課程名稱︰普通物理學乙
課程性質︰必修或選修可抵通識
課程教師︰張寶棣
開課系所︰物治系
考試時間︰2005.4.22 14：20 ～ 17：30
試題 :
1. A 0.100 kg sphere is tied to a string that is 0.8 m long. The sphere is held
to the left of the supporting point P until the string is taut. A nail, Q,
is in the path of the string 0.4 m below point P. Assume that the effects
of moving through air are small enough to be ignored. The sphere is at rest
and released from its initial position as described. (a) How fast will the
sphere be moving as the instant the sphere reaches its low point and the
string first touches Q ？ (b) Write a paragraph describing what happens
between this instant and the next return of the sphere to this lowest point
in its path. (10％)
2. A 5 kg block is held against a spring of force constant 20 N/cm,
compressing it 3 cm. the block is released and the spring extent, pushing
the block along a rough horizontal surface. The coefficient of friction of
friction between the surface and the block is 0.2. (a) Find the work done
on the block by the spring as it extends from its compressed position to
its equilibrium position. (b) Find the energy dissipated by friction while
the block moves 3 cm to the equilibrium position of the spring. (c) What is
the speed of the block when the spring is at its equilibrium position？ (d)
If the block is not attached to the spring, how far will it slide along the
rough surface before comimg to the rest？ (20％)
3. A 20.0 kg body is moving im the direction of the positive X axis with a
speed of 200 m/s, when owing to an internal explosion, it breaks into three
parts. One part, whose mass is 10.0 kg, moves away from the point of
explosion with a speed of 100 m/s in the direction of negative Y axis. A
second fragment, with a mass of 4.0 kg, moves in the direction of negative
X axis with a speed of 500 m/s. (a) What is the velocity of the third (6.00
kg) fragment？ (b) How much energy was released in the explosion？ Ignore
effects due to gravity. (10％)
4. A person pushes with a force of 2.00 NT at right angles to a stick
fastened to an object. The push is continuously applied to at a point that
is 3.00 m from the axis of an object on the approaching of the object. Its
moment of inertia is 4.00 kg-m/s about that axis. If the object had been
rotating at 5.00 rad/s, what will be the angular velocity 6.00 a later？
(10％)
5. Fig. 1 shows a thin bar of length L and M, and a small blob of putty pf
mass m. The system is supported on a frictionless horizontal surface. The
putty moves to the right with velocity v, strikes the bar at a distance d
from the center of the bar, and sticks to the bar at the point of contact.
First estimate the position of center of mass of the system in the vertical
direction. The rotational inertial of a bar is (1/12)M/L^2 when the axis is
through the center of the bar. And it changes to (1/12)M/L^2 + My^2 when
the axis is at a distance y from the center of the bar. Obtain expressions
of the velocity of the system's center mass and for the angular velocity of
the system about its center of mass. What is the energy dissipated in this
collision？ Describe the motion of the system after collision. (20％)
M
┌┐─
││↑
│││
│││
│││
─││ L
d↑│││
v ↓│││
○ ────────→ ─│││
m ││↓
└┘─
Figure 1：A moving blob of putty hits a bar
6. A commercial airliner is in level flight and traveling at a constant
velocity of 100 m/s. A passenger remembers the joy of their physics class
and decides to see what happens when a coin is dropped in the plane. Assume
that the coin shall have an acceleration of 9.8 m/s^2 down toward the earth
as it falls freely. Since she was a phycics student, she does have her seat
belt fastened. If her old physics teacher is leaning against an apple tree
and watching the plane go by, what is the magnitude of the coin's velocity
observed by the teacher 0.5 s after its release？ (10％)
7. Two waves are propagating on the same very long string. A generator at one
end of the string creates a wave given by
π
y = (6.0cm) cos ── [(2.5m^(-1)) x + (10.0s^(-1)) t],
2
and one at the other end creates the wave
π
y = (6.0cm) cos ── [(2.5m^(-1)) x - (10.0s^(-1)) t],
2
(a) Calculate the frequency, wavelength, and speed of each wave. (10％) (b)
Find the points on the string at which there is no motion (the nodes). (5％)
(c) At which points is the motion on the string a maximum (antinodes)？
(5％)
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