[心得] 台大機械筆試

看板SENIORHIGH作者ihliu011 (Guitle)時間18年前 (2006/04/02 19:59)推噓11(11推 0噓 2→)

留言13則, 8人參與討論串1/3 (看更多)

好像沒人PO耶... 那我來大概寫一下...記憶力沒有很好所以內容可能和實際有差還有圖的部分很抱歉...請自行想像XD 1.一木塊質量m，靜摩擦係數μs，動摩擦係數μk，受F之力，以4m/s之速度向上運動。 (1)請畫出摩擦力f，並計算它的大小。 (2)是否能用以上資訊求出施力F？若能，請求之，若不能，請寫出還需要哪些資訊？ 2.一汽車重W，重量由前後輪平均分擔，由前輪驅動，兩輪分受F1、F2之摩擦力。請畫出 F1及F2並求F1、F2之關係？ (1)汽車靜止時。(2)汽車向上坡運動時。 3.A paragraph about Isaac Newton (文章內容略) 中文問題(簡答)： (1)文中提到牛頓發現幾個物理定律？ (2)文中是否有提到牛頓與他人共同合作發展什麼學問？若有，是哪門學問？ (3)文中提到牛頓在哪些物理領域有貢獻？ (4)文中提到哪幾位科學家？ (5)文中提到牛頓在哪裡受教育？ 4.(1)一不倒翁由兩部分組成，上方為一質量為m之圓盤，下方為一質量為p之扇形盤，圓盤質心距地面Ym，扇形盤質心距地面Yp。請推導出整個不倒翁的質心位置YT？ (2)已知圓盤直徑為d，扇形盤半徑為R，兩盤由同一材質製成，密度ρ，兩盤厚度均為b 。以不倒翁穩定時與地面的接觸點為原點(0,0)，建立座標系，請問在此座標系中其質心的座標YT(x,y)為何？ (3)不倒翁如超越某傾斜角，即會失去平衡而翻倒。利用題(2)的結果，建立最大傾斜角Ψ max、扇形盤半徑R與質心位置YT的數學關係(提示：不倒翁與地面之接觸點隨會傾斜角而改變)。 5.一儲水裝置包含A、B兩水桶和輸水管，若A、B和輸水管之容量相同，又CD、DE、EF各段水管長度均等且截面積相同。若由水由A注入，試繪出A桶進水量與B桶儲水量的關係曲線圖(部分數值需考生自行估計)。 6.(1)請簡述熱氣球的飛行原理。 (2)若將一充飽之氫氣球(假設不會破)，瞬間移至背對太陽的月球後方，則其形狀會有何種改變？ (3)地球外之某太空艙外，甲乙兩太空人使用噴氣式推進器靜止在太空中，若兩人同時關閉推進器，則 (a)甲看乙，乙如何運動？ (b)由靜止太空艙內的觀察者看兩人如何運動？ (c)若甲知道他與乙之間的距離和自己移動的距離，能否推算出自己的速度？(提示如右圖)。 7.It's well known that the speed of light is C km/hr and the speed of voice is B km/hr. Now an investigator is driving a car which at speed of A km/hr along the highway. He is driving toward a highway gas staion and is X km away from it when the station exploded. (1)How much more distence do he drive until he see the light of the explosion? (2)How much more distence do he drive until he hear the sound of the explosion? (3)How much time do he drive until he reach the station after it's explosion? (4)If C>>B and B>>A,what is the approximate answer in (2)? 8.蜘蛛人從相距20公尺的兩大樓中用蜘蛛絲阻止一列沿軌道疾駛的電車，左圖是蜘蛛絲彈力及伸長量之關係圖，右圖是電車速度與距離之關係圖，試估計電車及乘客的總質量並寫出你用以估計的假設條件？ 9.Determine and prove the following sequences converge or diverge? ∞ ∞ (1){（1^49+2^49+3^49+…+n^49）/n^50} (2){（1+2/n）^n} n=1 n=1 ∞ ∞ ∞ (3){e^n/n} (4){sin（n）/n} (5){ln（n）/n} n=1 n=1 n=1 10.Reading comprehension: In 2002 both chipmakers and their suppliers had failed to achieve critical milestones in the development of the world's most sophisticated cameras-the lithography machines that project a circuit image onto a photochemical "resist" covering the silicon wafer, the disk that is later cut up into individual chips. A developing chemical removes, say, the exposed area, and then an etching chemical transfers the pattern into the wafer. The most common method of making circuits smaller is to reduce the wavelength of light with a machine that traces progressively tinier circuit features on a wafer. Lithography toolmakers had bumped up against numerous obstacles in making a machine that radiates wavelengths of 157 nanometers. Going from one lithography generation to another requires adoption of new lasers, masks (the stencillike pattern of circuits through which laser light is projected), lenses that reduce the image size and exposure, and photoresists. For 157 nanometers, equipment companies could not figure out how to fashion lenses from calcium fluoride with few enough defects and optical aberrations to form a clear image on the wafer. "There was a very large problem with the quality of materials and the manufacturing yields," notes George A. Gomba, senior manager of advanced lithography development at IBM Microelectronics. A way forward arrived during the summer of 2002 at a workshop on 157-nanometer lithography sponsored by Sematech, the semiconductor research consortium. At the meeting, Burn Lin, an executive from Taiwan Semiconductor Manufacturing Company, the world's largest contract chip manufacturer, was scheduled to give a speech on immersion lithography, a hand-me-down from Amici's ideas. Lin, who had researched immersion while at IBM during the 1980s, was supposed to describe how immersion might be used for 157 nanometers by exploiting a viscous machine oil. Instead he spent his lecture describing why lithography at that scale would not work-and why the industry should set its sights on applying immersion to a previous generation of already fielded lithographic equipment that employed a wavelength of 193 nanometers. By concentrating on immersion at 193 nanometers, chipmakers could enhance resolution of tried-and-true lithography equipment until it actually bested what 157-nanometer equipment was supposed to achieve. "That sort of caught the attention of all in attendance," Lin says. "And of course they forgave me for saying 157 nanometers was no good." Water, which is transparent to 193-nanometer radiation but not to 157, can enhance resolution because it enables a lithography machine to be built with a higher numerical aperture, a key factor in its ability to resolve fine detail. Water also improves the depth of focus-the distances from the camera at which the image projected onto the photoresist stays acceptably sharp. Depth of focus remains a particular concern in advanced chipmaking because the slightest unevenness on the wafer surface can spoil the image. from Scientific American,July 2005 中文問題（每題可能有一至五個答案）： (1)文中提到的" lithography"可以做什麼？ (a)切割晶圓(b)侵蝕化學阻膜(c)？？？(d)投影電路圖到阻膜上(e)製作光罩 (2)當入射光的波長降到157nm以下時會產生什麼問題？ (a)？？？(b)？？？(c)？？？(d)？？？(e)輻射會破壞阻膜 (3)使用水之後會產生什麼影響？ (a)光波之波長變短(b)？？？(c)提升numerical aperture (d)使影像變清晰(e)焦距變深 End -- ※ 發信站: 批踢踢實業坊(ptt.cc) ◆ From: 61.229.173.145

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ron0908

04/02 21:11, , 1^F

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azureblaze

04/02 21:15, , 2^F

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orange1986

04/02 21:30, , 3^F

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