SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO

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SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO Half-Yearly Exam 2013 Subject: Physics Level: Advanced Time: 3hrs Name: Course: Year: 1st This paper carries 200 marks which are 80%

1 SIR MICHELANGELO REFALO CENTRE FOR FURTHER STUDIES VICTORIA GOZO Half-Yearly Exam 2013 Subject: Physics Level: Advanced Time: 3hrs Name: Course: Year: 1st This paper carries 200 marks which are 80% of the examination. Answer all questions. g = 10 ms a) Experiments show that air friction F, retarding a falling object, can be approximated fairly well by the equation, F=cρAv 2 where ρ is the density of the air, v is the velocity of the object, A is the effective cross-sectional area and c is a numerical constant (with no units). a) Show that the given equation is homogenous. b) Derive an expression in terms of the symbols given above, for the terminal velocity of the object if it has a mass m. (Acceleration due to gravity = g). (4 +4 marks) 2. A kangaroo was seen to jump to a vertical height of 2.8 m. a) For how long was it in the air? b) Draw displacement time, velocity time and acceleration time graphs for the kangaroo s vertical motion of this one jump. Take upward direction as positive. c) If the kangaroo jumped with a horizontal speed of 6 m/s, how far away does it land on the ground? ( marks) 3. Two tug-of-war teams each pull on a rope with a force of 5000 N. The rope is horizontal. What is the tension in the rope at its mid-point? (2 marks) 4 a) From Newton s second law of motion, one can arrive at the equation F = kma. How was the constant eliminated from the equation? Page 1 of 6

2 b) Two blocks of masses m 1 = 1.0 kg and m 2 = 2.0 kg respectively, are placed in contact on a smooth horizontal surface, as shown in the diagram. The smaller block is pushed with a constant force F = 6.0 N so that both blocks move together and remain in contact. i) Determine their acceleration. ii) What is the value of the force which m 1 makes on m 2. iii) Identify a pair of action reaction forces in this situation. ( marks) 5. The diagram shows part of a smooth track with the curved section CDE forming part of a circular arc of radius 0.75 m. A model car of mass 6 x 10-2 kg is released from point A. a) Calculated the speed of the car i) at point B ii) at point D. b) Calculate iii) Calculate the force which the track exerts on the car at point D. Note that the car is moving in a circle at this point. (2+2+5 marks) 6. The engine of a motor boat delivers 30 kw to the propeller while the boat is moving at 10 m/s. What would be the tension in the tow rope if the boat were being towed at the same speed? (3 marks) 7. A sledge of mass 12 kg is travelling down a slope with a constant velocity of 6 m/s. The frictional force opposing the motion is constant and is equal to one fifth of its weight. a) Draw a diagram, labelling all the forces acting on the sledge. Page 2 of 6

3 b) What angle does the slope make with the horizontal? c) When the sledge reaches horizontal ground, over what distance will the sledge stop if the frictional force remains the same? ( marks) 8. A uniform ladder 4.0 m long, of mass 25 kg, rests with its upper end against a smooth vertical wall and with its lower end on rough ground. a) What is the N, normal reaction force of the ground on the ladder? b) Taking moments about base of ladder what is S, the normal reaction of the wall on the ladder? c) What is the frictional force of the ground on the ladder which keeps the ladder from slipping? d) If friction F =µn where µ is the coefficient of friction and N is the normal force pushing the surfaces together, what must be the least coefficient of friction to prevent it from slipping? ( marks) 9. The motion of a piston in a certain car engine is approximately simple harmonic with amplitude 40 mm. The frequency of oscillation is 120 Hz. Find a) the maximum acceleration b)the maximum speed of the piston c) Sometimes when starting the car, the body of the car starts vibrating violently because of resonance. What is meant by resonance? ( marks) 10. a) State the law of conservation of angular momentum and state the condition under which it acts. Page 3 of 6

4 b) Two small masses A and B, at the ends of a light horizontal rod, rotate in a horizontal plane about the midpoint O of AB. A has a mass of 0.2 kg and B has a mass of 0.1 kg. The rod rotates with an angular velocity of 10 rad/s. If the moment of inertia is given by mass multiplied by distance from pivot squared, calculate their total angular momentum about O, if the distance AB is 0.8 m. c)if while rotating under the conditions in (b), the mass B slips along the rod so that the distance BO becomes 0.3 m, calculate the new angular velocity of the system about O. ( marks) 11. a) A car is travelling at constant speed round a bend. Explain why, although the speed is constant, its velocity is not constant. b) Derive the equation: centripetal acceleration a =. c) To help a car turn around a bend, the road is banked. For a car moving with velocity v and intercepting a bend of radius r, derive an equation for the banking angle θ needed on a frictionless road. ( marks) 12. a) State Newton s Law of Gravitation. b) State what is meant by the period of a planet in its orbit. c) Use Newton s Law of Gravitation to derive an expression for the radius of the circular orbit of a planet around the Sun in terms of its period. d) The average radius of Pluto s orbit is 39.4 AU and its period is 9.04 x 10 4 days. However irregularity in Pluto s orbit has been observed. There has been speculation that another planet X exists. If X were to exist and if its period were twice that of Pluto, calculate at what average distance X would orbit around the Sun. ( 1 AU = 1.5 x m) ( marks) Page 4 of 6

5 13. a) A particular spring has a spring constant of 30 N/m. Two such springs are suspended in series from two more in parallel. What is the extension of the system for a load of 4 N? What is the spring constant for the whole system? b) When a mass is suspended to a spring, the gravitational potential energy the mass loses is twice the elastic potential energy stored in the spring. Why? (6 +3 marks ) 14. Oak has a density of about 700 kgm -3. Draw a free body diagram for a piece of oak floating in water, and show that 0.70 of its total volume is submerged. (The density of water is 1000 kgm -3 ) (3 +5 marks) 15. a) Describe an experiment in which you would determine Young s Modulus of a copper wire. b) The diagram shows stress strain graphs for various materials. Which graph represents the behaviour of a i) brittle material ii) ductile material. Give an example of each. iii) Which one is stiffer? iv) Which one is stronger? v) Which one is tough? Explain this term. vi) Mark on the graph of the ductile material the elastic limit E, the yield point Y, the proportionality limit P and the breaking point C. c) The Young s modulus for copper is 1.2 x Pa and its yield stress is 7.5 x10 7 Pa. A tensile load of 50 N is applied to a 3.0 m length of copper wire of cross Page 5 of 6

6 sectional area 1.0 mm 2. Explain whether such a load can be applied without the wire becoming permanently extended and calculate the extension produced by the load. ( marks) 16. Describe an experiment which can be done to find the specific latent heat of vaporization of water. (10 marks) 17. a) Explain what is meant by the statement: a glass of water is in thermal equilibrium with its surroundings. b) What is meant by the triple point of water? c) Describe briefly an experiment which shows that particles in a gas are moving randomly. d) Explain what is meant by internal energy. e) State the first law of thermodynamics. f) Current flows through a filament lamp and its temperature starts rising. Consider the instant when the filament is at 100 o C and its temperature is still rising, state whether (i)δu (ii)δw and (iii)δq is positive, negative or zero. ( marks) 18. An alpha particle of relative mass 4 is emitted from a nucleus of relative mass 226. If energy E is released as kinetic energy, find the ratio ke of alpha particle : ke of daughter nucleus (relative mass 222). (10 marks) END OF PAPER----- Page 6 of 6

Force, Energy & Periodic Motion. Preparation for unit test

Force, Energy & Periodic Motion Preparation for unit test Summary of assessment standards (Unit assessment standard only) In the unit test you can expect to be asked at least one question on each sub-skill.