課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰蔡爾成
開課學院：物理系開給化工系
開課系所︰化工系
考試日期（年月日）︰2009/11/10
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%]In Fig 6-53,a crate slides down an inclined right-angled trough.The
coefficient of kinetic friction between the crate and the trough is
uk.What is the acceleration of the crate in terms of uk,日,and g?
(圖可參考foundamental of physics 8e 習題6.69)
2. [10%]The magnitude of the gravitational force between a particle of mass m1
and one of mass m2 is given by
F(x)=G*m1*m2/x*x
when G is a constant and x is the distance between the particles.
(a)[6%]what is the corresponding potential energy function U(x)?
(b)[4%]How much work is required to increase the separation of the
particles from x=x1 to x=x1+d ?
3. [10%]An object,with mass m and speed v relative to an observer,explodes
into two pieces ,one three times as massive as the other;the explosion
takes place in deep place in 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?
4. [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 that the end on the floor doesn't slip.
(Hint:Consider the stick to be a thin rod and use the conservation of
energy principle)
5. [10%]A particle moves uniformly with constant speed lvl=Vo on a circle of
radius R=lxl centered at the origin.
(a)[4%]show that (vector v)*(vector x)=0 and (vector v)*(vector a)=0.
(vector v) is perpendicular to both (vector x) and (vector a),and therefore
vector a=c(vector x) (they are either parallel or anti-parallel)
(b)[4%]show that [vector a]*[vector x]+[vector v]*[vector v]=0 and
vector a = -(vector x)*v*v/R*R
(Hint:utilize
2
d _\ _\ d _\ _\
--------( x * x) = 2------(v * x )
2 dt
dt
_\
PS.vector v = v
6. [10%]For the force field F= xy i + z*z j+ x*x k,evaluate the work done on
moving a particle from (0,0,0) to (3,2,1)
(a)[5%]along a straight line
(b)[5%]along the curve x=3z,y=2z*z.
7. [10%]Hoe do we define the potential function U(x,y,z)for a conservative
force field F(x,y,z)?
8. [10%]For the elastic collison of two particles observed in the center of
mass frame,show that the initial speed remains equal to thefinal speed for
each of the two particles.
9. [10%]Given that the rotational inertia for a thin uniform spherical shell
of radius R abour any axis passing though the center of mass is 2/3*MR*R.
Show that the rotational inertia for a solid uniform spherical of radius R
about any diameter is 2/5*M*R*R.
10. [10%]For a system of particle,
(a)[4%]show that only external forces contribute to the total net force:
where Fi=Fi(internal)+Fi(external) with Fi(int) the internal force and
Fi(ext) the external force acting on particle i.
(b)[6%]show that,if the strong version of Newton's third law holds, only
external forces will contribute to the total net torque.
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