求證明過程~感謝

7. (II) Atwood's machine was an apparatus that allowed a direct verification of Newton's second law. It could also be used to measure g. Two equal blocks of mass M hang on either side of a pulley; see Fig. 5.56. A small square rider of mass m is placed on one block. When the block is released, it accelerates for a distance H till the rider is caught by a a ring that allows the block to pass. From then on the system moves at a constant speed which is measured by timing the fall through a distance D. Show that (2M + m)D 2mH12 where 1 is the time moved at constant speed. m2 M Hotez D M FIGURE 5.56 Problem 7

求解

Using Heisenberg's uncertainty principle, calculate the uncer- tainty in the position of (a) a 1.50-mg mosquito moving at a speed of 1.40 m/s if the speed is known to within +0.01 m/s; (b) a proton moving at a speed of (5.00 + 0.01) x 104 m/s. (The mass of a proton is given in the table of fundamental constants in the inside cover of the text.)

求這兩題詳解～😢😢

- ons is nilot od plass lo gorol arai (s) 29vom Sion los = 9 ) A 170 kg crate hangs from the end of affope of length L = 12.0 m. You push 人 horizontally on the crate with a varying force É to move it distance d = 3.50 m to L the side (Fig. 7-20). (a) What is the mag- nitude of † when the crate is in this final position? During the crate's displace-lid 250 bisw ment, what are (b) the total work done 32 on it, (c) the work done by the grav- 16 Hoold itational force on the crate, and (d) the kd work done by the pull on the crate from the rope? (e) Knowing that the crate is Figure 7-20 Problem 9. motionless before and after its displace- ment, use the answers to (b), (c), and (d) to find the work force + does on the crate. (f) Why is the work of your force not . ( equal to the product of the horizontal displacement and the answer to (a)? - -- your

求解答案是否正確

Multiple-choice questions: (70 points) write the letter of statement that is not true: 1. A.B.U The Drude Model: (a) It is a classical approach using concepts from the kinetic theory of gases. (b) A relaxation-time approximation is used where the probability of collision is l/t. (c) No forces act on the electrons in between collisions. (d) It predicts accurately the electronic heat capacity of metals. 2. The Sommerfeld Model: (a) The crystal potential is replaced by an average Coulomb potential. (b) The separation of states is so close that a continuum model can be applied. (c) The electrons are highly localized due to a strong crystal potential. (Q) The energy of the highest occupied state at 0 K is the Fermi energy. 3. Density of states in k-space, N(k): (a) N(k) is determined by the boundary value conditions. (b) For lattices in any dimensions, N(k) is constant in k-space. (C) N(k) depends on the direction and magnitude of k. (d) It is directly proportional to the volume of the crystal. E影響, c 4. The Fermi surface of a metal: (a) is responsible for many of the transport properties of the metal, (b) depends on the nature of the chemical bonds, (c) is always a sphere, (d) can involve mixing of electron orbitals. ✓ 5. The conductivity of a material () increases with the mobility of its carriers, (b) increases with the density of carriers, (C) it is inversely proportional to the energy gap. cogu changes with temperature. 6. BID Plasmons: (a) They are an important characteristic of the Sommerfeld electron gas model. (b) Plasmons occur spontaneously in metals. (c) They are related to charge density oscillations. (d) The Plasmon energy is typically of the order of 10 eV. The Fermi energy Ef in intrinsic semiconductors 8) is usually close to y E, at OK (b) it ACiD. can increase or decrease with temperature depending on the ratio of hole and electron effective masses, (c) it represents the point at which the probability of occupation is 12, even though there may not been any states with that energy, (d) its value relative to the electronic bands must remain unaffected in the presence of defects or interfaces.

有人知道這怎麼算嗎 ？ 畫黑線的那裡 （Cos25度）

The solution requires that we determine the component of the f because the component of the force that was pushing down on Fparallel (Force) (cos 25°) = (125 N)(0.906) = 113 N W = Fparalleld = (113 N)(56 m) = 630 J Getting a piano into a truck isn't easy, so we often use a ramp to the distance we have to apply the force is greater. So in a way, work done remains the same. Play around with the Ramp and Pi

請問第9題的第四小題，為何B選項1：2：3：4不是正確的答案呢！ 我個人認為B及D選項都是正確的！ 請高手說明，謝謝！

關係圖(a-t圖)應為下列何者? (A) a (m/s) (B) 0 a (m/s) f(s) (C) ( )(1)連續兩影像間的時間間隔為何? (A)0.01秒(B)0.1秒(C) 1 秒(D) 10 秒。 ( )(2)物體落下時的平均加速度為多少 公分/秒?(A)87 (B) 870 (C)175 (D)1750。 ( )(3) x 值為何?(A)32 (B)35.5 (C) 39.3 (D) 42 • 答案:(1)(B);(2)(B);(3)(C) 13.1-4.4 解析:(2) =870(公分/秒) 0.12 [(x-17.5)-13.1] (3) =870,X- t(s) 0 a (m/s) (D) o 0 a(m/s?) t(s) 0 o 13610 0.12 393。 出處:試題 難易度:難 9. 請在閱讀下列敘述後,回答下列問題。 在義大利佛羅倫斯的科學史博物館成立 於西元1927年,經兩年翻修後於西元2010 年6月10日重新開館,更名為伽利略博物 館(Museo Galileo) 館內收藏了一座十八世紀後期的一個演 示儀器,長寬高為544cmx39cmx124cm,作 者不詳,在史上最美的十項科學實驗這本書 裡,作者克里斯(Crease)將此面稱為 Belled Plane。 此演示器材有兩組鈴鐺,第一組鈴鐺是 受懸掛在斜面後方的單擺牽動,每擺到最高 點時會敲響鈴鐺,並發出等時間間隔的鈴鐺 聲。第二組是斜面上5個活動鈴绪組,沿著 斜面設置,當球自高處滾下來經過鈴錯時, 就會發出聲音,演示者可以一邊聆聽單擺敲 出的鈴鐺聲,一邊排列這組活動鈴鐺,使球 滾下來敲響的鈴鐺聲也是等時間間隔的,以 測量各組活動鈴绪的間距比例是否符合「等 加速度」的特性。 ( )(1)當球自斜面高處滾下來的過程屬 於何種運動?(A)等速度運動 (B)等加速度運動 (C)加速度 運動 (D)自由落體運動。 ( )(2)球自斜面高處滾下的加速度-時間 f(s) ( )(3)球自高處滾下來經過鈴鐺時,敲 響的鈴鐺聲也是等時間間隔的意 義為何?(A)經過每鈴鐺的時 間間隔相同(B)鈴鐺間距相同 (C)鈴鐺發出的音高相同(D) 經過每鈴鐺的速度相同。 ( )(4)「等加速度」的特性是每隔相同 時間間格球移動的距離比應為下 列何者?(A)1:1:1:1( B) 1:2:3:4 (C) 1:4:9 : 16 (D)1:3:5:7。 答案:(1)(B);(2)(A);(3)(A);(4 (D) 出處:習作 難易度:難 10. 阿美費盡九牛二虎之力爬上高樓的樓頂, 正在欣賞美景時,不小心口袋中拾圓硬幣 掉出,自樓頂自由落下到地面需時4秒, 若不計空氣阻力(g=9.8 m/s),試回 答下列問題: ( )(1)硬幣著地的速度為多少?(A) 9.8 m/s (B) 19.6 m/s (C) 29.4 m/s (D)39.2 m/s。 ( )(2)阿美爬上多高的樓頂?(A) 78.4 m (B) 44.1 m (C) 29.4 m(D)19.6m。 16 1 4 q 17

謝謝

Equilibrium constant calculations often have as much as 5% error X in them because (A)molar concentration and pressures are often used. (B)there is experimental error involved in measure K. (C)the chemical activity should be used. (D)approximation are often used to solve very difficult calculations. (E)all of the above. 【83 中興B)

請問有人知道這三題的算法跟答案嗎(´･ω･`)

線上盛一遊戲橘子 < > a physexp.thu.edu.tw/~APNC/NP/ 07 古 課程平台練習 科技與物理公告 講義 測驗成績 FB 連結至基礎應用數學 1.古典力學 NP-003 login P01 P02 P03 P04 POS P06 P07 P08 得分與答題次數 2.圓週運動與 文學 3.熱力學 Problem7(填充題) Three moles of helium are initially at 20 °C and a pressure of 1 atm(=1.01 x 10 Pa). (a)Calculate the initial volumne of the helium gas. What is the work done by the gas if the volume is doubled (b) at constant pressure, or (c) isothermally? 提示:可將氮氣視為理想氣體,等溫過程所做的功的公式為:W=nRT Ind)。 (03小題) 一熱力學定律(25) 「溫度(9) 下與美容量(24) ANP-L05 理想氣體與功(2 氣體運動論文 ANP-L06 ONP-003 4章皇 (a)the initial volume= 分數=2 可嘗試次數= 5 m3 m 相對誤差=0.05 目前剩餘 5次,可繼續嘗試 :30 5.學 6.波動與光 近代物理 更新剩餘次数 B. 近代科技1 9近代科技 機器學習 (b)work done at constant pressure , W= 分數= 2 可嘗試次數=5 相對誤差-0.05 ] 目前剩餘 5次,可繼續嘗試 10.近代科技 量子電腦 :31 VPYTHON https:/physexp thu edu tw/LAP 8/NP-Q03-T-07 php 重設

想問5-9 該怎麼算 ？ 第一個選項就可以了 謝謝

the sample size? (b) 250 ing? 211% -6208 *(a) 500 mg. *(c) 150 mg. Xloo to 10.4 ) X100% =0108 / mg 506 016 5-8. A method of analysis yields masses of gold that are low A by 0.4 mg. Calculate the percent relative error caused ylvila by this result if the mass of gold in the sample is 625 mg.6 20 (d) 70 (c) Dit X 106% 8.6 5-9. The method described in Problem 5-8 is to be used for the analysis of ores that assay about 1.2% gold. What minimum sample mass should be taken if the relatived) error resulting from a 0.4-mg loss is not to exceed *(a) -0.1%? (b) -0.4%? 5 * (c) -0.8%? (d) - 1.1%? Slastin 0 (14)。

力學 救救我 謝謝！（第三題不用）

1. Considerathin rod ofuniform linear mass density pL with mass 4/ and length /, find the gravitational potential。dp/有)。at a perpendicular distance Afrom the center ofthe rod. You may find the integral in (E.6) in Appendix E useful 2. A spherical planet of radius 人> consists ofacore of radius 有/ with uniform density pi. and a thick outer cloud of dust with umiform density p: Find the force (magnitude and direction) onamass箇inside the dust cloud ata position ARp from the planetcenter( 吃<訪<記), 3. Use Fermat's principle by applying calculus of variation to minimize the time oflight passing from medium ofrefractive index jg, to another medium ofrefractive index >, derive the Snells law ofrefraction: js光 名2s 銷 4. Consider the Atwood machine oftwo masses connected by amassless string oflength 7overapulley ofradius gas shown, (a) Write down the total kinetic energy and potential energy in terms of the coordinatex Hence obtain the Lagrangian ofthe system. (b) Derive the Lagrange's equation of motion and hence find the acceleration ofthe masses. x 和二 工