature at which thermal equilibrium of the aluminium and water is reached. (5marks) b) 20g of solid mercury at its melting point of 38 gains heat until it reaches room temperature of 18. If the specific latent heat of fusion of mercury is 11300Jkg 1 and the specific heat capacity of mercury is 140Jkg 1 K 1, calculate the amount of heat gained by the mercury. (4marks) c) The First law of Thermodynamics states that U = Q + W. (i) State the meaning of each of these quantities. (ii) Copy the table below and show whether these terms as well as change in temperature are positive; negative or zero during the following processes. Isothermal expansion Adiabatic expansion Isobaric expansion Heating at constant volume Adiabatic compression U Q W T (2, 5 marks) d) A gas at a pressure of 2.5 10 5 Pa and a volume of 0.08m 3 undergoes the following processes: Process 1: Heated at constant volume such that the temperature (and pressure) doubles. Process 2: Expands isothermally such that pressure returns to 2.5 10 5 Pa. Process 3: Cooled at constant pressure such that the value of volume returns to 0.08m 3. (i) Draw a pressure-volume graph showing the processes that the gas undergoes. (ii) Calculate the work done on the gas in process 3. P a g e 7

(iii) Copy the following table and fill in the missing values of U, Q, W. (Hint: at end of process 3, gas returns to original conditions) Process 1 Process 2 Process 3 Whole cycle U Q W 50kJ -27kJ Answer to (ii) (3, 2, 4 marks) 14. a) State Kirchoff s 1 st and 2 nd laws. (4 marks) b) The adjacent circuit is connected. Using Kirchoff s laws, determine: (i) the values of I 1, I 2, and I 3. (ii) the value of the p.d. across AB. (iii) the power delivered by each cell. (iv) the power of each resistor. (6, 1, 2, 2, 3 marks) c) A battery of e.m.f. equal to 8V and internal resistance equal to 2.5Ω is connected in the circuit shown. Find the readings of the ammeter and the voltmeter when (i) the switch is open (ii) the switch is closed. (iii) State the condition necessary for the terminal p.d. to approach the value of the e.m.f. of the cell. (2, 3, 2 mark) P a g e 8

15. a) Electrons are accelerated using an electron gun at a potential difference of 800V. Determine the velocity gained by the electrons. (4marks) b) These electrons enter horizontally in a vertical uniform electric field as shown in the adjacent diagram. (i) Define electric field strength at a point. (ii) Explain the meaning of uniform electric field. (2, 2 marks) c) If they move a horizontal displacement of 2.25cm and a vertical displacement of 0.618cm, determine: (i) the time of motion of the electrons inside the electric field. (ii) the vertical acceleration of the electrons. (iii) the electric field strength between the plates (weight of electrons can be neglected). (iv) the potential difference between the plates if the separation between the plates is 1.1cm. (2, 3, 3, 2 marks) d)two spheres of equal mass are hung as shown in the adjacent diagram. They are both given a positive charge; with charge Q 1 = 2 Q 2 The spheres move apart due to a repulsive force of 3.5 10 6 N such that distance r = 25cm. (i) Determine the values of Q 1 andq 2. (ii) If the length of each string is 30cm, determine the mass of each sphere. (4, 3 marks) P a g e 9

Data and Formula Sheet: Uniformly accelerated motion: v = u + at s = ut + 1 2 at2 v 2 = u 2 + 2as s = u+v 2 t Mechanics: Newton s second law: F = d(mv) dt Power: P = F v Momentum: p = mv Circular Motion and Rotational dynamics: Angular speed: ω = dθ dt = v r Angular acceleration: α = dω Centripetal Force: F = mv2 r Torque: τ = Iα dt = a r = mω 2 r Work done in rotation: τθ = ( 1 2 Iω2 ) Current Electricity: Current: I = nave Resistors in series: R total = R 1 + R 2 + Resistors in parallel: = 1 + 1 + R total R 1 R 2 Power: P = IV = V2 = I2 R Resistivity: ρ = RA l R Temperature coefficient of Resistance: α = R θ R 0 R 0 T Capacitance: Capacitance of parallel plates: C = ε 0ε r A Capacitors in parallel: C total = C 1 + C 2 +.. Capacitos in series: 1 d 1 C total = 1 C 1 + 1 C 2 + Energy stored: Energy = 1 2 CV2 Charging: Q = Q 0 (1 e t RC) Discharging: Q = Q 0 e t RC Simple Harmonic Motion: Displacement: x = x 0 Sin(ωt + ) Velocity: v = ωx 0 Cos(ωt + ) v = ±ω x 0 2 x 2 Acceleration: a = ω 2 x Period: T = 1 f = 2π ω Mass on a light spring: T = 2π m k Temperature: Celsius scale: θ( ) = θ(k) 273.15 Temperature (K) T = 273.16 P P tr Kelvin Fields: Electric field strength: E = F q = dv Uniform field: = F q = V d Forces between point charges: F = Q 1Q 2 4πε 0 r 2 E near a point charge: E = Q dr 4πε 0 r 2 Force between masses: F = GMm r 2 Electric potential: V = Q 4πε 0 r Gravitational potential: V G = GM r Electrical work: Work = qv P a g e 10

Gases: Ideal gas equation: pv = nrt Kinetic Theory of an ideal gas: pv = 1 3 Nmc2 Boltzmann s constant: k = R N A Principal molar heat capacities of ideal gas: γ = C P C V C P C V = R Adiabatic process: pv γ = constant Heat: Energy = mc θ Energy = ml Materials: Hooke s law: F = k x Stress: σ = F A Strain: ε = l l Young s Modulus: Y = σ ε Energy stored in a stretched wire: E = 1 2 k( l)2 First and Second law of thermodynamics: First law: U = Q + W Ideal heat engine: = 1 T C T H The following constants may be useful in answering some of the questions in the examination: Acceleration of free fall on and near the Earth s surface: g = 9.81ms 2. Boltzmann constant: k = 1.38 10 23 JK 1 Molar gas constant: R = 8.31Jmol 1 K 1 Avogadro s constant: N A = 6.02 10 23 mol 1 Charge of an electron: e = 1.6 10 19 C Mass of an electron: m e = 9.1 10 31 kg Coulomb s law constant: ElectronVolt: 1eV = 1.6 10 19 J 1 4πε 0 = 8.99 10 9 Nm 2 C 2 Gravitational constant: G = 6.67 10 11 Nm 2 kg 2 Permittivity of free space: ε 0 = 8.85 10 12 Fm 1 P a g e 11