作業一
1.
請估計下列數值（需簡述估計之方法）：
（一）千元大鈔有多厚
（二）10 Gbye 硬碟中每一 bit 所佔的面積約為多少
（三）一炷香的時間有多長
（四）中興大學理學院大樓有多重
（五）麻雀飛得有多快
（六）中興湖的水有多少
（七）台中市站前金沙百貨有多高
（八）台中市內有多少便利商店
2.
簡答題
（一）地球距離最近的銀河系約幾光年？
（二）中子直徑約為？pm (Pico Meter)
（三）太陽約有多重？
（四）地球年紀約幾歲
3.
4.
5.
（五）固體內原子熱震盪週期約為多少 fs (femto second)
A peregrine falcon dives at a pigeon. The falcon starts with zero downward
velocity and falls with the acceleration of gravity. If the pigeon is 76.0 m below
the initial height of the falcon, how long does it take the falcon to intercept the
pigeon?
A person standing at the top of
a hemispherical rock of radius
R kicks a ball (initially at rest
on the top of the rock) to give it
a horizontal velocity vi . (a)
what must be its minimum
initial speed if the ball is never
to hit the rock after it is kicked?
(b) With this initial speed, how
far from the base of the rock
does the hit the ground?
A river flows with a uniform velocity v. A person in a motorboat travels 1.00 km
upstream, at which time she passes a log floating by. Always with the same
throttle setting, the boater continue to travel upstream foe another 60.0 min and
then returns downstream to her starting point, which she reaches just as the same
log does. Find the velocity of the river. (Hint: The time of travel of the boast after
1
6.
it meets the log equals the time of travel of the log.)
An enemy ship is on the western side of mountain island as shown in the figure
below. The enemy ship can maneuver to within 2500m of the 180 m heigh
mountain peak and can shoot projectiles with an initial speed of 250 m/s. If the
eastern shoreline is horizontally 300 m from the peak, what are the distances
from the eastern shore at which a ship can be safe from the bombardment of the
enemy ship?
A skier moving with friction down a hill that has incline angle θ=5o . If his initial
speed is 20.0m/s, please determine his stopping distance if µk =0.18.
8. A 1.30 kg toaster is not plugged in. The coefficient of static friction between the
toaster and a horizontal countertop is 0.35. To make the toaster start moving, you
carelessly pull on its electric cord. (a) For the core tension to be as small as
possible, you should pull at what angle above the horizontal? (b) With this angle,
how large must be the tension?
9. A construction project in planned to build a new village in a hill. An geological
engineering study indicates the static friction coefficient between the top layer
soil will reduce to 0.4 during heavy rain season. Please find what’s least angle of
the slop of the hill that can be changed so as to prevent any slippage.
10. What horizontal force must be
m1
applied to the cart shown in the
figure below so that the blocks
F
remain stationary relative to the
m2
cart? Assume all surfaces, wheels,
and pulley are frictionless.
7.
M
2