課程名稱︰普通物理學甲上 課程性質︰必帶 課程教師︰陳智泓 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰102/12/5 考試時限（分鐘）：110分鐘 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : 普通物理學期中考 Exam hours: 10:20am ~ 12:10pm on 12/5/2013 → 2 ︿ 1. (10%)A force F =(cx-3x ) i acts on a particle as the particle moves along an → axis, with F in newtons, x in meters, and c a constant. At x=0m, the particle's kinetic energy is 19J; at x=4m, it is 11J. Find c. 2 2. An object of mass m is acted on by a conervative force given by F =-Ax-Bx , with F in newtons, x in meters, and A and B positive constants. Take the potential energy associated with the force to be zero when the object is at x=0. (a) (10%) Find an expression for the potential energy as a function of x. (b) (10%) What would be the answer if the potential energy of the system is taken to be -C when the object is at x=0? (c) (10%) If the particle has speed v at some point a distance d to the right of the origin, what speed will it have when it reaches the origin? 3. (10%) In the Fig. (1), block 2 (with mass m ) is at rest on a fritionless 2 surface and touching the end of an unstretched spring of spring constant k. The other end of the spring is fixed to a wall. Block 1 (with mass m ), 1 traveling at speed v , collides with block 2, and the two blocks stick 1 together. When the blocks momentarily stop, by what distance is the spring compressed? State your answer in terms of the given variables. 第三題的圖 Fig. 1: http://ppt.cc/9Ovs 4. The Fig. (2) shows a baseball of mass m just before and just after it → collides with a bat. Just before, the ball has velocity v and angle θ . 1 1 → Just after, it is traveling directly upward with velocity v . The duration 2 of the collisioin is Δt. What are the (a) (5%) magnitude and (b) (5%) direction (relative to the positive directioin of the x axis) of the impulse on the ball from the bat? 第四題的圖 Fig. 2: http://ppt.cc/q-sU 5. In the Fig. (3), a wheel of radius R is mounted on a frictionless horizontal axis. The rotational inertia of the wheel about the axis is I. A massless cord wrapped around the wheel's circumference is attached to a box of mass m. The system is released from rest. When the box has a kinetic energy of K, what are (a) (10%) the wheel's rotational kinetic energy and (b) (10%) the distance the box has fallen? Assume free-call acceleration to be equal to g. 第五題的圖 Fig. 3: http://ppt.cc/KlR2 6. (10%) In the Fig. (4), a small block of mass m slides down a frictionless surface through height h and then sticks to a uniform vertical rod of mass M and length d. The rod pivots about point O through angle θ before momentarily stopping. Find θ. 第六題的圖 Fig. 4: http://ppt.cc/u~Hj 7. (10%) A cockroach of mass m lies on the rim of a uniform disk of mass 3m that can rotate freely about its center like a merry-go-round. Initially the cockroach and disk rotate together with an angular velocity ω . 0 Then the cockroach walks halfway to the center of the disk. What then is the angular velocity of the cockroach-disk system? --

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