課程名稱︰普通物理學甲上
課程性質︰系必修
課程教師︰張寶棣
開課學院：理學院
開課系所︰數學系
考試日期（年月日）︰103.10.23
考試時限（分鐘）：120(有再延長20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.Please answer the following questions.
　　‧Why do we use vector in physics? If we add a constant term to the
　　　potential energy of an object, why doesn't this change the object's
　　　motion? (5%)
　　‧What is inertial frame? What is the advantage to use the center of
　　　mass frame as a reference frame? (5%)
　　‧Velocity and acceleration are frame dependent but force and mass in
　　　classical physics are not. Why is there no conflict for observers
　　　in different frames to describe a motion of an object? Are the laws
　　　of energy and momentum conservations hold in any frame?
　　　Explain your answer? (5%)
2.The water in a river flows uniformly at a constant speed of 2.50 m/s
between two parallel banks 80.0 m apart. You are to deliver a package
directly across the river, but you can swim only at 1.50 m/s. (a) If you
choose to minimize the time you spend in the water, in what direction
should you head? (b) How far downstream will you be carried? (c) What if?
If you choose to minimize the distance downstream that the river carries
you, in what direction should you head? (d) How far downstream will you be
carried? (16%)
3.To prevent a box from sliding down an inclined plane, student A pushes
on the box in the direction parallel to the inclined, just hard enough to
hold the box stationary. In an identical situation student B pushes on the
box horizontally. Regard as known the mass m of the box, the coefficient
of static fricion μs between box and incline, and the inclination angle θ.
(a) Determine the force A has to exert. (b) Determine the force B has to
exert. (c) If m = 2.00 Kg, θ = 25.0°, and μs = 0.160, who has easier
job? (d) What if μs = 0.380? Whose job is easier? (12%)
4.Two curved inclines of two identical wedge-shaped masses M smoothly merge
with a horizontal frictionless surface as indicated in Fig. 1. The curved
surfaces of the inclines are also frictionless. Another mass m is released
at rest from a height h on one of the inclines. (a) When m reaches the
horizontal plane, is the mechanical energy of m and M conserved? Is the
total momentum of m and M conserved when m reaches the horizontal surface?
Why?(5%) (b)After m reaches the horizontal plane, it encounters the
right-hand wedge and ascends it to some height h'? Please explain.(5%)
(c)Please express h'? in terms of m, M, and h using the ideas in (a) and
(b).(10%)
Ｍ Ｍ
│\▄← m /｜↑
│﹨ ∕｜｜
│ \ / ｜｜
│ Λ Λ ｜｜
│ ﹨ ∕ ｜｜
│ ﹨ 兩個物體「相連」 ∕ ｜｜h
│ ˋ 但是沒有「相黏」 ˊ ｜｜
│ ╲ ╱ ｜｜
｜ ╲ │ ╱ ｜｜
｜ ︿ ↓ ︿ ｜｜
｜ ‵*-,,-*′ ｜↓
￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣￣
FIG. 1: An object slides in two identical blocks. (圖改自99-1考古題)
5.A ball at the end of a pendulum of length L is released at rest from an
initial position in which the pendulum string is horizontal (Fig. 2) The
floor is just beneath the low point of the swing. The string is cut after
the ball has passed the low point with the string at an angle α = θ- 90
to the vertical. Find the horizontal distance that the ball travels from
the low point before it bounces on the floor. (7%)
＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿＿
　　　　　　　｜←－Ｌ－→
　　　　　　　○－－－－－●ｍ
　　　　　　／θ
　　　　　／
　　　　／(cut)
　　　／ String is cut at
　　／ angle θ
　●
　　　　　　Fig. 2
6.A curve of radius 30 m is banked so that a 950-kg car traveling at
40.0 km/h can round it even if the road is so icy that the coefficient
of static friction is approximately zero. You are commissioned to tell
the local police the range of speeds at which a car can travel around
this curve without skidding. Neglect the effects of air drag and rolling
friction. If the coefficient of static friction between the road and the
tires is 0.300, what is the range of speeds you tell them? (8%)
7.A 5-kg block is held against a spring of force constant 20 N/cm,
compressing in 3 cm. The block is released and the spring extends,
pushing the block along a rough horizontal surface. The coefficient of
friction between the surface and the block is 0.2. (a) Find the work done
on the block by the spring as it extends from its compressed position to
its equilibrium position. (b) Find the energy dissipated by friction while
the block moves 3 cm to the equilibrium position of the spring. (c) What
is the speed of the block when the spring is at its equilibrium position?
(d) If the block is not attached to the spring, how far will it slide along
the rough surface before coming to the rest? (20%)