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(PHYS111)[1998](f)midterm~=tkk933^_26277.pdf
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Physics 111
Final Examination, 17 December, 1998

Answer all questions. Numerical answers should be given to 3 significant figures. The following constants are provided:
gravitational acceleration g = 9.8 ms .2

gravitational constant G = 6.67 . 10-11 Nm2kg-2
mass of Earth ME = 5.98 . 1024 kg
radius of Earth rE = 6.37 . 106 m
velocity of sound in air v = 340 ms-1
atmospheric pressure 1 atm = 1.01 . 105 Nm-2

1. A rocket is fired vertically from the surface of Earth at an initial velocity of 15 kms-1.


(a) Find the velocity of the rocket when it reaches a height equal to the radius of Earth.
(b) Find its velocity when it has escaped from Earth. [10]



2. Consider a comet travelling around the Sun in an ellipse. When it is nearest to the Sun, the Sun-to-Comet distance is 2 times the Sun-to-Earth distance. When it is furthest away from the Sun, it is 10 times the Sun-to-Earth distance. Using Keplers law for planetary motion, find the period of the comets orbit. [5]



3. A block of mass m=1 kg rests on a smooth horizontal plane and is attached to a spring of force constant k=5 Nm-1. The block is pulled until the spring is stretched by a displacement of 0.1 m and is released with an initial velocity of 0.2 ms-1.


(a) Find the period of oscillations.
(b) Find the amplitude of the oscillations. [10]

4. A string is stretched with a tension of 20 N, and has a mass per unit length of 0.001 kgm-1.


(a) Find the wave velocity on the string.
(b) A sinusoidal wave of frequency 100 Hz and amplitude 0.1 m travels along the string. If the equation of wave motion is given by

yxtAkxt(,)),..sin(.


what are the values of A, k and .?
(c) If the string has a length of 1 m, find the frequencies of the lowest two harmonics on the string. [15]

Please turn over
5. (a) A police car moves forward with a velocity 20 ms-1 and transmits a siren of frequency 1200 Hz. The sound is reflected from a Porsche moving towards the police car with a velocity of 25 ms-1. What is the frequency of the reflected sound as detected by the police car itself?
(b) A jet plane flies at 1.5 times the speed of sound at a height of 5000 m. A man on the ground saw the plane directly overhead. How much time does it take him to hear the sonic boom? [10]

6. Gas in a chamber is initially at state A at a pressure of 1 atmosphere and a volume of 0.02 m3. It undergoes a cycle ABC in 3 steps:



AB: heating at constant volume from pressure 1 atm to 2 atm.
BC: expansion along a linear path.
CA: cooling at constant pressure from 0.04 m3 to 0.02 m3.


(a) Find the work done by the gas during BC.
(b) Find the amount of heat absorbed by the gas during the cycle. [10]


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