課程名稱︰力學下 課程性質︰系定必修 課程教師︰楊信男 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2008/04/23 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.(5%)State the postulates of special relativity. 2.(12%)It is possible to produce a neutral pion in an energetic proton-proton collision, i.e., p+p-->p+p+pi0. Find the required minimum kinetic energy of incident proton , in the laboratory frame, for this reaction to take place and the corresponding three-momentum and velocity. Express your results for the energy , three-momentum and the velocity, in units of MeV, MeV/c, amd c, respectively. The masses of the proton and the neutral pion pi0 are Mpc^2=938.27 MeV and mpi0*c^2=134.96 MeV. 3.(15%)A monochromatic light signal with frequency v propagates in a direction that makes an angle of degree 60 with the +x-axis in the reference frame K of its source. In K' frame , the source is moving at speed 4/5c in the +x-direction toward an observer at rest in the K' frame, where his x'-axis is parallel to the x-axis. What are the frequency and direction of the wave as measured in the K' frame? x2' │ │ x2 │ * observer │ │ │ │________________x1' │ │ │______________ x1 4.(18%)Consider a system of n particals. Show the following results. (a)(6%) The total angular momentum about an original is the sum of the angular momentum of the center of mass (CM) about the origin and the angular momentum of the system about the position of CM. (b)(6%) dL ---=N(e) dt where Ni(e) denotes the external torque exerts on particle i, if the internal force are central. (c)(6%) The total kinetic energy of the system is equal to the sum of the kinetic energy of a particle of total mass M moving with the velocity of the CM and the kinetic energy of motion of the individal particles relative to the CM. 5.(10%)A torsion pendulum consists of a vertical wire attached to a mass that may rotate about the vertical. Consider three torsion pendulums that consist of identical wires from which identical homogeneous solid cubes, of mass M and side of length b , are hung. One cube is hung from a corner, one from midway along the edge, and one from the middle of the face. What are the ratio of periods of the three pendulums? Explain/shoe how you obtain your answer. 6.(20%) Chien-Ming Wang is pitching in Yankee stadium at lattitude h in the northen hemisphere, and throws a fastball at velocity v from North to South. Assume the distance between the mound and the home plate is l, and the angular velocity of the earth is w. Ingoring the centrifugal force and correction direction to Coriolis force in the North-South and vertical directions, find the deflection in the east-west direction when the ball reachs the catcher's glove. 7.(20%) Consider a thin disk composed of two homogenous halves connected along a diameter of the disk. If one half has density p and the other half has density 2p. The disk rolls without slipping along a horizontal surface. (a)(5%) Find the center of mass. (b)(5%) Find the moment of inertial with respect tio an axis perpendicular to the disk and through the center of mass. (c)(5%) Find the velocity of the center of mass. (d)(5%) Find the total kinetic energy of the system. --

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