小班講義高一物理第9講牛頓運(yùn)動(dòng)定律的應(yīng)用2—臨界問題

1、龍 文 教 育精品小班課程輔導(dǎo)講義講義編號 2013秋季 輔導(dǎo)科目： 物理 年級： 高一課 題第9講：牛頓運(yùn)動(dòng)定律的應(yīng)用2臨界問題教學(xué)目標(biāo)教學(xué)重點(diǎn)、難點(diǎn)教學(xué)內(nèi)容在應(yīng)用牛頓定律解題時(shí)常遇到臨界問題，它包括：平衡物體（a=0）的平衡狀態(tài)即將被打破而還沒有被打破的瞬間；動(dòng)態(tài)物體（a0）的狀態(tài)即將發(fā)生突變而還沒有變化的瞬間。臨界狀態(tài)也可歸納為加速度即將發(fā)生突變的狀態(tài)。加速度發(fā)生突變的本質(zhì)原因是物體的外力發(fā)生了突變，物體處于臨界狀態(tài)，必然隱含著某些力（如彈力、摩擦力等）的突變。抓住這些力突變的條件，是我們解題的關(guān)鍵。一、和繩子拉力相聯(lián)系的臨界情況例1. 小車在水平路面上加速向右運(yùn)動(dòng)，一質(zhì)量為m的小球用一

2、條水平線和一條斜線（與豎直方向成30角）把小球系于車上，求下列情況下，兩繩的拉力：（1）加速度；（2）加速度。解析：小車處于平衡態(tài)（a=0）對小球受力分析如下圖所示。當(dāng)加速度a由0逐漸增大的過程中，開始階段，因m在豎直方向的加速度為0，角不變，不變，那么，加速度增大（即合外力增大），oa繩承受的拉力必減小。當(dāng)時(shí)，m存在一個(gè)加速度，物體所受的合外力是的水平分力。當(dāng)時(shí)，a增大，（oa繩處于松弛狀態(tài)），在豎直方向的分量不變，而其水平方向的分量必增加（因合外力增大），角一定增大，設(shè)為a。當(dāng)時(shí)，。當(dāng)，有：（1）（2）解得當(dāng)，有：。點(diǎn)評：1. 通過受力分析和對運(yùn)動(dòng)過程的分析找到本題中彈力發(fā)生突變的臨界狀態(tài)

3、是繩子oa拉力恰好為零；2. 彈力是被動(dòng)力，其大小和方向應(yīng)由物體的狀態(tài)和物體所受的其他力來確定。二、和靜摩擦力相聯(lián)系的臨界情況例2. 質(zhì)量為m=1kg的物體，放在=37的斜面上如下圖所示，物體與斜面的動(dòng)摩擦因數(shù)，要是物體與斜面體一起沿水平方向向左加速運(yùn)動(dòng)，則其加速度多大？解析：當(dāng)物體恰不向下滑時(shí)，受力分析如下圖所示，解得當(dāng)物體恰不向上滑時(shí)，受力分析如下圖所示， 解得 因此加速度的取值范圍為：。點(diǎn)評：本題討論涉及靜摩擦力的臨界問題的一般方法是：1. 抓住靜摩擦力方向的可能性。2. 最大靜摩擦力是物體即將由相對靜止變?yōu)橄鄬瑒?dòng)的臨界條件。本題有兩個(gè)臨界狀態(tài)，當(dāng)物體具有斜向上的運(yùn)動(dòng)趨勢時(shí)及當(dāng)物體具有

4、斜向下的運(yùn)動(dòng)趨勢時(shí)。三、和滑動(dòng)摩擦力相聯(lián)系的臨界條件例3. 如下圖所示，傳送帶與地面的傾角為，從a到b的長度16m，傳送帶以10m/s的速率逆時(shí)針方向轉(zhuǎn)動(dòng)，在傳送帶上端無初速地放一個(gè)質(zhì)量為的物體，它與傳送帶之間的動(dòng)摩擦因數(shù)為0.5，求物體從a到b所需的時(shí)間是多少？（）解析：，物體的初速為零，開始階段，物體速度小于傳送帶的速度，物體相對于傳送帶斜向上運(yùn)動(dòng)，其受到的滑動(dòng)摩擦力斜向下，下滑力和摩擦力的合力使物體產(chǎn)生加速度，物體做初速度為零的勻加速運(yùn)動(dòng)。當(dāng)物體與傳送帶速度相等的瞬時(shí)，物體與傳遞帶之間的摩擦力為零，但物體在下滑力的作用下仍要加速，物體的速度將大于傳送帶的速度，物體相對于傳送帶向斜向下的方

5、向運(yùn)動(dòng)，在這一時(shí)刻摩擦力方向?qū)l(fā)生突變，摩擦力方向由斜向下變?yōu)樾毕蛏稀Ｎ矬w的下滑力和所受的摩擦力的合力使物體產(chǎn)生了斜向下的加速度，由于下滑力大于摩擦力，物體仍做勻加速運(yùn)動(dòng)。因，物體的初速為零。開始階段，物體相對于傳送帶斜向上運(yùn)動(dòng)，其受到的滑動(dòng)摩擦力斜向下，下滑力和摩擦力的合力使物體產(chǎn)生加速度，物體做初速度為零的勻加速運(yùn)動(dòng)。根據(jù)牛頓第二定律 物體的速度與傳送帶速度相等需要的時(shí)間為物體下滑的位移為由于，物體在重力的作用下繼續(xù)加速，當(dāng)物體的速度大于傳送帶的速度時(shí)，傳送帶給物體一斜向上的滑動(dòng)摩擦力。根據(jù)牛頓第二定律，得設(shè)后一階段物體滑至底端所用的時(shí)間為，由運(yùn)動(dòng)學(xué)公式得解得所以，物體由a到b所用時(shí)間為。

6、點(diǎn)評：1. 從對運(yùn)動(dòng)過程的分析中發(fā)現(xiàn)本題臨界狀態(tài)是滑動(dòng)摩擦力方向的突變。2. 注意和的區(qū)別。四、和彈簧彈力相聯(lián)系的臨界條件例4. 如下圖所示，兩塊質(zhì)量分別為和的物塊，用勁度系數(shù)為的輕彈簧連在一起，放在水平面上，將物塊1下壓一段距離后釋放，它在做簡諧運(yùn)動(dòng)，在運(yùn)動(dòng)過程中，物塊2始終沒有離開水平面，且對水平面的最小壓力為零，則物塊l的最大加速度的大小是多大？物塊2對水平面的最大壓力是多大？解析：以物塊1為研究對象，彈簧對物塊1的彈力和物塊1的重力的合力是物塊1做簡諧運(yùn)動(dòng)的恢復(fù)力。彈簧彈起的初階段，彈簧處于被壓縮狀態(tài)，向上的彈力大于重力，物塊1向上做變加速運(yùn)動(dòng)，加速度逐漸減小，其方向豎直向上。當(dāng)彈力等

7、于重力時(shí)，物塊1的加速度為零，而速度達(dá)到最大（平衡位置）。然后，彈簧處于伸長狀態(tài)，物塊1受到的彈力向下，彈力逐漸增大，加速度逐漸增大，達(dá)到最高點(diǎn)時(shí)，加速度最大，方向豎直向下。當(dāng)物塊1下落至最低點(diǎn)時(shí)，物塊1的加速度也達(dá)到最大值，但方向豎直向上。以物塊2為研究對象，根據(jù)題設(shè)條件可知，當(dāng)物快1達(dá)到最高點(diǎn)時(shí)，物塊1受到的向下的彈力最大，此時(shí)，物塊2受到的向上的彈力也最大，使地面對物塊2的支持力為零。當(dāng)物塊1落至最低點(diǎn)時(shí)，其加速度與最高點(diǎn)的加速度等值反向，彈簧對物塊1的彈力（方向向上）。此時(shí)，彈簧對物塊2的彈力也最大，方向豎直向下，因此，物塊2對地面的壓力達(dá)到最大值。（1）研究物塊1上升的過程。以物塊1

8、為研究對象，物塊1在最高點(diǎn)處，加速度最大，且方向豎直向下，最大。以物塊2為研究對象，最大時(shí)，所以物塊1的最大加速度為。（2）研究物塊1下落的過程。物塊1落至最低點(diǎn)處，其受到向上的彈力最大，加速度達(dá)到最大值，但方向豎直向上（簡諧振動(dòng)的對稱性）。對物塊2受力分析，根據(jù)牛頓第三定律，物塊2對地面的壓力的大小為點(diǎn)評：臨界問題的處理辦法：1. 找臨界狀態(tài)（1）做好受力分析、運(yùn)動(dòng)過程分析和狀態(tài)分析，抓運(yùn)動(dòng)過程中的“轉(zhuǎn)折點(diǎn)”。（2）利用假設(shè)法討論，假設(shè)某命題成立，推理或判斷物體的狀態(tài)是否會發(fā)生突變。2. 分析隱含條件（1）彈力的突變（2）摩擦力的突變。 第 9 次課后作業(yè)學(xué)生姓名： 例1：如圖所示，質(zhì)量m=

9、1kg的物塊放在傾角為的斜面上，斜面體質(zhì)量m=2kg，斜面與物塊間的動(dòng)摩擦因數(shù)，地面光滑，。現(xiàn)對斜面體施加一水平推力f，要使物體m相對斜面靜止，力f應(yīng)為多大？（設(shè)物體與斜面間的最大靜摩擦力等于滑動(dòng)摩擦力，）答案：14.34nf33.6n例2：如圖所示，有一塊木板靜止在光滑足夠長的水平面上，木板的質(zhì)量為m=4 kg，長度為l=1 m；木板的右端停放著一個(gè)小滑塊，小滑塊的質(zhì)量為m =1 kg，其尺寸遠(yuǎn)遠(yuǎn)小于木板長度,它與木板間的動(dòng)摩擦因數(shù)為=0.4,已知最大靜摩擦力等于滑動(dòng)摩擦力.求:(1)為使木板能從滑塊下抽出來,作用在木板右端的水平恒力f的大小應(yīng)滿足的條件.(2)若其他條件不變,在f=28 n

10、的水平恒力持續(xù)作用下,需多長時(shí)間能將木板從滑塊下抽出.答案 (1)f 20 n (2)1 s例3：（2009重慶模擬）如圖所示,把質(zhì)量m1=4 kg的木塊疊放在質(zhì)量m2=5 kg的木塊上.m2放在光滑的水平面上,恰好使m1相對m2開始滑動(dòng)時(shí)作用于木塊m1上的水平拉力f1=12 n.那么,至少應(yīng)用多大的水平拉力f2拉木塊m2,才能恰好使m1相對m2開始滑動(dòng)?答案 15 n例4：如圖所示，一根輕彈簧上端固定，下端掛一質(zhì)量為m0的平盤，盤中有一物體，質(zhì)量為m，當(dāng)盤靜止時(shí)，彈簧的長度比其自然長度伸長了l，今向下拉盤使彈簧再伸長后停止，然后松手放開，設(shè)彈簧總處在彈性限度內(nèi)，則剛松開手時(shí)盤對物體的支持力為

11、多少？例5：（2005年全國3）如圖所示，在傾角為的光滑斜面上有兩個(gè)輕質(zhì)彈簧相連接的物塊a、b，它們的質(zhì)量分別為ma、mb，彈簧的勁度系數(shù)為k，c為一固定擋板。系統(tǒng)處于靜止?fàn)顟B(tài)。現(xiàn)開始用一恒力f沿斜面方向拉物塊a使之向上運(yùn)動(dòng)，求物塊b剛要離開c時(shí)物塊a的加速度和從開始到此時(shí)物塊a的位移d。重力加速度為g例6：如圖所示，在勁度系數(shù)為k的彈簧下端掛有質(zhì)量為m的物體，開始用托盤托住物體，使彈簧保持原長，然后托盤以a勻加速下降（ag），求經(jīng)過多長時(shí)間托盤與物體脫離？例7：如圖所示，彈簧秤秤盤b的質(zhì)量為1.5kg，彈簧質(zhì)量不計(jì)，勁度系數(shù)k=800n/m，物體a的質(zhì)量為10.5kg，靜置在秤盤上?，F(xiàn)給a施

12、加一個(gè)豎直向上的力f，使a向上做勻加速直線運(yùn)動(dòng)。已知力f在前0.2s內(nèi)位變力，0.2s后為恒力，求a勻加速運(yùn)動(dòng)的加速度及力的最大值與最小值。（取g=10）例8：如圖所示，小車車廂內(nèi)壁上掛著一個(gè)光滑小球，球的質(zhì)量為20kg，懸繩與豎直廂壁成角（g取10），則：（1） 當(dāng)小車以4的加速度水平向左勻加速運(yùn)動(dòng)時(shí)，繩子對小球的拉力t及小球?qū)噹诘膲毫各為多大？（2） 要使小球?qū)噹诘膲毫榱?，小車向左勻加速運(yùn)動(dòng)的加速度至少為多大？winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over eng

13、land, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering from a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first poo

14、l match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, closely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest i

15、n the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.id give every award back in a heartbeat just to get across the line this weekend,

16、 said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism taskforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i

17、have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to him first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of europea

18、n footballs governing body, has also ordered an immediate investigation into the referees actions.cska said they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission abort

19、ed.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move thro

20、ugh the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb higher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. a

21、s he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will slowly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught c

22、old in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to the final and so far history has repeated itself here - the last try they conceded was scored by englands josh charnley in the opening game of the tournament.that could be

23、classed as a weakness, a team under-cooked - but i have been impressed by the kangaroos focus in their games since then.they have been concentrating on the sort of stuff that wins you tough, even contests - strong defence, especially on their own goal-line, completing sets and a good kick-chase. the

24、yve been great at all the unglamorous stuff that often goes unnoticed in the stands but not by your team-mates.it is as though their entire tournament has been preparation for the final.in johnathan thurston, cooper cronk, cameron smith and either billy slater or greg inglis at full-back they have a

25、 spine that is unmatched in rugby league. they have played in so many high-pressure games - a priceless asset going into saturday.the kiwis are a lot less experienced but winning a dramatic match like their semi-final against england will do wonders for their confidence.they defeated australia in th

26、e four nations final in 2010 and the last world cup, and know they can rise to the big occasion.winger tuivasa-sheck, who scored two tries in the kiwis 20-18 semi-final win over england, has been passed fit after a lower-leg injury, while slater has been named at full-back but is still recovering fr

27、om a knee injury aggravated against usa.both sides boast 100% records heading into the encounter but australia have not conceded a try since josh charnleys effort in their first pool match against england on the opening day.aussie winger jarryd hayne is the competitions top try scorer with nine, clo

28、sely followed by tuivasa-sheck with eight.but it is recently named rugby league international federation player of the year sonny bill williams who has attracted the most interest in the tournament so far.the kiwi - with a tournament high 17 offloads - has the chance of becoming the first player to

29、win the world cup in both rugby league and rugby union after triumphing with the all blacks in 2011.待添加的隱藏文字內(nèi)容3id give every award back in a heartbeat just to get across the line this weekend, said williams.the (lack of) air up there watch mcayman islands-based webb, the head of fifas anti-racism ta

30、skforce, is in london for the football associations 150th anniversary celebrations and will attend citys premier league match at chelsea on sunday.i am going to be at the match tomorrow and i have asked to meet yaya toure, he told bbc sport.for me its about how he felt and i would like to speak to h

31、im first to find out what his experience was.uefa hasopened disciplinary proceedings against cskafor the racist behaviour of their fans duringcitys 2-1 win.michel platini, president of european footballs governing body, has also ordered an immediate investigation into the referees actions.cska said

32、they were surprised and disappointed by toures complaint. in a statement the russian side added: we found no racist insults from fans of cska. baumgartner the disappointing news: mission aborted.the supersonic descent could happen as early as sunda.the weather plays an important role in this mission

33、. starting at the ground, conditions have to be very calm - winds less than 2 mph, with no precipitation or humidity and limited cloud cover. the balloon, with capsule attached, will move through the lower level of the atmosphere (the troposphere) where our day-to-day weather lives. it will climb hi

34、gher than the tip of mount everest (5.5 miles/8.85 kilometers), drifting even higher than the cruising altitude of commercial airliners (5.6 miles/9.17 kilometers) and into the stratosphere. as he crosses the boundary layer (called the tropopause),e can expect a lot of turbulence.the balloon will sl

35、owly drift to the edge of space at 120,000 feet ( then, i would assume, he will slowly step out onto something resembling an olympic diving platform.they blew it in 2008 when they got caught cold in the final and they will not make the same mistake against the kiwis in manchester.five years ago they cruised through to