Well, the aim of today s lesson is to understand how he came to this idea and how he interpreted the motion of the Moon around the Earth.

Transcription

1 1) Inteogation oale d un élève su la patie : the gavity field, taitée au cous pécédent : Pévoi de faie paticipe les autes élèves au besoin. - Last time, we spoke about fields in physics; could you give examples of field? Magnetic field, electic field, gavitational field - What is a field? This is a space aea (zone) whee something undegoes a foce - What is esponsible fo a magnetic field? Pemanent magnets o cuents - Fo an electic field? Electic chages - Fo a gavitational field? Masses - How is a field usually epesented in physics? By aows (vectos) - Pictue the gavity field on the blackboad - Something is missing, can you help him (he) - Is thee only one point in space? - What does the same length mean? It means that the field is the same eveywhee (has the same size) - How do we detect the gavity field? When we dop something, it falls vetically - What ae the units fo g? m/s² o N/kg - What is the unit m/s² usually used fo? It is used fo acceleation - Which acceleation does it coespond to? It coesponds to the gavity acceleation (o acceleation of fee fall) And the unit N/kg coesponds to the gavity field O - What was Newton s hypothesis concening the fee fall acceleation and the gavity field? - What was Newton s hypothesis concening weight and gavitational foce? He suggested they wee equal. Well, the aim of today s lesson is to undestand how he came to this idea and how he intepeted the motion of the Moon aound the Eath.

2 B) Foces change velocities 2) Read the second pat by youself (fom Newton explains that to velocity ). Undeline one key sentence in each paagaph, pointing out the effect of foces on velocities. Pepae youself to justify. 1: fom Newton explains to sometimes both 2: fom This is connected to elative 3: fom This is a fa cy to thei velocity Laisse du temps, inteoge nominativement plusieus élèves su le même paagaphe. Réponses possibles : Faie note les éponses su le cahie. 1: Newton explains that wheneve a velocity is changed, a foce must be involved o Accoding to Newton, foces change velocities-sometimes in magnitude (speed), sometimes in diection, sometimes both Thanks to the change in velocity, eithe in diection o in magnitude, we can ecognize the existence of a foce; the change in velocity is an evidence fo a foce, even if we cannot see it. 2: No foce, no change in velocity o Movement itself needs no foce How do you eact to this statement? It is shocking because in usual life, we need lage foces to let things move. So it is incedible that motion should exist without foce. 3: They (the planets) just keep going unless a foce changes thei velocity. In looking at the sky, we know that a foce should exist. Without it, stas would not go in cicula path but staight on. 3) To keep on studying the effect of foces on velocities, we can look at the pictues besides. - What ae the fou examples of motion in fig 3? Ball lobbed in tennis, footballe deflecting the ball, comet appoaching the Sun, Moon obiting the Eath. - What do the aows in the pictues stand fo? They stand fo velocities o changes in velocity. - Do you emembe what the tip-to-tail ule consists in? Conside a vecto: This is the tip This is the tail To add two vectos, you must stick the tip of the fist to the tail of the second one The esultant is in ed: Fo velocities, it is the same: Old velocity + change in velocity = new velocity

3 old velocity Take the example of the ball lobbed in tennis: 4) Label the othe examples the same way I did: Old velocity in geen Change in velocity in black, pecise what the change is due to New velocity in ed new velocity change in velocity (due to gavity) Inteoge plusieus élèves au tableau pou coige les constuctions change due to the footballe s action change due to the pull of the Sun on the comet change due to the pull of the Eath on the Moon 5) In the last example (Moon obiting the Eath), velocity changes and speed stays the same. But what is the link between change in velocity and foce? change in velocity time = acceleation and foce = mass acceleation C) How can we wok out acceleation, when only velocity changes and not speed? 5 a) I give you a dawing with some keys. The class will be split in two pats: you have two sots of dawing. Each of you must wite instuctions to you school fiend to make him (he) daw it. La classe est sépaée en deux, chaque patie a un dessin à décie aux autes Pemie dessin : A TEAM A θ B Cicula obit Radius Duing time Δt, adius tuns though θ

4 deuxième dessin : TEAM B A Constant speed v B v 1 Old velocity v 1 θ New velocity v 2 + v 2 Δv Change in velocity Δv Duing time Δt, velocity tuns though θ Inteogation oale : un membe de l équipe A décit le dessin à un membe de l équipe B, puis on pemute les ôles. Quand les deux dessins sont au tableau, on pose des questions à l ensemble de la classe. 5 b) Now, copy both dawings on the empty fig 4. AB 5 c) What is the elation between AB, and θ (ad) in the fist dawing? θ (ad) = (1) 5 d) What is the elation between change in velocity Δv, speed v and θ (ad) in the second dawing? Δv θ (ad) = (2) v 5 e) At constant speed, what is the elation between AB, v and Δt? Reaange in (1). 5 f) Thanks to (1) and (2), expess the acceleation. 6) Now the final question is: D) How did Newton explain the motion of the Moon aound the Eath? Fist, he used a geometical agument developed in the fist paagaph: 6a) Read the fist paagaph concening Newton s gavitational law (fom Newton had thought to and so on ) and ewite the undelined phases in mathematical language. Laisse du temps ; Donne le pemie exemple. An invese squae law involves a quantity (a foce fo example) which is invesely popotional to the squae of the adius, so we would wite F 1/² The squae of the distance = d² One quate = ¼ Distance doubles = d x 2 One ninth = 1/9 Distance tebles = d x 3

5 6b) To illustate the popeties of the gavitational law we can use the fig 5. In this figue, quote the pictue: - that shows the invese squae law in geomety : (c) - that shows the invese squae law in calculus : (b) - that shows all paticles attact each othe: (a) 7) Now we have all the data Newton used to explain the motion of the Moon aound the Eath. Look at fig 6: Laisse du temps Fist pictue: - What does the dawing stand fo? The tajectoy of the Moon aound the Eath. - What does the time coespond to? The peiod of evolution. - What does the distance coespond to? The length of the obit. - How do we calculate the speed? By dividing the distance coveed on the obit by the peiod. - What is the esult? One thousand twenty mete pe second. - How do we calculate the acceleation? By dividing the squaed speed by the adius of the obit. - What is the esult? Tansfom it into powes of ten? Two point seven times ten to the powe of minus thee metes pe second squaed. Second pictue: - What is the adius of the Moon s obit? Thee hunded and eighty fou thousand kilometes. - What is the value of the Eath s adius? Six thousand fou hunded kilometes. - What is the atio between them? One ove sixty. - How did Newton calculate the gavity acceleation at Moon s obit? By dividing by sixty squaed. - Why? Because gavitational law is an invese squae law. - Does it fit the pevious esult? Yes - So what conclusion can we daw? The acceleation of the Moon is due to gavity, the same as the one that makes things fall on the Eath. - Which sentence in the second paagaph of Newton s gavitational law (fom While sitting in an ochad to a Moon ) confims this conclusion. Movement on Eath and motion in the heavens became all the same thing. - Undeline it. As a conclusion: execise