課程名稱︰普通物理學甲上 課程性質︰電機系必修 課程教師︰賀培銘 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰107/11/8 考試時限（分鐘）： 是否需發放獎勵金：是 試題 : 1. (30%) Which one (ones) of the following is (are) correct? (a)For arbitary vectors A and B, we always find A‧(A X B) = 0 and B‧(A X B) =0. (b)The Coriolis force in a rotating reference frame with constant angular vel- ocity is parallel axis of rotation. (c)For planets with elliptic orbits, the sun is located in the middle of the two foci. (d)The magnitude of the centripetal force for the uniform circular motion with velocity v and radius R for an object of mass m is mv^2/R^2. (e)The force F=2xy ^x + x^2 ^y is conservative. (f)The gravitational potential nergy of a mass m inside a spherical shell of mass M is independent of its location, as long as it is inside the hollow she- ll. (g)Fix one end of a rope on the edge of the table and let go of the other end of the rope. For the rope in this process, its toalt momentum is conserved. (h)When the x-component of the total external force vanishes, the x-component of the total momentum of a system is not necessarily conserved because the y-component of the total external force may be non-zero. (i)When you push a box to move on the floor, the work done bu the friction to the floor equals the heat created in the process. (j)A point particla moving in 1D with the acceleration a(t) = t. If it starts at x = 0 and v = 0 at t = 0, we find x(t) = (t^3)/2 2. (10%) A block of mass M moves down a slide (at angle theta) from rest at height h, pulling a box of mass m up through a string over a pulley. (See fig- ure on the right.) Assume that the frictions and the masses of the pulley and the string can all be ignores. How fast is the block moving when it reaches the bottom of the slide? 3. (10%) Two blocks of amsses M1 and M2 are pressed together on a frictionless , horizontal surface, compressing a light spring of spring constant k between them by the change of ΔL in the length of the spring. The two blocks are rel- eased simultaneously from rest. What is the maximal speed of each block? 4. (15%) (a)What is the gravitational potential energy of a thin shell of radius R and mass M? (b)What is the gravitational potential energy of the system composing of two concentric thin shells of radius R1, R2 and masser M1, M2, respectively? Assume that both shellsare uniform and R2 > R1. (Do not forget the energies of the shells themselves.) 5. (15%) Two pieces of clat of equal mass m with initial velocities v1 =^xa + ^yb and v2 = ^xc + ^yd collide and then they are turned into one big piece of clat of mass 2m. (ignore all other forces.) (a, b, c, d are constant.) (a)What is the final velocity of the big piece of clay? (b)What is the center-of-mass velocity of the system? (c)How much kinetic energy is turned into heat? 6. (20%) The polar coordinates of a point particle of mass m moving on the x-y plane are r(t) = (v0)t and θ(t) = (ω0)t, where v0 and ω0 are constant. (1)What is the velocity v(t) in polar coordinates? (2)What is the acceleration a(t) in polar coordinates? --

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