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(PHYS011)[2008](f)final~id-^_10525.pdf
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Final Exam PHYS011 (2008, Dec, 13)
(Full grade 90 points)
Attentions:
(1) Steps of your solutions should be given in your answers! Grades are given according to steps.
(2) Steps should include (a) define any physical quantities that appear in your solution but not given in the problems. (b) State what physical laws that you use in your solution.
(3) Hand writing should be clear and recognizable.
1. (10 points) Calculate the following physical properties of the Earth motion.
(a) Translational and rotational kinetic energy
(b) Potential energy due to the Sun gravitation (set the potential at infinite distance as zero)
(c) Linear Momentum
(d) Angular momentum of orbiting the Sun
(e) Angular momentum of its self-rotation
Mass of the Earth: 61024 kg, Radius of the Earth: 6.4x106 m,
Radius of Earth orbit around the Sun: 1.5x1011 m
2. (15 points) A massless spring of spring constant K and equilibrium length L is connected to a block of mass M on a frictionless flat horizontal surface. The other end of the spring is fixed at point O. The block is doing uniform circular motion around O.
(a) Write down the angular frequency . of the blocks motion in term of K, L, M and the circular radius R. What is the highest frequency? At what condition this frequency will be obtained?
(b) Write down the kinetic energy, elastic potential energy and total mechanic energy in term of K, L, M and the circular radius R.
(c) Suppose the kinetic friction coefficient .k between the block and the surface is suddenly becoming non-zero when the block is moving with radius R, the speed of the block is reduced to zero after a time .t. Calculate the average power given by the friction force. Calculate the average torque of the friction force exerted on the block.
3. (15 points) A mass m moves to the right at a frictionless horizontal surface with a speed vi . It strikes and sticks to the end of a stationary rod of uniform mass M and length d. The rod is lying freely on the frictionless horizontal surface.
(a) Calculate the position of the center of the mass of the system at the y direction before and after the collision. Describe the motion of the center of the mass before and after the collision (is it translational, rotational or both?)
(b) Find the translational speed of the system after the collision.
(c) Find the angular speed of the system about its center of mass after the collision.
(d) Calculate the loss in mechanical energy due to the collision.
4. (15 points) A hammer knocks at one end of a Copper rod of length L. At the other end, two vibration pulses are recorded by a sensitive instrument although the hammer only knocks once.
(a) Explain why the instrument records two vibration pulses according to table 12.1 on page 348.
(b) The instrument measures the time interval between the two pulses as 0.01s. What is the length of the rod? (copper densi