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(PHYS111)[1999](f)final~cyyuaa^_99843.pdf
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Physics 111
Final Examination, 21 December, 1999
Answer all questions. Numerical answers should be given to 3 significant figures. The following constants are provided:
gravitational acceleration g = 9.8 ms-2
velocity of sound in air v = 340 ms-1
universal gas constant R = 8.314 Jmol-1K-1
atmospheric pressure 1 atm = 1.013 . 105 Nm-2
1. A physical pendulum consists of a uniform stick with mass M = 0.6 kg and length L = 1 m. The upper end of the stick is free to swing about a pivot, and the lower end has a bob with mass m = M attached firmly to it.
(a)
Given the rotational inertia of the stick about its centre of mass is I = ML2/12, what is the total rotational inertia of the combination of the stick and the bob about the pivot? What is the distance between the pivot and the centre of mass of the combination?
(b)
Suppose a simple pendulum swings with the same period as this physical pendulum. What is the length of the simple pendulum?
(c)
The angular displacement of the physical pendulum is given by
. (t) ..m cos(.t ..).
Suppose at time t = 0, the pendulum is given an initial angular displacement of .(0) = 0.1 rad, and an initial angular velocity of ..(0) = 0.3 rad s-1. What are the values of .m, . and . in the above expression? [15]
2. (a) A guitar string is stretched with a tension of 336 N, and has a mass per unit length of 0.0018 kgm-1. What is the wave velocity on the string?
(b)
If the string has a length of 0.9 m, what is the fundamental frequency of the string?
(c)
An organ pipe with an open end and a closed end has a length of 0.531 m, what is the fundamental frequency of the pipe?
(d)
Which are the lowest two harmonics of the pipe that can have resonance with suitable harmonics of the guitar string in part (a)?
(e)
If the organ pipe is placed on a van travelling with a velocity of 2 ms-1 towards the guitarist, what are the beat frequencies detected by the guitarist between the two resonating harmonics of the guitar string and the organ pipe in part (d)? [25]
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3. (a) At a temperature of 300 K, one mole of oxygen gas has a pressure of 1 atm. Considering oxygen as an ideal diatomic gas, how much heat is absorbed by the gas if the temperature of the gas is increased from 300 K to 507 K at constant volume?
(b)
If the temperature of the gas is increased from 300 K to 507 K at constant pressure, how much heat is absorbed by the gas?
(c)
If the temperature of the gas is increased from 300 K to 507 K, and the pressure increases linearly with the volume from 1 atm to 1.3 atm as shown in the figure, what is the work done by the gas?
(d)
In part (c), how much heat is absorbed by the gas? [20]
V1 V2 V
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