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.
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