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(PHYS111)[2010](f)final~=tkk933^_56158.pdf
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Name: _______________ Physics 111 (Fall 2010) ID: __________
Final Examination, 15 December, 2010
Time allowed: 3 hours. Total: 100 marks

Answer all questions. Show all steps. Numerical answers should be given to 3 significant figures. Answer Questions 4(c) and 5(a) on the question sheet using Figs. 4 and 5 respectively, 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 an end I = ML2/3
Gravitational acceleration g = 9.80 ms-2
Gravitational constant G = 6.67 . 10.11 Nm2kg.2
Mass of Moon MM = 7.36 . 1022 kg
Radius of Moon rM = 1.74 . 106 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. (15 marks) As shown in Fig. 1, a physical pendulum consists of a uniform disk with radius r = 0.100 m and mass 0.500 kg attached to a uniform rod with length L = 0.500 m and mass 0.240 kg.
(a)
What is the distance between the center of mass of the pendulum and the pivot point P?

(b)
Calculate the rotational inertia of the pendulum about the pivot point P.

(c)
Calculate the period of oscillation.


2. (10 marks) Consider the physical pendulum with the same structure and parameters as in Question 1. As shown in Fig. 2, a particle with mass 0.100 kg moves at velocity
10.0 ms.1 along a horizontal line through the center of the disk. After colliding with the disk, the particle bounces in the opposite direction with velocity 5.00 ms.1, and the pendulum swings upward.
(a)
Calculate the angular velocity of the pendulum after the impact.

(b)
Calculate the maximum angle that the pendulum swings after the impact.


P P



Fig. 1 Fig. 2
3. (15 marks) A projectile is shot directly away from Moons surface. Neglect the rotation of Moon.
(a)
If the initial speed is . times the escape speed vesc from Moon, calculate the velocity of the projectile when it reaches a distance rM from Moons surface, where rM is the radius of Moon. Give your answer in multiples of vesc.

(b)
If the initial speed is . times the escape speed from Moon, calculate the maximum distance from Moons surface that the projectile can reach. Give your answer in multiples of rM.

(c)
If the initial speed is 2 times vesc, calculate the velocity of the projectile when it is far away from Moon.


4. (15 marks) Figure 3A and B show two snapshots of a transverse traveling wave on a long string.
(a)
Calculate the amplitude, wave velocity, wave number, angular frequency, and frequency of the wave.

(b)
Calculate the wave displacement at x = 5.00 m and t = 0.800 s.

(c)
The wave superposes with another traveling wave in the same direction with the same amplitude, but