[試題] 99上 蔡爾成 普通物理學甲上 期末考

[jimwjma (小馬)]

課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰蔡爾成
開課系所︰機械系
考試日期（年月日）︰2011/1/14
考試時限（分鐘）：120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.[10%](13-59) Three identical stars of mass M form an equilateral triangle

that rotates around the triangle's center as the stars move in a common circle

about that center. The triangle has edge length L. What is the speed of the

stars?

2.[10%](14-65) The figure below shows a stream of water flowing through a hole

at depth h in a tank holding water to height H. At what distance x does the

stream strike the floor?


│    │
├──┼
│↑  │h →
│H   ┼→v
│↓  │
└──┘←─x─→

3.[10%](16-83) A sinusoidal transverse wave of amplitude Ym and wavelength λ

travels on a stretched cord. Find the ratio of the maximum particle speed

(the speed with which a single particle in the cord moves transverse to the

 wave) to the wave speed.

4.[10%](18-63) A wall consisting of four layers with thermal conductivities

k1,k2,k3 and k4. The layer thicknesses are L1,L2,L3 and L4 as shown below.

Energy transfer through the wall is steady. Express the interface temperature

T34 in terms of k1,k2,k3,k4,L1,L2,L3,L4,T1 and T4.




                 ↓T1                    ↓T34   ↓T4
                 ┌───┬───┬───┬───┐
                 │      │      │      │      │
                 │  k1  │  k2  │  k3  │  k4  │
                 │      │      │      │      │
                 └←L1→┴←L2→┴←L3→┴←L4→┘


5.[10%] The damped oscillator satisfies the equation


                 mx'' + bx' + kx = 0
          2
Assuming b < 4mk, find the solution x(t) that satisfies the initial condition

x(0) = Xo and x'(0) = 0.


6.[10%] Explain why the beat frequency for two waves with nearly identical

frequency is |f1-f2|? In other words, explain why the time interval Δt

between two beats or two times of maximum amplitude is  1 / |f1-f2| ?



7.[10%] For a sound wave with bulk modulus B = -V dp/dV, assuming the

displacement is described by s(x,t) and the equilibrium pressure is Po,

show that the pressure

                             ∂s(x,t)
              p(x,t) = Po-B ─────
                               ∂x

8. Given that the Maxwell's probability distribution (density) function of

molecular speeds in a gas
                                  2
                                mv
                             - ──
                           2   2kT
                 P(v) = C v  e


              2
      ∞  -αv       1         1/2
and ∫   e     dv = ─  (π/α)
      0              2


(a)[5%] What is the value of C ?

(b)[5%] show that the average of the kinetic energy

                          m   2     3
                  〈K〉= ─〈v 〉= ─ KT
                          2         2


 9.[10%] For an ideal gas, show that the molar specific heat C  =  C  + R
                                                              p     v

10.[10%] The second law of thermodynamics may be formulated in terms of

entropy change; i.e., in any thermodynamic process that proceeds from one

equilibrium state to another, the entropy of the system + environment remains

unchanged or increases. Show that the alternative statement "there are no

perfect heat engines" for the second law can be deduced from this entropy

statement of the second law.


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