課程名稱︰普通物理學丙上
課程性質︰森林環境學群、生物材料學群必修，兼通識A7*
課程教師︰李慶德老師
開課學院：如課程性質所說
開課系所︰如課程性質所說
考試日期（年月日）︰ 101 年 11 月 7 日
考試時限（分鐘）： 120 分鐘
是否需發放獎勵金：是，謝謝您 =)
（如未明確表示，則不予發放）
試題 :
Do any 5 of the exam problems given below!
1.A cheetah can hit 108 km/h in 2 s and maintain this speed for 15 s. After
this time it must rest. An antelope can reach 90 km/h in 2 s and sustain
this speed for a long time. Suppose they are initially separated by 80 m
and the antelope reacts in 0.6 s. Assume also that they both start from
rest and reach their maximum speeds through constant accelerations.
(a) Can the cheetah catch the antelope? If it can, how long does it take?
If not, how close does it get?
(b) What distance must the antelope initially separated from the cheetah so
that it will not get caught by the cheetah?
2. A ball is thrown with a velocity of 19.6 m/s at 37°above the horizontal
from the top of a roof 49 m high. Find:
(a) the time of flight;
(b) the horizontal range;
(c) the angle at which the ball hits the ground;
(d) the velocity when it is 19.6 m below the roof.
3. A satellite of mass m is in circular orbit of radius γ around a central
body of mass M. The force of gravity provides the centripetal force.
(a) Find the orbital speed of the satellite.
(b) Derive Kepler's third law associated this circular motion of the
satellite around the central body.
(c) Earth satellites are launched into orbits only about 150 km above the
earth's surface. Find the periods of the earth satellites in these
orbits. Take the radius of the earth to be 6400 km and κE = 4π^2/
(GM_E) = 9.9 × 10^-14 s^2/m^3, where M_E is the mass of the earth
and G the gravitational constant.
4. A rocket has a net acceleration of 3.2 m/s^2 directed at 53°above the
horizontal. What is the apparent weight of a 60-kg astronaut near the
earth's surface?
5. On fast highways the outside edge of curve is raised. Such banking prevents
vehicles from slipping sideways if there is not enough friction to provide
the centripedal force. A car of mass 1500 kg round a circular curve of
radius 20 m that is banked at 37°to the horizontal. The road is slippery,
so the coefficient of static friction is only 0.15.
(a) Find the maximum safe speed at which the car can travel without
skidding.
(b) Is it possible for a car to go around a banked curve even if there is
not friction?
6. There blocks with masses 4M, 2M, and 8M are connected as shown in figure 1.
The tensions in the rope are T_1 and T_2. Ignore friction and the masses
of the ropes and the pulley. In terms of M, g, and θ, obtain expressions
for:
(a) the accerleration;
(b) T_1 - T_2.
(c) Evaluate your expressions for (a) and (b) with M = 1.5 kg and θ=37°.
picture is here: http://ppt.cc/UGb1
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