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(PHYS111)[2008](f)final~=tkk933^_80925.pdf
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Physics 111 (Fall 2008)
Final Examination, 17 December, 2008
Time allowed: 3 hours. Total: 100 marks

Answer all questions. Show all steps. Numerical answers should be given to 3 significant figures.
Gravitational constant G = 6.67 . 10.11 Nm2kg.2
Mass of Sun MSun = 1.99 . 1030 kg
Distance between Earth and Sun 1 AU = 1.5 . 1011 m
Gravitational acceleration g = 9.8 ms.2
Velocity of sound in air v = 343 ms-1
Boltzmann constant k = 1.381 . 10.23 JK.1
Avogadros number NA = 6.023 . 1023
Universal gas constant R = 8.315 Jmol.1K.1
Atmospheric pressure 1 atm = 1.013 . 105 Nm.2
Absolute zero 0 K = .273oC
Sum formula 2cos22sinsinsin BABABA ....

1. (15 marks) Comet Ikeya-Zhang (Chinese name: - ) was discovered in 2002. Its furthest and nearest distances from Sun are 102 AU and 0.5 AU respectively, where 1 AU is the average distance between Earth and Sun.
(a) What is the eccentricity of the comets orbit?

(b) Using the fact that Earths orbital period is 1 year, calculate the orbital period of the comet. Give your answer in years.

(c) Using the conservation of energy, calculate the orbital velocity of the comet at its furthest point from Sun.


2. (15 marks) A physical pendulum consists of a solid disk of mass M = 0.2 kg and radius R = 0.3 m. It is hinged in a vertical plane by a pivot located at a distance 2R/3 from the centre of the disk. (The rotational inertia of a disk about its centre is MR2/2.)
(a) What is the rotational inertia of the disk about the pivot?

(b) What is the period of small oscillations of the pendulum?

(c) A simple pendulum swings with the same period as this physical pendulum. What is the length of the simple pendulum?


pivot centre

Please turn over
1
3. (15 marks) Two loudspeakers are connected to the same signal generator and placed in open air at positions x = +x0 and x = .x0, where x0 = 1.5 m. A signal of 300 Hz is produced, and the sound waves produced by the loudspeakers at position x and t are given by, respectively,
y (x,t) . y sin(kx ..t . kx ),
10 0
y (x,t) . y sin(kx ..t . kx ).
20 0
(a)
What are the values of . and k?

(b)
What is the amplitude of the resultant wave at x = 0.7 m? Express your answer as a fraction of the maximum amplitude of the resultant wave.

(c)
Find all positions x in the range .x0 < x < x0 where the resultant wave has maximum amplitude.


4. (10 marks) A fire engine moves at a speed of 10 ms.1 and emits a siren at a frequency of 1600 Hz. A car moves at 20 ms.1 approaching the fire engine in the opposite direction.
(a)
What is the frequency detected by the car?

(b)
What is the frequency of the sound reflected by the car as detected by the fire engine?


5. (5 marks) A Boeing-747 jet B flies at a speed of Mach 0.85, and a Concorde jet C flies at a speed of Mach 2, both in the same horizontal direction. At t = 0, jet C is 5000 m directly above jet B. What