課程名稱︰普通物理學甲
課程性質︰
課程教師︰張顏暉
開課系所︰電機工程學系
考試時間︰11/08 星期二 早上10:30~中午12:30
試題 :
1.A free falling body of mass m is subjected to a friction force -bv. Find the
terminal speed of this body.(5)
2.The force on a particle is F=Fo(X/Xo-1). Find the work done by the force in
moving the particle from X=0 to X=2Xo.(5)
3.A hot air balloon of mass M is descending vertically with downward
accerlation of magnitude a. How much mass(ballast)must be thrown out to give
the balloon an upward accerlation of magnitude a? Assume that the upward
force from the air(the lift) does not change because of the decrease in mass.(10)
4.A worker wishes to pile a cone of sand onto a circular area in his yard. The
radius of the circle is R, and no sand is to spill onto the surrounding area.
If μs is the static coefficient of friction between each layer of the sand
along the slope and the sand beneath it, what is the greatest volume of the
sand that can be stored in this manner?(The volume of the cone is Ah/3, where
A is the base area and h is the cone's height) (10)
5.A stone with weight w is thrown vertically upward into the air from ground
level with speed Vo. If a constant force f due to air drag acts on the stone
throughout its flight.(a) What's the maximum height can be reached by the
stone?(b) What's the speed of the stone when it reaches the ground?
6.A small ball of mass m is, with a slight seperation, aligned above a large
ball of mass 1kg and the two are dropped simultaneously from height of h=2m
(Assume the radius of each ball is negligible relative to h) (a)If the larger
ball rebounds elastically from the floor and then the smaller ball rebounds
from the largerball, what value of m results in the larger ball stoping when
it reaches the ground?(10)
7.At t=0, particle A of mass 1 kg is located at (1,0) (in meter) with a velocity
of 1 m/s in positive x-direction, and particle B of mass 1 kg is located at
(1,0) with velocity 1 m/s in positive y direction. What is the velocity of
the center of mass and total angular momemtum with respect to O of this two
particles system? A force of 1Nt in the postive y-direction acts on particles
for 1s. 10s after the force is removed, what is the velocity of the center of
mass and total angular momemtum with respect to O of this two-particle system.
8.Calculate the rotational inertial of a thin rod of length L and mass M about
an axis perpendicular to the rod, through the center of mass? Use parallel
axis theorem to find the rotational inertial of the same rod about an axis
passing through one end of the rod. This rod can pivot about a horizontal
frictionless pin through one end. It is released from horizontal position,
find the augular speed of the rod when it makes an angle Θ with the
horizontal axis. Find also the force acting on the pivot.
9.A uniform solid disk of radius R and mass M is given an initial angular
velocity ωo and the lowered on to a flat horizontal surface
(Icm=1/2MR平方). The coefficient of kinetic friction between the surface and
the cylinder is μk. Initially the disk slips as it moves along the surface,
but after a time t0 pure rolling without slipping begins. (a) what is the
value of t0? (b) What are the kinetic energies (transtional plus rotational)
of the sphere at t=0 and t=t0? (c) What is the distance (S) traveled by the
CM from t=0 to t=t0 and what is the angle (ΔΘ) rotated by a point P at the
edge of the disk? (d) Show that the difference in the total kinetic energy at
t=0 and t=t0 equal to the friction force times the difference between S and
RΔΘ. (20)
10. Write down your opinion on this course. Does the professor explain things
in a way you can understand? Do tou like his teaching style? What could be
done to improve the teaching of this course. You need to write down more
the 5 lines to get the extra 5 points.(5)
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