課程名稱︰普通物理學乙
課程性質︰必修
課程教師︰蔡爾成
開課系所︰
考試時間︰2006.04.26 15:30~17:20
試題 :
1. [10%](a)[5%] What is "work-energy" theorem? 何謂"work-energy"定律？
(b)[5%] What is "conservative force field"? 何謂保守力場？
2. [10%] Deduce Kepler's third law from Newton's universal law of gravity.
T^2
i.e., show that ─── is the same for any two planets about the sun.
r^3
Assuming the orbit of any planet is a circle with radius r. 由萬有引力
T^2
定律，導出星球運動 ─── 對每星球皆相同，假設星球軌道為半徑 r 之圓。
r^3
3. [10%] Our lungs contain hundreds of millions of alveoli. Explain how and
why we may exhale without muscle action with the help of these alveoli.
人體有上億肺泡，解釋為何這些肺泡可使人類呼氣而不須肌肉動作。
4. [10%] For an ice skater spinning on the tip of her skate with her arms
extended initially, explain why her rate of spin increases when she pulls
in her arms. 一溜冰舞者開始旋轉時手臂伸出，解釋為何手臂網內收縮時旋轉加速。
5. [10%] Assume the initial speed of one mass is v_1 and the initial speed
of the other mass is zero. (a) Prove that for a collision of equal masses,
1 2 1 2 1 2
─ m v_1 = ─ m v_1' + ─ m v_2' + m v_1' v_2' cosθ where θ is the
2 2 2
angle between the velocities of the two masses after collision, and the
final speeds after collision are v_1' and v_2'.
(b) Show θ us a right angle if the aforementioned collision is elastic.
6. [10%] The moment of inertia of a long rod spun about an axis through one
end perpendicular to its length is ML^2/3. Why is the greater than it would
be if you spun a point mass M at the location at the center of mass of the
rod (at L/2)?
7. [10%] What is the final velocity of a hoop that rolls without slipping down
a hill of height h, starting from rest?
8. [10%] The flow rate of blood in a coronary artery has been reduced to half
its normal value by plaque deposits. By what factor has the radius of the
artery been reduced, assuming no turbulence occurs? given
(1/2)^(1^2) = 0.707, (1/2)^(1^3) = 0.794,(1/2)^(1^4) = 0.841,
(1/2)^(1^5) = 0.871, (1/2)^(1^6) = 0.891.
9. [10%] When water freezes, its volume increase by 9.05% (i.e.,
-2
ΔV/V = 9.05 * 10 ). What force per unit area is water capable of exerting
9 2
on a container when it freezes? The Bulk modus for water is 2.2 * 10 N/m .
10. [10%] Write down the Bernoulli's equation in Fluid Dynamics. For every
variable in this equation, you need to explain what the corresponding
physical quantity is. For example, we may have g in this equation and then
you need to say that g is the acceleration of gravity. (But you do not need
to derive this equation.) 寫下 Bernoulli's equation 且說明方程式內每一變數
含意。
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※ 編輯: Nzing 來自: 140.112.240.198 (04/26 18:00)