課程名稱︰普通物理學甲 課程性質︰化工系必帶 課程教師︰梁啟德 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2015/11/12 考試時限（分鐘）：120分鐘 試題 : 1.If a particle travels along a circle or circular arc with radius r at constant speed v, it is i uniform circular motion. prove that the particle has an accerleration a of magnitude a=v^2/r 2.Three vectors are given by → ^ ^ ^ → ^ ^ ^ a=3.0i+3.0j-2.0k, b=-1.0i-4.0j+2.0k → ^ ^ ^ → →→ → → → → → → c=2.0i+2.0j+1.0k. Please find (a) a‧(bxc)(5%)(b) a‧(b + c)(5%)(c) ax(b + c) 3.The kinetic energy K at a high speed is given by K=mc^2x[(1/√1-(v/c)^2)-1] where c is the speed of light in vacuum, v is the velocity of the particle and m is the mass of the particle. Please prove that in the classical limit (v<<c) , K~1/2mv^2 (10%). ~ 4.A particle of mass 1.18 kg is attached between two identical springs on a horizontal, frictionless table top. Both springs have sprinig constant k and are initially unstressed. (a) The particle is pulled a distance x along a direction perpendicular to the initial configuratioin of the spring as shown in Fig.1. Please prove that the force exerted by the springs on the particle is given by → ▁▁▁▁ ^ ^ F=-2kx(1-L/√x^2+L^2 )i, where i is the unit vector in the x-axis (10%). (b)Please prove that the potential energy of the system is given by U(x)=kx^2+2kL(L-√x^2+L^2) (10%) http://imgur.com/a/MJBO2 top view 5.Please prove that the rotational inertia of a slab(mass M)about perpendicular axis through its center is given by M I=—(a^2+b^2) (10%). Please 12 see Fig.2 http://imgur.com/wRCEnPV 6.Please prove that the rotation inertia of a hoop(mass M) about any diameter is given byI=MR^2/2 (5%).[Hint:Perpendicular axis theorem] Please see Fig.3 http://imgur.com/X5gkpwe 7.Please explain, in your own words, what is an inertial reference frame(10%)? 8.Suppose the coefficient of static friction between the road and the tires on a Formula One car is 0.60 during a Grand Prix auto race. What speed will put the car on the verge of sliding as it rounds a level curve of 30.5 m radius? 9.A spaceship of rest length 100m races past a timing station at a speed of 0.60c. (a)What is the length meausured by the timing station?(5%).(b)What time interval will the station clock record between the passage of the front and back ends of the spaceship?(5%)[Hint:Length contraction] -- A census taker once tried to test me. I ate his liver with some fava beans and a nice chianti. --

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