課程名稱︰普通物理學甲上 課程性質︰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）︰2011/01/13 考試時限（分鐘）：10:20~14:00(220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. In Fig. 1, find the rotational inertia of a solid cylinder (mass M) about its central diameter.(10 points) Fig. 1 http://www.wretch.cc/album/show.php?i=bugsblog&b=42&f=1522510948&p=4 2. A blower throws a bowling ball of radius R=11 cm along a lane. The ball (Fig. 2) slides on the lane with initial speed Vcom,0=8.5 m/s and initial angular speed W0=0. The coefficient of kinetic friction between the ball and the lane is 0.21. The kinetic friction force Fk acting on the wall 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 W has increased enough, the ball stops sliding and then rolls smoothly. (a) How long does the ball slide? (b) How far does the ball slide? (c) What is the linear speed of the ball when smooth rolling begins?(3, 3, 4 points) Fig. 2 http://www.wretch.cc/album/show.php?i=bugsblog&b=42&f=1522510949&p=5 3. In Fig. 3, a small 50 g block slides down a frictionless surface through height h=15 cm and then sticks to a uniform rod of mass 100 g and length 35 cm. The rod pivots about point O through angle θ before momentarily stopping. Find θ.(g=9.8 m/s^2)(10 points) Fig. 3 http://www.wretch.cc/album/show.php?i=bugsblog&b=42&f=1522510950&p=6 4. Fig. 4a shows a horizontal uniform beam of mass mb and length L that is supported on the left by a hinge attached to a wall and on the right by a cable at angle θ with the horizontal. A package of mass mp is positioned on the beam at a distance x from the left end. The total mass is mb+mp=61.22 kg. Fig. 4b gives the tension T in the cable as a function of the package's position given as a fraction x/L of the beam length. The scale of the T axis is set by Ta=500 N and Tb=700 N. Evaluate (a) angle θ, (b) mass mb, and (c) mass mp.(4, 3, 3 points) Fig. 4 http://www.wretch.cc/album/show.php?i=bugsblog&b=42&f=1522510951&p=7 5. Find the gravitation force between a circular disk and a particle of mass m, a distance h from the disk as shown in Fig. 5. The circular disk has mass M and radius R.(10 points) Fig. 5 http://www.wretch.cc/album/show.php?i=bugsblog&b=42&f=1522510952&p=8 6. The 3.00 kg cable in Fig. 6 has edge length d=6.00 cm and is mounted on an axle through its center. A spring (k=1200 N/m) connects the cube's upper corner to a rigid wall. Initially the spring is at its rest length. If the cube is rotated 3度 and released, what is the period of the resulting SHM.(10 points) Fig. 6 http://www.wretch.cc/album/show.php?i=bugsblog&b=42&f=1522510953&p=9 7. A uniform rope of mass m and length L hangs from a ceiling. (a) Show that the speed of a transverse wave on the rope is a function of y, the distance from the lower end, and is given by v=(gy)^(1/2). (b) Show that the time a transverse wavetakes to travel the length of the rope is given by t=2(L/g)^(1/2).(4, 6 points) 8. Proof that the speed of sound in a medium with bulk modulus B and density ρ is given by v=(B/ρ)^(1/2).(10 points) 9. Fig. 7 shows a hypothetical speed distribution for a sample of N gas particles (note that P(v)=0 for speed v>2v0). What are the values of (a) vavg/v0, and (b) vrms/v0?(5, 5 points) Fig. 7 http://www.wretch.cc/album/show.php?i=bugsblog&b=42&f=1522510954&p=10 10. In an industrial process the volume of 30.0 mol of a monatomic ideal gas is reduced at a uniform rate from 0.616 m^3 to 0.308 m^3 in 2.00 h while its temperature is increased at a uniform rate from 27.0度C to 450度C. Throughout the process, the gas passes through thermodynamic equilibrium states. What are (a) the cumulative work done on the gas, (b) the cumulative energy absorbed by the gas as heat, and (c) the molar specific heat for the process? (To evaluate the integral for the work, you might use 對x積分((a+bx)/(A+Bx)) = bx/B + (aB-bA)*ln(A+Bx)/B^2 an indefinite integral.)(3, 3, 4 points) 11. Expand 1.00 mol of an monatomic gas initially at 8.00 kPa and 600 K from initial volume Vi=1.00 m^3 to final volume Vf=2.00 m^3. At any instant during the expansion, the pressure p and volume V of the gas are related by p=5.00exp[(Vi-V)/a], with p in kilopascals, Vi and V in cubic meters, and a=1.00 m^3. What are the final (a) pressure and (b) temperature of the gas? (c) How much work is done by the gas during the expansion? (3, 3, 4 points) 12. A box contains N gas molecules. Consider two configurations: configuration A with equal numbers of molecules in all three thirds of the box, and configuration B with equal numbers of molecules in each half of the box divided into two equal parts rather than three. What is the ratio WA/WB of the multiplicity of configuration A to that of configuration B?(10 points) --

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