課程名稱︰普通物理學甲上
課程性質︰必修
課程教師︰趙治宇
開課學院：工學院
開課系所︰機械系
考試日期（年月日）︰102年11月14日
考試時限（分鐘）：170 mins
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
Fig: http://ppt.cc/4I3D
1. Derive the moment inertia of the object shown in Fig. 1. (10%)
Notice: this is NOT a thin-rod problem.
2. A ball with mass m is launched vertically from the ground with an initial
velocity v0. Consider the air friction is proportional to the velocity square
(f = μv^2). Find the velocity of this ball when it hits back to the ground
again. (10%)
3. Find the moment inertia of a hollow sphere (mass M) with inner and outer
radius R1 and R2, respectively. (10%)
4. (a) The x-component of the initial velocity of particle 1 is 50 m/2, and
that of particle 2 is -25m/s. The mass of the particle 1 is 15 kg, and 25 kg
for particle 2. Assume the collision coefficient is 0.6, find the final
velocity of particle 1 and 2. (6%)
(b) If above collision is elastic, what will be the final velocity of
particle 1 and 2. (4%)
5. Derive (a) the rocket equation and (b) the formula for finding the final
velocity of an accelerating rocket whose fuels are decreased with time. (10%)
6. A uniform spherical shell of mass M = 4.5 kg and radius R = 8.5 cm can
rotate about a vertical axis on frictionless bearings (Fig. 2). A massless
cord passes around the equator of the shell, over a pulley of rotational
inertia I = 3.0 x 10^-3 kg m^2 and radius r = 5.0 cm, and is attached to a
small object of mass m = 0.60 kg. There is no friction on the pulley’s axle;
the cord does not slip on the pulley. What is the speed of the object when it
has fallen 82 cm after being released from rest? (10%)
7. In Fig. 3, a baseball is hit at a height h = 1.00 m and then caught at the
same height. It travels alongside a wall, moving up past the top of the wall
1.00 s after it is hit and then down past the top of the wall 4.00 s later,
at distance D = 50.0 m farther along the wall. (a) What horizontal distance
is traveled by the ball from hit to catch? (b) What is the magnitude of the
ball’s velocity just after being hit? (c) How high is the wall? (10%)
8. In Fig. 4, a 1.34 kg ball is connected by means of two massless strings,
each of length L = 1.70 m, to a vertical, rotating rod. The strings are tied
to the rod with separation d = 1.70 m and are taut. The tension in the upper
string is 35N. What are the (a) tension in the lower string, (b) the net
force Fnet on the ball, and (c) speed of the ball? (10%)
9. A single conservative force F(x) acts on a 1.0 kg particle that moves
along an x axis. The potential energy U(x) associated with F(x) is given by
U(x) = -4xe^(-x/4) J, where x is in meters. At x = 5.0 m the particle has a
kinetic energy of 2.0 J. (a) What’s the maximum kinetic energy of the
particle has a kinetic energy of 2.0 J. (a) What’s the maximum kinetic
energy of the particle and the value of x at which it occurs? (b) Determine
an expression for F(x) as a function of x and for what value of x does F(x) =
0? (5%, 5%)
10.Two blocks, of masses M = 2.0 kg and 2M, are connect to a spring of spring
constant k = 200 N/m that has fixed, as shown in Fig. 5. The blocks are
released from rest with the spring released. (a) What is the combined kinetic
energy of the two blocks when the hanging block has fallen 0.090 m? (b) What
is the kinetic energy of the hanging block when it has fallen that 0.090 m?
(c) What maximum distance does the hanging block fall before momentarily
stopping? (10%)
11.A small ball of mass m is aligned above a larger ball of mass M = 0.63 kg
( with a slight separation, as with the baseball and basketball of Fig. 6-a
), and the two are dropped simultaneously from a height of h = 1.8 m. (Assume
the radius of each ball is negligible relative to h.) (a) If the larger ball
rebounds elastically from the floor and then the small ball rebounds
elastically from the larger ball, what value of m results in the larger ball
stopping when it collides with the small ball? (b) What height does the small
ball then reach (Fig. 6-b)?
12.In Fig. 7, a thin uniform rod (mass 3.0 kg, length 4.0 m) rotates freely
about a horizontal axis A that is perpendicular to the rod and passes through
a point at a distance d = 1.0 m from the end of the rod. The kinetic energy
of the rod as it passes through the vertical position is 20 J. (a) What is
the rotational inertia of the rod about axis A? (b) What is the (linear)
speed of the end B of the rod momentarily stop in its upward swing? (10%)
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