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推 liuzihau:樓上0分! 11/03 23:16
課程名稱︰普通物理甲
課程性質︰大一必修
課程教師︰梁啟德
開課系所︰
考試時間︰2004.11.13
試題 : → → → →?→ →
1.Three vectors (向量) are given by a = 3.0 i + 3.0 j -2.0 k , b = -1.0 i
→ → → → → →
- 4.0 j + 2.0 k ,and c = 2.0 i + 2.0 j + 1.0 k .Please find
→ → →
(a) a ˙ ( b ×c ) (5分)
→ → →
(b) a ˙ ( b + c ) (5分)
→ → →
(c) a × ( b + c ) (5分)
2.If a particle travels along a circle or circular are with radius(半徑)
γ at constant speed ν,it is in uniform circular motion(等速率圓周運動)
Prove that the particle has an acceleration a of magnitude a=ν^2/γ.
(10分)
3.Please prove the parallel axis theorem(平行軸定理)Ι=Ιcm + Μh^2 where
Ι is the rational inertia(轉動慣量)of a body about any axis,Ιcm is the
rational inertia of the body about an axis that passes through its center
of mass(質心),h is the perpendicular distance between the two axes ,and
Μ is the mass of the body.(10分)
4.The position of a particle is given by x(t)=4+ln(t)sin(2t) where t is the
time in units of second.Please find the velocity v(t)(5分)and the
acceleration a(t)(5分)
5.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分)
6.Two particles of equal masses have an elastic collision,the target particle
being initially at rest.Show that(unless the collision is head-on),the two
particles will always move off perpendicular to each other after the
collision(碰撞後兩者運動方向互相垂直)(10分)
7.The two blocks(with m = 16kg and M = 88kg)shown in Fig.1 are not attached.
The coefficient of static friction between the blocks is μs=0.38 but the
surface beneath the larger block is frictionless. →
What is the minimun magnitude of the horizontal force F required to keep
the smaller block from slipping down the larger block?(10分)
m
┌───┬──────┐
│ → │ │
│ F │ │
└───┤ M │frictionless
│ │ ↓
────┴──────┴───
Fig.1
8.A 2.0kg block is dropped from a height of 0.40m onto a spring constant
k=1960N/m(Fig.2).Find the maximun distance the spring is compressed(10分).
┌───┐
│ 2.0kg│
└───┘┬ ─
│ ↑
│ 40cm
│ ↓
─── ┴ ─
╲
／
╲
／ k=1960N/m
╲
╱
───
Fig.2
9.In your own words,please explain what a conservative force(保守力)is?(10分)
Can you name one conservative force?請舉例說明一保守力(5分)
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課程名稱︰普通物理甲上
課程性質︰必修
課程教師︰李文忠老師
開課系所︰化工系
考試時間︰2004/11/11
試題 :
1.如圖所示，小木塊 m 及斜面大木塊 M，所有摩擦力皆為零； ◣◥◣ ← m
→ → █◣
試寫出 m 及 M 之加速度 am 及 aM 滿足之必要方程式 ██◣
→ → ███◣
(不必解出am 及 aM) M → ████◣
2.如圖所示，一球質量 M ，半徑 R ，滾下一仰角 β 之斜坡
(1)求球之角加速度α (2)球摩擦力 fμ ◣○
█◣
██◣
███◣
████◣
==================================================================================
課程名稱︰普通物理學
課程性質︰
課程教師︰林敏聰
開課系所︰電機系
考試時間︰2004.11.11
試題 :
1.please write down and derive the "equivalent" expression of Newton's second
law in both translational and angular forms. What are the assumption for
their application in classic mechanics? Are those "equivalent" forms really
equivalent? Why?(15%)
2.Two particles,each of mass m and speed v,travel in opposite directions along
parallel lines separated by distance d.(a)In terms of m,v,and d find an
expression for magnitude L of angular momentum of the two-particles system
around a point midway between the two lines.(b)Does the expression change if
we change the point about which L is calculated?(c)Now reverse the direction
of travel for one of the particles and repeat(a)and (b).(15%)
3.Please prove the parallel-axis theorem and calculate the rotational inertial
of body(a),(b),(c) (20%)
(a) 一圓柱長L 半徑R 參考軸通過圓柱一邊末端的圓心
(b) Solid sphere 直徑2R 參考軸在 Solid sphere 之表面
(c) 一長寬l,t的矩形 軸垂直矩形面 在矩形的一個角上
"這原本應該有圖的"= =||
4.Consider a damped simple harmonic motion with the total force sigma F=-kx-bv
,where k is force constant of the spring,x the displacement,v the velocity,b
the damping constant.Please write down and solve the (differential) equation
of motion from Nentow's Sencond Law.(10%)
5.(20%) A small ball with mass m and velocity v moves toward the end of
suspend
-ed rod ,having mass M and length L and sticks to it after collision.
(a) What is the rotational inertia of the rod about the pivot O?
(b) What is the angular velocity w after collision?
(c) Is this collision completely-inelastic? Why or Why not?
(d) If v small enough,find the osillation frequency of the composite system
about the pivot.
6.(10%) A spring (k=200N/m) is fixed at the top of a frictionless plane which
is inclined at angle θ=40度.A 1.0 Kg block is projected up the plane,from
an initial position that is distance d=0.60 m from the end of the relaxed
spring,with an kinetic energy of 16 J.
(a) What is the kinetic energy of the block at instant it has compressed the
spring 0.2m?
(b) With what kinetic energy must the block be projected up the plane if it
is to stop momentarily when it has compressed the spring by 0.4m?
7.(10%) Block 1 of mass m1 slides from rest along a frictionless ramp from
height h=2.50m and then collides with stationary block 2,which has mass m2=
2.00m1.After the collision,block2 slides into a region where the coefficient
of kinetic friction μk is 0.500 and comes to a stop in distance d within
that region.What is the value of the distance d if the collision is
(a) elastic and (b)completely inelastic?
8.Good luck!!!!
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3.設位能 U(r) = A/r^12 － B/r^6 ， A、B 皆大於 0 ，
→
求 F(r) ， 以及平衡點 r 之值 ， 分析其穩定與否 ，
畫出 U 及 F 與 r 之相依圖
→ → →
4. 一直點作直線運動，其受力 F ＝ －r v ， v 為其速度 ， r 為阻力係數 ，
已知 v(0) = v0 ， x(0) = x0
(1) 求 v(t) (2) 求 x(t)
5.推導在地球重力場中之火箭運動(Rocket motion)之運動方程式
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