推 jamtu:辛苦啦同系推 11/16 21:39
課程名稱︰普通物理學甲上
課程性質︰
課程教師︰張顏暉
開課學院：電資學院
開課系所︰電機系
考試時間︰11/16 10:30~12:30
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
1.Two particles, both og mass m are connected by a light rope(of mass zero)
and are at rest on a horizontal frictionless surface. A third particle also
mass m in approaches the system with velocity v=v0i, strikes on one of the
two particles and bounces off with the velocity v=v0j. What is the resulting
motion of the center of mass of the two particles system?(10)
2.A horizontal force F acts on a billiard ball placed on a pool table for a
short time t. The billiard ball has radius R, mass M, and rotational inertia
(2/5)MR^2 with respect to an axis passing through its center of mass. The
billiard ball then rolls without slipping on the pool table. Find the
position of the contact point between the force and the biiliard ball.(10)
3.A uniform sphere of weight W and radius r is being held by a rope (solid
line in the figure) attached to a frictionless wall a distance L above the
center of the sphere, as is shown in Fig 1. Find (a) the tension in the rope
and (b) the force exerted on the sphere by the wall. If the wall is not
frictionless, the extension of the rope does not need to pass through the
center of the sphere,(c)find the direction of the frictional force acting on
the sphere if the sphere is attached to the wall by the dashed line in the
figure.(10)
4.A uniform flexible chain of length L, with mass per unit length λ,passes
over a small frictionaless peg; see Fig 2. It is released from a rest
position with a length of chain x hanging from one side and a length L-x
from the other side. Find the acceleration as a function of t.(10)
5.Derive the parallel axis theorem. I=Icm+Mh^2, here Icm is the rotational
inertial with respect to the axis passing through the center of mass of the
object. I is the rotational inertial with respect to an axis that is
parallel to the axis with Icm and h is the distance between the two
parallel axis.(10)
6.A wheel of mass M and radius R is fixed on a fricionless table and is free
to spin around the fixed axis. A particle of mass m moving on the table with
velocity v=-v0i+voj collides with the wheel, originally at rest, at r=Ri
(take the center of the wheel as origin); see Fig 4. The collision is
completely inelastic,i.e., after the collision the particle and the wheel
stick together. Find the angular velocity of the combined particle-wheel
system after the collision. The rotational inertial of the wheel is Icm=MR^2
(10)
7.Tazarn, who weighs 60 kg, swings from a cliff at the end of a convenient 20 m
vine;see Fig3. From the top of the cliff to the bottom of the swing, Tazarn
will fall by 2 m, the vine has a breaking strength of 2000 N. Will the vine
break? Take g=10m/s^2.(10)
8.Find the angle,θ,of the inclined plane, below which a disk of radius R and
mass M could roll without slipping down the plane. Assume the static
friction coefficient between the disk and the plane is μs.(10)
9.The force on a particle constrained to move along the z axis is given by
F(z)=(k/(z+a)^3)-(k/(z-a)^3),where k and a are fixed constants. Assume that
U(z)=0 when z=∞,find U(z).(10)
10.Find the precession angular speed of the spinning top shown in Fig 5. The
angular momentum of the spinning top is L, its mass is M and the distance
between the center of mass and point O in the figure is r.
11.Write down your opinion on this course. Does the professor explain things in
a way you an understand? Do you like his teaching style? What could be done
to improve the teaching of this course? You need to write down more than 5
lines to get the extra 5 points.(5)
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