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(PHYS111)[2009](f)final~=tkk933^_39374.pdf
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Name: _______________ Physics 111 (Fall 2009) ID: __________
Final Examination, 17 December, 2009
Time allowed: 3 hours. Total: 100 marks

Answer all questions. Show all steps. Numerical answers should be given to 3 significant figures. Answer Question 4(b) on the question sheet, and the rest of the questions in the answer book.
Rotational inertia of a disk about center I = MR2/2
Rotational inertia of a rod about center I = ML2/12
Gravitational constant G = 6.67 . 10.11 Nm2kg.2
Mass of Sun MSun = 1.99 . 1030 kg
Distance between Earth and Sun rE = 1 AU = 1.5 . 1011 m
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. (10 marks) A uniform disk of mass m and radius 2r is free to rotate about an axis through its center. A uniform rod of mass 4m and length r lies at the top of the disk, and the centers of the disk and rod coincide, as shown in Fig. 1(a). Initially, the disk and rod rotate together with an angular velocity of 5 rads.1. Then a slight disturbance causes the rod to slide to a distance of r from the disk center, with the rod maintaining a perpendicular direction with the radius through the center of the rod, as shown in Fig. 1(b). Afterwards, the disk and the rod rotate together without further sliding.
(a)
What is their final angular velocity?

(b)
What is the ratio Kf/Ki, where Ki and Kf are the initial and final kinetic energies respectively?


(b)(a)






Fig. 1

Please turn over
1

2. (15 marks) As shown in Fig. 2, a block of mass m = 0.5 kg rests on a horizontal frictionless table. It is attached to the wall by a spring of force constant k = 600 Nm.1. At t = 0, the block is held at a position that extends the spring by x0 = 0.03 m and ejected with an initial velocity v0 = 1.2 ms.1.
(a)
Calculate the period of oscillations of the spring-block system.

(b)
Calculate the amplitude of the oscillations.

(c)
The blocks position is described by x(t) . xm cos(.t ..) . Calculate ..


v

Fig. 2

3. (15 marks) A transverse wave on a string is given by
y(x,t) . (0.21m)sin(20.x . 360.t).

(a)
What are the wavelength, frequency and traveling velocity of the wave?

(b)
The mass per unit length of the string is 0.16 kg per meter. What is the tension of the string?

(c)
The transverse wave is reflected at the fixed end at x = 0.12 m. The reflected wave is given by


yr (x,t) . (0.21m)sin(20.x . 360.t ..).

Calculate ..
4. (10 marks) As shown in Fig. 3(a), a cylinder with the upper end opened is filled with water such that the air column above the water level has a height h. A student held a tuning fork of frequency f at the mouth of a cylinder. He found that when h = 41.9 cm, there is