課程名稱︰普通物理學甲上
課程性質︰系定必修
課程教師︰梁啟德
開課學院：
開課系所︰材料系
考試日期（年月日）︰2007年11月12日
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1. Three vectors(向量)are given by a=3.0i+3.0j-2.0k, b=-1.0i-4.0j+2.0k, and
c=3.0i+2.0j+1.0k. Please find (a) a‧(bxc) (5%) (b) a‧(b+c) (5%) (c) ax(b+c)
(5%) Hint:Right-hand rule. ixj=k, jxk=i, and ixk=-j, i,j and k are unit
vectors.
2. If a particle travels along a circle or circular arc with radius (半徑) r
at constant speed v, it is in uniform circular motion(等速率圓周運動). Prove
that the particle has an acceleration a of magnitude a=v^2/r (10%)
3. Please solve the following differential equation(微分方程式)
dy(x)/dx=-((a2-x2)^0.5)/x), where a is a constant. Boundary condition: we know
that when x=a, y=0 (10%)
4. A rod lies parallel to the x axis of inertial reference frame S, moving
along this axis at a speed of 0.630c where c is the speed of light in vacuum.
Its rest length is 1.70m. What will be its measured length is frame S? [Hint:
Length contraction and c~3x10^8 m/s]
5. A block of wood floats in water with two-thinds(2/3) of its volume
submerged(浸入). In oil the block floats with 0.90 of its volume submerged.
Find the density of (a) the wood (5%) and (b) the oil. (5%)
6. A solid cylinder is attached to a horizontal massless spring so that it can
roll without slipping along a horizontal surface. The spring constant k is
3.0 N/m. If the system is released from rest at a position in which the sprig
is stretched by 0.25m, find (a) the translational kinetic energy(移動動能)
(5%) and (b) the equilibrium position. (5%) (c) Show(證明) that under these
conditions the center of mass of the cylinder executes simple harmonic motion
with period T=2pi(3M/2k)^0.5, where M is the mass of the cylinder (Hint: Find
the time derivative of the total mechanical energy).
M k
●/\/\/\/\/|
------------
7. Sally (at point A) and Sam's spaceship (of proper length L0) pass each other with
constant relative speed v. Sally measures a time interval of 3.57μS for the
ship to pass her (from the passage point B to the passage point C). (a) What
is the speed parameter β=v/c between Sally and the ship, where c is the speed
of light. (5%). If Sam also measures the passage time of the ship, (b) which
measurement, if either, is a proper time (5%) and (c) which measurement is
smaller (5%)?
Sally
A
‧
----(||||♂||||)→------
C Sam B
8. A 55kg woman runs up a flight of stairs with a height of 4.5m in 3.5s. What
average power(平均功率) is required of her? (10%) [Hint: g=9.8m/s^2]
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※ 編輯: NBL123 來自: 140.112.240.174 (01/15 19:27)
※ 編輯: NBL123 來自: 140.112.240.174 (01/29 16:49)