課程名稱︰普通物理學甲
課程性質︰系定必修
課程教師︰梁啟德
開課學院：
開課系所︰
考試日期（年月日）︰97年11月11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 = 2.0i + 2.0j + 1.0k. Please find (a) a dot b cross c (5%) (b)
a dot (b + c) (5%) (c) a cross (b + c) (5%) [Hint right-hand rule, i, j, and
k are the unit vectors in the x-, y- and z- directionsn, respectively.]
2. Please explain, in your own words, what is an inertial reference frame (10%)?
3. Certain neutron stars are believed to be rotating at about 1 rev/s. If such
a star has a radius of 20 km, what must be its minimum mass so that material
on its surface remains in place during the rapid rotation (10%)? [Hint: The
gravitational constant G = 6.67 * 10^-11 N m^2/kg^2]
4. The position of a particle is given by x(t) = 4 + ln(t)cos(2t) where t is
the time in units of second. Please find the velocity v(t)(5%) and the
acceleration a(t)(5%) [Hint: ln(t) = log_e (t), where e is a mathematical
constant, the base of the natural logarithm, which equals approximately
2.718281828, and is also know as Euler's number. e^x is the exponential
function. de^x/dx = e^x]
5. A block of wood floats in water with two-thirds (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. The system in Fig. 1 is in equilibrium. A concrete block of mass 225 kg
hangs from the end of the uniform strut of mass 45.0 kg. For angles φ=30.0°
and θ=45.0°, find (a) the tension T (5%) in the cable and (b) horizontal
(5%) and (c) vertical components (5%) of the force on the strut from the
hinge. [Hint: sin15°≒0.2588]
／∕∕
T ／ ∕∕|
／ ∕∕ |
／ ∕∕ ▓←(block)
／ ∕∕←(strut)
／φ ∕∕θ
￣￣￣ (Hinge)￣￣￣￣￣
7. A horizontal vinyl record of mass 0.10 kg and radius 0.10 m rotates freely
about a vertical axis through its center with an angular speed of 4.7 rad/s.
A wad of wet putty of mass 0.020 kg drops vertically onto the record from
above and sticks to the edge of the record. What is the angular speed of the
record immediately after the putty sticks to it (10%)?
8. Figure 2 shows a stream of water flowing through a hole at depth h = 10 cm
in a tank holding water to heitht H = 40 cm. (a) At what distance x does the
stream strike the floor? (5%) (b) At what depth should a second hole be made
to give the same value of x? (5%)
│ ｜
├───────┤
│↑ ↑｜
│｜ h｜
｜｜ ↓｜ v→
│ H →→→(水噴出來的地方)
｜｜ ｜
│｜ ｜
│↓ ｜
└───────┘←─x─→≡（水落地的地方)
9. 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 1.70 m. What will be its measured length is frame S?
(10%) [Hint: Length contraction]
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