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PART B – ANSWER TWO OUT OF THREE QUESTIONS IN THIS PARTTERM 1 TEST Physics Instructions to Candidates
Date:Tuesday 14th December 2010 Location:Nazarbayev University Block 4, Canteen, 3rd floor Time:2:30 – 4.30 pm Length: 2 Hours
The total mark for the exam is 120 marks. Part A has 96 marks and Part B has 24 marks. Part A comprises 80% of the total mark and Part B comprises 20% of the mark. Gravitational Constant g = 9.81 ms-2 Speed of Light c = 3 × 108 ms-1
PART A – ANSWER ALL QUESTIONS IN THIS PART
Question 1
A man of mass m = 65 kg climbs the stairs to the second floor of the Eiffel Tower, rising a height of 116 m. To lift himself to this height in 15 minutes, what must his average power output be? (4 marks) Question 2
A particle moving in one dimension along the x-axis and has the following velocity-time diagram as shown in the figure below.
a) Find: i) the total distance the ball moves over 20 s, ii) its displacement after 20 s. b) Sketch the acceleration-time diagram for the motion of the ball from time t = 0 s to t = 5.0 s and from t = 5 s to t = 20 s. (6 marks) Question 3
An airplane flies in a loop (i.e. a circular path in a vertical plane) of radius 150 m. The pilot has a mass of 70 kg, and he sits in his chair and his head always points towards the centre of the loop. (a) At the top of the loop, the pilot feels weightless. What is the speed, in ms-1, of the airplane at this point? (b) At the bottom of the loop, what is the force exerted on the pilot by the chair? (8 marks)
Question 4
A ray of light travelling in water of refractive index 1.33 strikes the surface at an angle of incidence of 28º.
(a) Find the angle θa at which it emerges into air.
A layer of oil of refractive index 1.44 is poured onto the surface of the water.
(b) Find the angle αo at which the ray enters the oil, and then show that the ray still emerges into air at the same angle θa. (c) Calculate the speed of light in oil. (10 marks) Question 5
A mass m is on a rough inclined plane that makes an angle q with the horizontal. The maximum angle qmax for which the mass remains in equilibrium is 30°.
Calculate the coefficient of static friction, μS. (8 marks)
Question 6
(8 marks)
Question 7
When monochromatic, coherent light passes through two slits of separation d, a number of bright fringes separated by dark fringes are observed on a screen at a distance D from the slits.
(a) Explain the meaning of monochromatic light and coherent sources. (b) Draw a diagram of the double slit experiment to show the interference pattern and the path difference between two waves that arrive in phase at a point P on the screen. (c) What are the conditions for a bright and a dark fringe?
(8 marks) Question 8
A rotating neutron star of frequency 3 ×10- 4 Hz collapses under the influence of its own gravity to 1/1000 of its radius. The star’s mass is conserved and the star may be considered to be a uniform sphere. (The moment of inertia of a sphere of mass, m, and radius, R, is given by the equation I = 2mR2/5.)
(a) Calculate the star’s new rotational period (b) Calculate the ratio of rotational energy before the collapse to the rotational energy after the collapse of the star.
(10 marks) Question 9
Monochromatic light of 750 nm wavelength is diffracted through a diffraction grating that has 20,000 slits per metre.
(a) Calculate the angular separation between the zero and first interference maxima. (b) What is the maximum number of bright fringes seen on each side of the normal?
Light of the same wavelength is incident on a single slit of width 4 × 10-3 mm.
(c) Calculate the angular separation between the first and the third diffraction minima.
(10 marks) Question 10
A uniform ladder stands on a rough horizontal surface and leans against a smooth vertical wall. The ladder is inclined at an angle θ to the horizontal. The bottom of the ladder is 3 m from the wall. The magnitude of the reaction force at the bottom of the ladder is twice the reaction force at the top of the ladder.
(a) Calculate the length of the ladder. (b) Calculate the angle θ. (10 marks)
Question 11
(a) Define transverse and longitudinal waves, and give one example for each kind. (b) A transverse wave in air is described by the wave equation, where x, y are in metres and t in seconds:
Calculate the following parameters of the wave:
(i) Amplitude (ii) Wavelength (iii) Frequency (iv) Wave speed
(c) For this wave, calculate the maximum velocity of vibration of the particles. (d) Calculate the acceleration of a particle at x = 1.5 m and t = 2.0 s.
(14 marks) PART B – ANSWER TWO OUT OF THREE QUESTIONS IN THIS PART Question 1
The end of the string of a yo-yo (figure below) is held stationary while the cylinder of mass M = 0.2 kg and radius R = 10 cm is released with no initial motion. The string unwinds but does not slip as the cylinder drops and rotates. The moment of inertia, I, of the cylinder is equal to 10-3 kg m2.
(a) Calculate the speed of the centre of mass of the cylinder, vcm, after it has dropped a distance h = 0.5 m.
(b) The same yo-yo drops a height 0.5 m without rotating. Calculate its final speed. (c) Compare the speed found in (b) to the value of vcm found in (a) and explain why they are different. (d) The same yo-yo moves on a horizontal surface such that the initial speed of its centre of mass, vcm, is 4.0 ms-1. The coefficient of static friction between the yo-yo and surface is 0.15, and the yo-yo rotates without sliding. Calculate the number of revolutions the yo-yo rotates before it comes to rest.
(12 marks) Question 2
(a) A tennis player drops a tennis ball from her hand. The ball has a mass of 56.7 g and falls a vertical height of 0.80 m. The ball bounces back up to a height of 0.76 m. If the ball is in contact with the ground for 12 ms, what is the average force exerted on the ball by the ground?
(b) She then serves the ball with her racket. On leaving the racket, the ball is at a height of 2.5 m, has a velocity of 40 ms-1 and its direction is 16° below the horizontal. At what distance from the player’s feet will the ball hit the floor, assuming horizontal ground? (12 marks)
Question 3 A wooden block of mass 2.5 kg that is attached to a spring with spring constant k = 180 N/m rests on a smooth plane while a bullet of 0.02 kg and speed of 60 ms-1 enters the block and remains there while both are displaced a distance d as shown.
If the system executes SHM, calculate:
(a) The speed of the system of masses immediately after the impact (b) The magnitude of the maximum displacement (c) The period T (d) The displacement from equilibrium and velocity of the masses 0.25s after the impact. (e) The displacement from equilibrium when the kinetic energy of the masses is half the kinetic energy on impact. (12 marks)
Date: 2015-12-11; view: 1074
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A block A rests on a rough surface, as shown. The weight w is 12.0 N and the system is in equilibrium. Calculate the tension forces T1, T2 and T3 in all three strings.
