課程名稱︰普通物理學甲上 課程性質︰物理系必修 課程教師︰高涌泉 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰99/11/18 考試時限（分鐘）：110分鐘 （10:20 ~ 12:10） 是否需發放獎勵金：是 1.(15%) At time t=0, a ball of mass m is dropped off from the top of a high building. Assume that the air resistance is proportional to the speed v and the damping coefficient is b. Solve the equation of motion for the speed v of the ball at a later time t (before it reaches the ground). 2.(10%) We are told that an object of mass m moves on a plane and its position is given by (t=time) x(t)=C1(t^2)+C2t y(t)=C3t +C4 with C1, C2, C3, C4 constants. Find the potential function U(x,y) for the total force acting on the object. 3.(10%) Suppose we have a mass m attached to a spring of spring constant R. The mass slides on a rough surface with coefficient of sliding friction μ. The mass starts from rest with the spring extended in the positive direction to a distance A. How large must μbe so that we get an "overdamped" situation? You can assume that the static friction plays no role here. 4.(15%) Suppose that the radius of the Earth decreased uniformly by 1% without any change in mass. What would be the change in the kinetic energy of rotation (spin)? 5.(15%) A solid uniform cylinder of mass M and radius R is projected up an inclined plane with angle θ.It rolls without slipping from an initial speed Vo of the center of mass. What distance S does the center of the cylinder travel before it starts to fall back? 6.(15%) A solid uniform cylinder of mass m and radius R is fitted with a frictionless axle along the cylinder's long axis. A horizontal spring (spring constant k) is attached to the axis (see fig.1). Under the influence of the spring, the cylinder rolls back and forth without slipping on a horizontal surface. What is the frequency of this motion? ╭╮ ╰╯ │ ／ ／---～～～～---┤ ╭╮ │ ╰╯ 圓柱 彈簧 牆面 圖畫的不好...請見諒 裝置大致上就是滾筒狀的 7.(20%) Explain (a)resonance in forced (driven) harmonic motion ; (b)how Newton explained Kepler's 2nd law in his "Principia". ※ 編輯: ray86047 來自: 140.112.4.196 (11/18 16:53)