课程名称︰普通物理学甲上 课程性质︰必修 课程教师︰蔡尔成 开课系所︰机械系 考试日期（年月日）︰2011/1/14 考试时限（分钟）：120分钟 是否需发放奖励金：是 （如未明确表示，则不予发放） 试题 : 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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