推 catherinekao:好強的圖！ 11/09 22:21
課程名稱︰普通物理學
課程性質︰必修
課程教師︰蔡爾成
開課學院：工學院
開課系所︰工科海洋系
考試日期（年月日）︰96/11/09
考試時限（分鐘）：兩節課
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.page 192 8.36 The potential energy of a diatomic molecule ( a two atom system
like H2O or O2 ) is given by
A B
U = ── - ──
r^12 r^6
where r is the separation of the two atoms of the molecule and A and B are
positive 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 with the force on each atom is zero (b)[5%]
Is the above equilibrium configuration stable?
2.[10%]After complete inelastic collision, two objects of the same mass and
same initial speed. Find the angle between the initial velocities of the two
objects.
3.[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 to the
initial rotational kinetic energy?
4.[10%]A girl of mass M stands on the rim of a frictionless merry-go-round of
radius R and rotational inertia I that is not moving. She throws a rock of
mass m horizontally in a direction that is tangent to the outer edge of the
merry-go-round. The speed of the rock, relative to the ground, is υ.
Afterwards what is the angular speed of the merry-go-rounds?
→ ^ ^ ^
5.For the force field F = xyi -z^2j x^2k , 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^2.
→ ^ ^ ^
6.(a)[5%]Is the force field F(x,y,z) = -yi +xj +2k conservative? Why? [Hint]
Consider the work done on moving a point particle along the unit circle
centered at the origin in the xy plane. (b)[5%]For a conserved force field
→ →
F(x,y,z) with potential energy U(x,y,z), show that F is perpendicular to the
equipotential surface U(x,y,z) = constant.
7.[10%]The total kinetic energy for a system of particles depends on the
inertial reference frame. Prove that the total kinetic energy observed in
the center of mass frame is minimal.
8.[10%]For the elastic collision of two partical observed in the center of mass
frame, show that the initial and the final speed for each of the two
particales remain the same.
9.[10%]Show that the rotational inertia for a thin uniform spherical shell
about any axis passing through the center of mass is (2/3)mR^2.
10.A particle of mass m is moving along the interior of a frictionless
→
hemispherical bowl of radius r, which is kept at rest. The force F acting on
→ → → →
the partical is equal to N + mg where N is the normal force and mg is the
gravitational force in the vertical direction.
← r →∣
__ —＋— __
（ __ ∣ __ ）
＼ —＋╲ ╱
＼ ∣Θ╲╱
＼ ∣ ╱m
︶
∣
(a)[5%] Show that the component of the angular momentum in the vertiacal
direction is conserved. (b)[5%] Show that "υh"×sinθ is a constant
where "υh" is the horizontal speed and θ,as indicated in the above figure,
is the angle between the the direction of the particle and the direction
→
of g .
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