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課程名稱︰普通物理甲上
課程性質︰系定必修
課程教師︰趙治宇
開課學院：工學院
開課系所︰化工系
考試日期（年月日）︰97.01.17
考試時限（分鐘）：180分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Final Exam Instructor: CY Chao
1.When n moles of an ideal gas doubles its volume in a free expansion. Derive
the entropy change is nRln2 using (1)thermodynamics and (2)statistical
mechanics.(5%,5%)
2.Derive the gravitational force at a point P, a distance z from a disk along
its central axis. This disk is uniform, and radius R and total mass M.(8%)
(The mass of the point is m)
3.Three waves y(x,t)1,y(x,t)2, and y(x,t)3 have the same wavelength and travel
in the same direction along a string. Their amplitudes are ym1=4.0mm, ym2=3.0mm
, and ym3=5.0mm, and their phase constant are 0, π/3, and π/2 rad,
respectively. What are the amplitude y'm and phase constant β of the result
wave?(4%,4%)
4.Describe (a)the evidence of the universe expansion. (b)the working principle
of laser cold trapping invented by Prof. Steven Chu.(2%,4%)
5.(a)Describe the working principle of a strain gauge for small strain
measurements. (b)Design an experiment to accurately measure the moment inertia
of any-shaped object.(4%,4%)
6.Two cylinders with radii R1 and R2 and rotational inertias I1 and I2 about
the central axis are supported by axes perpendicular to plane of Fig.1. The
large cylinder is initially rotating with angular velocity ω0. The small
cylinder is moved to the right until it touches the large cylinder and is
caused to rotate by the frictional force between the two. Eventually, slipping
ceases, and the two cylinders rotate at constant rates in the opposite
directions. Find the final angular velocity ω2 of small cylinder in terms of
I1, I2, R1, R2, and ω0.(10%)
7.A bowler throws a bowling ball of radius R=11cm along a lane. The ball(Fig.1)
slides on the lane with initial Vcom,0=8.5m/s and initial angular speed ω0=0.
The coefficient of kinetic friction between the ball and the lane is 0.21. The
kinetic frictional force fk acting on the ball causes a linear acceleration of
the ball while producing a torque that causes an angular acceleration of the
ball. When speed Vcom has decreased enough and angular speed ω has increased
enough, the ball stop sliding and then rolls smoothly. (a)How long does the
ball slide? (b)How far does the ball slides? (c)What is the linear speed of the
ball when smooth rolling begins?(3%,3%,4%)
8.In Fig.2, a solid cylinder attached to a horizontal spring(k=3.00N/m) rolls
without slipping along a horizontal surface. If the system is released from
rest when the spring is stretched by 0.250m, find the period of this simple
harmonic motion under these conditions.(8%)
9.The p-V diagram in Fig.3 shows two paths along which a sample of gas can be
taken from state a to state b, where Vb=3V1. Path 1 requires that energy equal
to 5.0p1V1 be transferred to the gas as heat. Path 2 requires that energy equal
to 5.5P1V1 be transferred to the gas as heat. What is the ratio p2/p1?(6%)
10.(a)For an ideal gas, prove that the relation between the pressure and volume
during an adiabatic process is PV^γ=constant, where γ=Cp/Cv.(b)1 mol oxygen
(O2) at initial pressure 2 atm undergoes an adiabatic expansion from an initial
volume of 12L to a final volume of 19L. What is the work done by the gas during
this volume change?(6%,4%)
11.In Fig.4, and aluminum wire, of length L1=60.0cm, cross-sectional area
1.00×10^-2cm^2, and density 2.60g/cm^3, is jointed to a steel wire, of density
7.80g/cm^3 and the same cross-sectional area. The compound wire, loaded with a
block of mass m=10.0kg, is arranged so that the distance L2 from the joint to the
supporting pulley is 86.6cm. Transverse waves are set up on the wire by an
external source of variable frequency; a node is located at the pulley. (a)Find
the lowest frequency that generates a standing wave having the joints one of
the nodes. (b)How many nodes are observed at this frequency?(4&,4%)
12.A certain triple-star system consists of two stars, each of mass m,
revolving in the same circular orbit of radius r around a central star of mass
M(Fig.5). The two orbiting stars are always at opposite ends of a diameter of
the orbit. Derive an expression for the period of revolution of the stars.(8%)
P.S. All figures comes from Fundamentals of Physics Eight Edition
Fig.1 of No.6 P.271 FIG. 10-51
Fig.1 of No.7 P.298 FIG. 11-37
Fig.2 P.412 FIG. 15-60
Fig.3 P.506 FIG. 18-58
Fig.4 P.442 FIG. 16-45
Fig.5 P.358 FIG. 13-54
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