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.