推 vchenkoshe :梁啟德必推 11/12 17:47
※ 編輯: newacc 來自: 140.112.240.3 (11/12 18:32)
※ 編輯: newacc 來自: 140.112.240.3 (11/12 19:48)
課程名稱︰普通物理學甲
課程性質︰系訂必修
課程教師︰梁啟德
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰98/11/12
考試時限（分鐘）：110(13:20-15:10)
是否需發放獎勵金：是，謝謝
（如未明確表示，則不予發放）
試題 :
1.Please explain, in your own words, what is an inertial reference frame (10%)?
2.Three vectors (向量) are given by a = 3.0i + 3.0j - 2.0k,
b = -1.0i - 4.0j + 2.0k, and c = 2.0i + 2.0j + 1.0k. Please find (a) a‧b×c
(5%) (b) a‧(b+c) (5%) (c) a×(b+c) (5%) [Hint right-hand rule, i, j, and k
are the unit vectors in the x-, y- and z- directions, respectively.]
3.A supertrain (rest length 100.0 m) travels at a speen of 0.9500c as it passes
through a tunnel (proper length 50.00m). As seen by a trackside observer, is
the train ever completely within the tunnel? (5%) If so, how much space is
there to spare (tunnel length minus the train length)? (5%) [c=3*10^8 m/s]
4.Please prove that the relativistic expression for the kinetic energy of a
particle is given by 1
K=(--------------- -1)mc^2
√[1-(v/c)^2]
where v is the speed of the particle, c is the speen of light and m is the
rest mass (靜止質量) of the particle, respectively. (5%) Please show that in
the low speed limit v<<c, the kinetic energy is given by K=1/2 mv^2 (5%).
5.Figure 1 represents the total acceleration of a particle moving clockwise in
a circle of radius 2.50m at a certain instant of time. At this instant, find
(a) the radial acceleration (徑向加速度), (5%) (b) the speed of the particle,
(5%) and (c) its tangential acceleration (切線加速度) (5%).
︵
. * * . a=15.0m/s^2
.* ／＼ θ=30.0度
.` ／ / ＼
: ／θ/ :↘v向量
(←2.50m→。 a向量 )
: :
`. .`
。 。
`‧. .‧`
︶
6.A particle of mass 1.18 kg is attached between two identical springs on a
horizontal, frictionless tabletop. Both springs have spring constant k and
are initially unstressed.
(a) The particle is pulled a distance x along a direction perpendicular to
the initial configuration of the springs as shown in Fugure 2. Show that the
force exerted by the springs on the particle is L
F=-2kx(1- -------------)i
(5%) √(x^2+L^2)
(b) Show that the potential energy of the system is given by
U(x) = kx^2 + 2kL(L-√(x^2+L^2) (5%)
┌──────┬────────────┐
│ │ ＼k │
│ L│x ＼ │
├──────┼───m───────→x┤
│ │ ／ │
│ L│ ／ │
└──────┴────────────┘
7.A 5.00-kg block is set into motion up an inclined plane with an initial speed
of 8.00 m/s (fig. 3). The block comes to rest after traveling 3.00 m along
the plane, which is inclined at an angle of 30.0度 to the horizontal. For
this motion, determine (a) the change in the block's kinetic energy, (5%) (b)
the change in the potential energy of the block-Earth system, (5%), (c) the
friction force exerted on the block (assumed to be constant). (5%) (d) What
is the coefficient of kinetic friction? (5%)
v=8.00m/s ╲ ╱▏
↗ 3.00m ◇╱ ▏
╲ ╱ ▏
◇╱ ▏
╱ ▏
╱ 30度 ▏
￣￣￣￣￣￣
8.What horizontal force must be applied to the cart shown in Figure 4 so that
blocks remain stationary relative to the cart? Assume all surfaces, wheels,
and pulley are frictionless. Notice that the force exerted by the string
accelerates m1.(10%)
┌─┐
│m1├─────╮
┌──┴─┴────◎│
│ ├┴┐
F →│ M │m2│
│ ├─┘
└─⊙─────⊙─┘
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