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）︰2015/11/20
考試時限（分鐘）：170
試題 :
1. What is the principle of time-of-flight mass spectroscopy? (10%)
2. Describe the principle of scan tunneling microscope? (10%)
3. Find the center of mass of a solid uniform hemisphere. (10%)
4. (a) Prove the rotation inertia (moment of inertia) I is written as
I=Σmiri^2.
(b) Prove the parallel-axis theorem in rotation dynamics. (10%)
5. A rocket (V0 = 0) whose initial mass Mi is 850 kg consumes fuel at the rate
R = 2.3 kg/s. The speed u of the exhaust gases relative to the rocket
engine is 3000 m/s.
(a) What trust (effective force) does the rocket engine provide;
(b) What is the intial acceleration of the rocket; and
(c) What is its final speed when its fuel is exhausted down to 250 kg?
(10%)
6. (a) The x-component of the intial velocity of particle 1 is 50 m/s, and
that of particle 2 is -25 m/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.
(b) If above collision is elastic, what will be the final velocity of
particle 1 and 2. (10%)
7. A football kicker can give the ball an initial speed of 25 m/s. What are the
(a) least and (b) greatest elevation angles at which he can kick the ball
to score a field goal from a point 50 m in front of goalposts whose
horizontal bar is 3.44 m above the ground? (10%)
8. In Fig. 1, a chain consisting of five links, each of mass 0.100 kg, is
lifted vertically with constant acceleration of magnitude a = 2.50 m/s^2.
Find the magnitudes of (a) the force on link 1 from link 2, (b) the force
on link 3 from link 4, (c) the force on link 4 from link 5. Then find the
→
magnitudes of (d) the force F on the top link from the person lifting the
chain and (e) the net force accelerating each link. (10%)
http://imgur.com/RIXEOp7
9. In Fig. 2, a slab of mass m1 = 40 kg rests on a frictionless floor, and a
block of mass m2 = 12 kg rests on top of the slab. Between block and slab,
the coefficient of static friction is 6.0, and the coefficient of kinetic
friction is 0.40. A horizontal force F of magnitude 120 N begins to pull
directly on the block, as shown. In unit-vector notation, what are the
resulting acceleration of (a) the block and (b) the slab? (10%)
http://imgur.com/CotnBA2
10. A can of sardines is made to move along an x axis from x = 0.25 m to
x = 2.25 m by a force with a magnitude given by F = exp(-4x^2), with x in
meters and F in newtons. (Here exp is the exponential function.) How much
work is done on the can by the force? (10%)
11. In Fig. 3, a small block of mass m = 0.032 kg can slide along the
frictionless loop-the-loop, with loop radius R = 10 cm. The block is
released from rest at point P, at height h = 5.0R above the bottom of the
loop. How much work does the gravitational force do on tje block as the
block travels from point P to (a) point Q and (b) the top of the loop? If
the gravitational potential energy of the block-Earth system is taken to
be zero at the bottom od the loop, what is that potential energy when the
block is (c) at point P, (d) at point Q, and (e) at the top of the loop?
(8%) http://imgur.com/ctyLpBx
12. A raindrop with radius R = 1.5 mm falls from a cloud that is at height
h = 1200 m above the ground. The drag coefficient C for the drop is 0.60.
Assume that the drop is spherical throughout its fall. The density of
water ρw is 1000 kg/m^3, and the density od air ρa is 1.2 kg/m^3. Given
the drag force D = (1/2)CρAv^2, where ρ is the fluid density and A is
the effective cross-section area of the body, what is the terminal speed
of the raindrop? (12%)