課程名稱︰普通物理學乙
課程性質︰系定必修
課程教師︰蔡爾成
開課學院：
開課系所︰職治
考試日期（年月日）︰2007/4/18
考試時限（分鐘）：120
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.[10%]
(a)[5%]
What is the "work-kinetic energy theorem" for a particle? (Hint:What is the
relationship between the change of kinetic energy and the work done on a
particle.)
(b)[5%]
A bullet of mass m moving at a horizontal speed of v comes to a stop at a
distance d within a solid wall. What is the magnitude of the average force
from the wall stopping it?
2.[10%]
An object, with mass m and speed v relative to an observe, explodes into two
pieces, one three times as massive as the other; the explosion takes place in
deep space. The less massive piece stops relative to the observer. How much
kinetic energy is added to the system during the explosion, as measured in
the observer`s reference frame?
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 and just before it hits the floor,
assuming that the end on the floor dose not slip. Note that for a rod of mass
M and length L, the rotational inertia with respect to an axis perpendicular
to the rod and passing through the end point of the rod is 1/3ML^2.
4.[10%]
A body of radius R and mass m is rolling smoothly with speed v on a horizontal
surface. It then rolls without sliding up a hill to a maximum height h. If
h = 3v^2/4g , what is the body`s rotational inertia about the rotational axis
through its center of mass?
5.[10%]
A beam of length L is carried by three men, one man at one end and the other
two supporting the beam between them on a crosspiece placed so that the load
of the beam is equally divided among the three men. How far from the beam`s
free end is the crosspiece placed? (Neglect the mass of the crosspiece.)
6.[10%]
Asumme a planet is a uniform sphere of radius R that has a narrow radial
tunnel through its center. Also assume we can position an apple anywhere along
the tunnel or outside the sphere. Let F_R be the magnitude of the gravitational
force on the apple when its is located at the planet`s surface. How far from
the surface is there a point where the magnitude of the gravitational force on
the apple is 1/2F_R if we move the apple(a)[5%] away from the planet and (b)
[5%] into the tunnel?
7.[10%]
Water is moving with a speed of v_0 through a pipe with a cross-sectional area
of A. The water gradually descends a distance of h as the pipe cross-sectional
area increase to 2A. (a)[5%] What is the speed at the lower level? (b)[5%] If
the pressure at the upper level is P_0,what is the pressure at the lower level?
8.[10%]
Two particles are of the same mass and one of them is at rest before collison.
Prove that these two particles move in directions that are perpendicular to
each other after an elastic collision.
9.[10%]
A planet of mass m moves, uder the influence of gravitational force, around the
Sun, whose mass is M. We assume that M>>m, so that the center of mass of the
planet-Sun system is approximately at the center of the Sun. Assume we have
chosen the origin to be the center of the Sun. For the planet, show that
(a)[5%]its angular momentum L is a constant vector and (b)[5%]its orbit must
lie on a plane.
10.[10%]
A round uniform body rolls smoothly without slipping down a ramp. A static
friction force f_s acts at the point of contact between the body and the ramp.
Explain why f_s does no work on the round body?
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