李威儀 物理 (一) 小考
====
> [!Note]
> **本文為歷屆威儀老師的小考考古統整**
> `NCTU` `NYCU` `CS` `course`
## CHAPTER 1 物理發展與物理量簡介

>[color=#51e2c3]
>
>- **請將下列物理發展史上的重要人物與其生存年代相對應的中國朝代配對。
(每人考卷上會隨機出現其中一個)**
>
> | 亞里斯多德 | 柏拉圖 | 托勒密 | 伽利略 | 克卜勒 | 哥白尼 | 花喇子密 |
> | ---------- | ------ | ------ | ------ | ------ | ------ | -------- |
> | 戰國 | 戰國 | 西漢 | 明朝 | 明朝 | 明朝 | 唐朝 |
>
> - **請盡可能詳細的說明托勒密的地⼼說如何解釋某些星體在天空上看起來忽進忽退。**
>
> :::spoiler <font color=red>ans</font>
> 托勒密為了解釋行星乎近乎退的現象，創出了「大輪、小輪」之說。小輪之心環繞地球以等速圓周運動，而行星則在小輪上繞小輪之心。
>
> :::
>- **以下是伽利略用望遠鏡看到黑子移動的照片，請問從這幾張照片中發現了什麼?**
> :::spoiler <font color=red>ans</font>
> 太陽會自轉
> :::
>
> - **在哥白尼的 [天體運行論] 中，哪個天體被提到的次數最少?**
> (1)水星 (2)金星 (3)火星 (4)哈雷彗星
>
> :::spoiler <font color=red>ans</font>
> 哈雷彗星
> :::
>
## CHAPTER 2 向量
## CHAPTER 3 等加速度運動
> [color=#51e2c3]
> - **慣性座標的定義？**
> :::spoiler <font color=red>ans</font>
> 靜止或等速度運動的坐標系或牛頓第一運動定律永遠成立的座標系,在慣性座標中未受淨力的物體,會恆維持等速度運動。
> :::
>
> - **The position of a particle moving in a straight line is given by $x=5+2t+4𝑡^{2}- 𝑡^{3}$,where x is in meters.Find an expression for the instantaneous velocity as a function of time.**
> :::spoiler <font color=red>ans</font>
> $v(t)=2+8t-3𝑡^{2}$
> :::
>

## CHAPTER 4 牛頓定律
> [color=#51e2c3]
>- **請解釋什麼是機械守恆系統？**
> :::spoiler <font color=red>ans</font>
> 
> :::
>
>- **請以牛頓定律評估，在不危及生命安全的前提下，一個 100 公斤的人從靜止加速到光速，少要多少時間，並請述明假設理由。**
> :::spoiler <font color=red>ans</font>
> 在安全範圍內，人可承受之加速度大小約為3~5g(g為重力加速度)，此處取4g計算
> $3\times{10}^{8} =(4g)t (以g=9.8估計)$
> t ≒ 7653061 秒
> :::
>
>- **In Figure the force acting on a body for x < 10 m is ${F}{x}$=0.2x and the force for x > 10 m is constant at ${F}{x}$=2N.what is the work done in going from x = 0 to x = 15 m?**
>
> :::spoiler <font color=red>ans</font>
> W = FS = $0.5\times10\times2+(15-10)\times2=20$ J
> :::

## CHAPTER 5 功，能量及功率
> [color=#51e2c3]
> - **A pump is needed to lift 10 kg of water per second from a well 10 m deep. The water is ejected with a speed of <font color=red> 5 </font>m/sec. What must be the power output of the pump?
> (紅色部分每人數字不同)**
>
> :::spoiler <font color=red>ans</font>
> $10\times10\times10+0.5\times10\times5^{2}=1125$
> :::
>
>- **An X kg man ascends a 10 m high staircase in Y sec.What is his horsepower ?
> (X Y 部分每人數字不同)**
>
> :::spoiler <font color=red>ans</font>
> $W = F x S = X (kg) \times 9.8 (g) \times 10 = 98X (J)$
> $P = \dfrac{98X}{Y} (sec) (W)$
> ${H}{p} = \dfrac{98X}{746Y} hp ( 1 hp = 746 W )$
> :::

## CHAPTER 6 動量與碰撞
> [color=#51e2c3]
> - **An object at rest in space explodes into three equal parts. The velocities two of them are respectively <font color=red>2</font>i and <font color=red>-4</font>i.Find the resulting velocity of the third part.(紅色數字每人不同)**
>
> :::spoiler <font color=red>ans</font>
> -2i,4j
> :::

## CHAPTER 7 轉動與圓周運動
> [color=#51e2c3]
>- **為何地球自轉對使用牛頓定律影響不大？**
>
> :::spoiler <font color=red>ans</font>
> 
> :::
>
>- **回答以下問題**
>
> :::spoiler <font color=red>ans</font>
> 
> :::

## CHAPTER 8 轉動動力學
> [color=#51e2c3]
> - **Although most people are concerned about the horsepower of a car’s motor, the important parameter is the amount of Torque that can be given to the rear wheels. The torque of the motor is turned at right angles to the wheels by the differential gear. Assume that in low gear the angular velocity of the rear wheels is 0.1 that of the motor. If the motor has 200hp and is turning over at a rate of 1400 rev/min , how much torque is delivered to the rear wheels ?**
>
> :::spoiler <font color=red>ans</font>
> $τ=\dfrac{P}{ω}=\dfrac{200\times746}{1400\times0.1\times\dfrac{2pi}{60}} = 1.02 \times 10^4 Nm$
> :::
>
>- **A bug sits on a phonograph record 0.18 m from the center. If the record turns at 30 rev/min, what is the radial acceleration of the bug? If it has a mass of 0.5 mg, what is the centripetal force acting on it?**
>
> :::spoiler <font color=red>ans</font>
> ${a}{c}=0.18\times{\dfrac{30\times2pi}{60}}^2$
> :::
>
>- **回答以下問題**
>
>
> :::spoiler <font color=red>ans</font>
> 
> :::

## CHAPTER 9 熱力學與氣體動力學
> [color=#51e2c3]
> - **請寫出理想氣體定律公式及其中壓力與溫度的公制因次單位。**
>
> :::spoiler <font color=red>ans</font>
> $PV = nRT$
> $P = \dfrac{N}{{m}^{2}} ( Pa )$
> $T = K$
> $R = 8.314 \dfrac{J}{{mole}\times{K}}$
> :::
## CHAPTER 10 振盪
> [color=#51e2c3]
>- **A mass is oscillating with amplitude A.
When the displacement is x = $\dfrac{1}{2}$A what fraction of the energy is potentialand what fraction is kinetic?**
>
> :::spoiler <font color=red>ans</font>
> $Ep = \dfrac{1}{2}kx^{2} = \dfrac{1}{2}k( \dfrac{1}{2}A)^2 = ( \dfrac{1}{4})(( \dfrac{1}{2})kA^2) = ( \dfrac{1}{4})Etotal$
> $Ek = ( \dfrac{3}{4})Etotal$
> :::
>
>- **Two springs with force constants ${k}{l} = 100 N/m$ and
>${k}{2} = 100 N/m$ are connected to opposite ends of a block of mass 3kg**
>
> (a) If the block is displaced <font color=red>$O.1m$</font>to the right, what is the net force exerted by the springs on the block? The block is released from that position.
>
> :::spoiler <font color=red>ans</font>
> $2 \times 100 \times O.1 = 20$
> :::
>
> (b) What is the amplitude of the motion?
>
> :::spoiler <font color=red>ans</font>
> O.1 m
> :::
>
## CHAPTER 11 波動
> [color=#51e2c3]
> - **At t=0, a pulse is described by $y(x) = \dfrac{A}{B+{x}^{2}}$.
> Pulse moves in +x direction at 3m/s. Wave function at t?**
>
> :::spoiler <font color=red>ans</font>
> $y(x,t) = \dfrac{A}{B+{( x-vt )}^{2}} =\dfrac{A}{B+{(x - 3t)}^{2}}$
> :::
>
>- **人耳最敏感、接收最清楚的聲波頻率為 3000Hz,由此請試著推算出人耳道的大約長度,假設聲速為每秒 340 公尺。**
>
> :::spoiler <font color=red>ans</font>
> 人的耳道可以視為一開一閉的管子,波長等於耳道長度的四倍。
> $V = f \times L$
> $340 = 3000 \times L$
> $L/4 = 0.028m ( 2.8 cm )$
> :::
>
>- **人西元1801年,楊氏(Thomas Young)如何證明光具有波動性?他的實驗中最困難的部分是甚麼?**
>
> :::spoiler <font color=red>ans</font>
> 楊氏通過雙狹縫實驗證明光有干涉的特性,來證明光具有波動性。
> 實驗中最困難的部份是要得到兩同調(相干)的光源。
> :::
>
## CHAPTER 12 波的干涉
> [color=#51e2c3]
> - **請解釋何謂波的線性相加原理**
>
> :::spoiler <font color=red>ans</font>
> ${y}{t}( total wave function ) = {y}{1}+ {y}{2} + … +{y}{n}$
> 兩波相遇 → 產生干涉( 相消or相長 )
> 兩波翻開 → 保持各自原有的波形( 兩個波動之間不會相互造成彼此的改變 )
> :::
>
## CHAPTER 13 - 15 靜電學
> [color=#51e2c3]
> - **帶電量$3.2\times{10}^{-19}$的粒子通過$3V$的電壓所需的能量為多少電子伏特?**
>
> :::spoiler <font color=red>ans</font>
> $\dfrac{3.2\times{10}^{-19}}{1.6\times{10}^{-19}}\times3 = 6$
> :::
>
> - **A copper wire 15 m long has $8\times10^{26}$ mobile electrons. What is the drift velocity of the electrons if the current in the wire is 5 A?**
>
> :::spoiler <font color=red>ans</font>
> $$
> \dfrac{5}{A} = \dfrac{(8\times10^{26})}{15\times A}\times(1.6 \times 10^{-19})\times v_d
> $$
> $$
> v_d = 5.86\times10^{-7}
> $$
> :::
>
## CHAPTER 16 合作無間的電與磁
> [color=#51e2c3]
> - **自然界中原子產生磁場的兩個主要原因?**
>
> :::spoiler <font color=red>ans</font>
> (1)電子繞著原子核運動(公轉) → 產生 atomic current → 產生 磁場
> (2)電子自轉 → 自轉電流 → 產生磁場
> :::
>
> - **判斷電流中移動的帶電粒子是帶正電還是負電?請解釋如何判斷**
> 
> :::spoiler <font color=red>ans</font>
> 負電
> $F = i x B$
> 移動帶電粒子受力方向向下
> 電板下方累積負電荷
> 故帶電粒子帶負電
> :::