課程名稱︰普通物理學 課程性質︰ 課程教師︰林敏聰 開課系所︰電機系 考試時間︰2004.11.11 試題 : 1.please write down and derive the "equivalent" expression of Newton's second law in both translational and angular forms. What are the assumption for their application in classic mechanics? Are those "equivalent" forms really equivalent? Why?(15%) 2.Two particles,each of mass m and speed v,travel in opposite directions along parallel lines separated by distance d.(a)In terms of m,v,and d find an expression for magnitude L of angular momentum of the two-particles system around a point midway between the two lines.(b)Does the expression change if we change the point about which L is calculated?(c)Now reverse the direction of travel for one of the particles and repeat(a)and (b).(15%) 3.Please prove the parallel-axis theorem and calculate the rotational inertial of body(a),(b),(c) (20%) (a) 一圓柱長L 半徑R 參考軸通過圓柱一邊末端的圓心 (b) Solid sphere 直徑2R 參考軸在 Solid sphere 之表面 (c) 一長寬l,t的矩形 軸垂直矩形面 在矩形的一個角上 "這原本應該有圖的"= =|| 4.Consider a damped simple harmonic motion with the total force sigma F=-kx-bv ,where k is force constant of the spring,x the displacement,v the velocity,b the damping constant.Please write down and solve the (differential) equation of motion from Nentow's Sencond Law.(10%) 5.(20%) A small ball with mass m and velocity v moves toward the end of suspend -ed rod ,having mass M and length L and sticks to it after collision. (a) What is the rotational inertia of the rod about the pivot O? (b) What is the angular velocity w after collision? (c) Is this collision completely-inelastic? Why or Why not? (d) If v small enough,find the osillation frequency of the composite system about the pivot. 6.(10%) A spring (k=200N/m) is fixed at the top of a frictionless plane which is inclined at angle θ=40度.A 1.0 Kg block is projected up the plane,from an initial position that is distance d=0.60 m from the end of the relaxed spring,with an kinetic energy of 16 J. (a) What is the kinetic energy of the block at instant it has compressed the spring 0.2m? (b) With what kinetic energy must the block be projected up the plane if it is to stop momentarily when it has compressed the spring by 0.4m? 7.(10%) Block 1 of mass m1 slides from rest along a frictionless ramp from height h=2.50m and then collides with stationary block 2,which has mass m2= 2.00m1.After the collision,block2 slides into a region where the coefficient of kinetic friction μk is 0.500 and comes to a stop in distance d within that region.What is the value of the distance d if the collision is (a) elastic and (b)completely inelastic? 8.Good luck!!!! --

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