課程名稱︰普通物理學甲上 課程性質︰必修 課程教師︰蔡爾成 開課系所︰物理系開給大氣系 考試時間︰94/11/07 試題 : (10% for each problem) 1.A block of mass M is pulled along a horizontal (*frictionless) surface by a rope of mass m. A horizontal force F(->) acts on the rope. (a) show that the rope must sag, even if only by an imperceptible amount. Then, assuming the sag is negligible, find (b) the tension in the rope at its midpoint. 2.A student want to determine the coefficients of static friction and kinetic frinction between a box and a plank. She places the box on the plank and gradually raises one end of the plank. When the angle of inclination with horizontal reaches θ, the box starts to slip, and it then slides distance s down the plank in time T at constant acceleration. What are the coeffcient of static friction and the coefficient of kinetic friction between the box and the plank. 3.After a completely inelastic collision, two objects of the same mass and same initial speed are found to move away together at 1/2 their initial speed. Find the angle between the initial velocities of the objects. 4.A rigid rod of length L and negligible mass has a ball with mass m attached to one end and its other end fixed, to form a pendulum. The pendulum is released at rest from horizontal position. At what angle from the vertical does the tension in the rod is equal to weight of the ball? 5.How do we define the potential energy for a conservative force field such that the sum of the kinetic energy and potential energy is a constant? 6.A paticle moves from (0.0.0) to (1,2,3) on a straight line. What's the work done by the force field F(->) =xy i -z^2 j +7x^2 k on this particle? (*i,j,k means unit vectors <1,0,0> <0,1,0> <0,0,1>) 7.What's the force field due to the potential energy field U(x,y,z)=xyz? 8.The total kinetic energy of a system of particles depends on the inertial reference frame. Prove that the total kinetic energy is minimal in the center of mass frame. 9.For the elastic collision of two particles observed in the center of mass frame, show that the initial and final speed for each of two particles remain same. 10.Two particles are of the same mass and one of them is at rest before collision. Show that these two particles move in directions that are perpendicular to each other after an elastic collision. ----------------------------------------------------------------------- 課程名稱︰普通物理甲上 課程性質︰必修 課程教師︰蔡爾成 開課系所︰電機系 考試時間︰2004/11/11 試題 : 1.The potential energy of a diatomic molcule(a two atom system like H2O or O2) is given by U= A/r^12 - B/r^6 (A,B >0) where r is the separation of the two aToms of the molecule and A and B are constants.This potential energy is associated with the force that binds the two atoms together. (a)[5%]Find the equilibrium separation-that is , the distance between the atoms at which the force on each atom is zero. (b)[5%]Is the above equilibrium configuration stable? 2.[10%]Consider a rocket that is in deep space and at rest initially relative to an inertial reference frame.The rocket's engine is to be fired for a certain interval. Derive the rocket equation to evaluate the rocket's mass ratio (ration of initial to final mass) if the rocket's final speed relative to the inertial frame is to be equal to the exhaust speed(speed of the exhaust products relative to the rocket). 3.[10%]A meter stick is held vertically with one end on the floor and is then allowed to fall.Find the speed of the other end just before it hits the floor,assuming the end on the floor does not slip. 4.[10%]The rotational inertia of a collapsing spinning star drops to 1/3 its initial value.What is the ratio of the new rotational kinetic energy? 5.[10%]If the two particals are of the same mass and one of them is at rest before collision,show that these two particals move in directions that are perpendicular to each other after an elastic collision. 6.[10%]Show that the rotational inertia for a thin spherical shell about any axis that is tangent to the spherical shell is 5/3mR^2. 7.[10%]Prove that for a general rigid body motion about a fixed point,the kinetic energy K is given by → → → K=1/2L‧ω → where L is the total angular momentum of the rigid body and ω is the instantaneous angular velocity. 8.[10%]To get a billard ball to roll without slipping from the start,the cue must hit the ball at a hight 2/5R above the center.Prove the result.The rotational inertia for a homogeneous shere is 2/5mR^2. 9.[10%]For a particle in a central force field → ^ ^ ^ F (x,y,z)=g(x,y,z)(xi+yj+zk), prove that the orbit of the particle must be on a plane. 10.[10%]A particleis projected horizontally along the interior of a frictionless hemisherical bowl of radius r,which is kept at rest. We wish to find the initial speed required for the partical to just reach the top of the bowl.Find as a function of θ,the initial angular position of the partical. 考古題版找到的普物甲上期中考就這兩個 --

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