課程名稱︰普通物理學甲上 課程性質︰化學系必修 地質系選修兼通識 課程教師︰王明儒 開課學院：理學院 開課系所︰物理系 考試日期（年月日）︰2019/11/7 考試時限（分鐘）：120min 試題 : 1.Find the transform formula between two orthogonal frames in a plane where the two frames share the same origin and the angle between the x' and x is θ. 2.What's the total displacement for a particle traveling along the x axis between 0 and 5 sec with the accleration as a function of time a(t)=t^2+2t+1m/s? The particle is at rest at t=0 sec. 3.A small object slides along the frictionless loop-the-loop with a diameter of 3m. What's the minimum speed must it have at the top of the loop in order to remain in contact of the loop? Determine the minimum initial height above ground to release the small object at rest to fulfill the above condition. https://imgur.com/rAoL0nH 4.Find the work done by the force F(x,y)=xy^2i+x^2yj alone the line y=3x from the point (0,0) to (1,3). Is the force conservative? 5.A car acclerates form rest through a measured track distance in time T with the engine operating at a constant power P. If the track crew can increase the engine power by dP, what is the change in time required for the run? Assuming that the friction loss in negilible. 6.During a rock slide, a 150kg rock slides from rest down a hillside that is 500m long and 300m high. The coefficient of kinetic friction between the rock and the hill surface is 0.20. What is the speed of the rock as it reaches the bottom of the hill? 7.A body of mass=2.0kg makes an elastic collision with another body at rest and continues to move in the original direction but with one fourth of its original speed. What's the mass of another body? 8.What is the roatational inertia of a uniform cylinder with radius R, length L, and mass M? The rotational axis is passing through the center of mass of this cylinder and is perpendicular to its long side (i.e. with length L). 9.A uniform solid sphere rolls down and incline. What must be the incline angle if the linear accleration of the center of the sphere is to have a magnitude of 0.15g? If a block slides down the incline at that angle with the same 0.15g accleration, what is the coefficient of kinetic friction between the block and the incline? 10.A uniform cube of side length L rests on a horizontal floor. A horizontal push is applied perpendicularly on the middle line of one vertical face of the cube at a distance h above the floor. As the push is slowly increased, the cube will either begin to slide or to tip. Describe a method to determine the coefficient of static friction between the cube and floor. -- 願使歲月靜好，現世安穩。 --

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