Julius Sumner Miller Lesson 6: Concerning Falling Bodies & Projectiles

00:14:07
https://www.youtube.com/watch?v=EV9wIJF6PaE

Summary

TLDRDans cette vidéo, Julius Suna Miller présente le sujet des corps en chute libre et le mouvement des projectiles. Elle explique que tous les objets, peu importe leur masse, tombent à la même vitesse sous l'effet de la gravité, illustré par la seconde loi de Newton (f = ma). Les facteurs environnementaux comme la viscosité et la friction peuvent influencer ces chutes. Elle revient sur les travaux de Galilée qui a établi que les objets en chute libre décrivent une parabole et que les distances parcourues forment une progression arithmétique (16 ft, 48 ft, 80 ft, etc.). À travers divers exemples et expériences pratiques, Miller démontre l'indépendance des composants horizontale et verticale du mouvement. Elle aborde également l'effet immédiat de la gravitation sur les projectiles lancés horizontalement et l'ajustement des viseurs pour compenser cette chute. En conclusion, elle invite à réaliser une expérience pour démontrer l'effet de la chute libre et clôture avec une mention de Galilée.

Takeaways

  • 📉 Les objets en chute libre tombent à la même vitesse, peu importent leurs masses.
  • 🌀 La viscosité et la friction modifient le mouvement des objets en chute libre.
  • 🔄 Le mouvement d'un projectile est une parabole, comme découvert par Galilée.
  • ⏲️ Tous les objets font face à la gravité de la même façon et touchent le sol simultanément.
  • 🚗 Le mouvement horizontal est indépendant de la composante verticale.
  • 🔬 Les distances en chute libre forment une progression des nombres impairs.
  • ⚙️ Utilisez des viseurs ajustés pour compenser la chute des projectiles.
  • 🪂 Une expérience avec des balles et une corde démontre la chute libre.
  • 🎯 La gravité affecte immédiatement les projectiles horizontalement tirés.
  • ⚗️ Recréer des expériences pratiques pour mieux comprendre ces phénomènes.

Timeline

  • 00:00:00 - 00:05:00

    La vidéo commence avec l'animateur présentant le sujet de la physique concernant la chute libre et le mouvement des projectiles. Il rappelle que selon la seconde loi de Newton, tous les corps tombent à la même vitesse quelle que soit leur masse. Un rappel est fait de l'expérience où une pièce et un papier tombent à la même vitesse dans un tube à vide, malgré l'échec de la démonstration à cause d'une fuite d'air. Il explique le comportement d'un corps en chute libre en précisant les distances parcourues dans des séquences de temps spécifiques (16 pieds, 48 pieds, 80 pieds, etc.), une relation découverte par Galilée. Galilée a découvert que les distances sont proportionnelles aux carrés des nombres entiers (1, 4, 9, etc.) lors de la chute d'un corps.

  • 00:05:00 - 00:14:07

    L'animateur poursuit avec des expériences démonstratives pour illustrer la simultanéité de la chute de deux corps : un lancé horizontalement et l'autre tombant librement d'une même hauteur, expliquant que leur temps d'impact est identique, démontrant l'indépendance des vitesses horizontale et verticale. Il illustre cela avec un chariot lançant une balle verticale et rattrapant la balle pendant son déplacement. Il continue avec l'expérience du 'sing et chasseur', démontrant qu'un projectile visé directement à un cible ne frappera jamais le centre à cause des forces gravitationnelles. Il aborde finalement une expérience maison avec des boules attachées à une corde, se rapprochant proportionnellement pour démontrer les distances de chute libre, reliant à nouveau aux découvertes de Galilée sur les distances parcourues et leur proportion avec les nombres impairs et leurs carrés.

Mind Map

Mind Map

Frequently Asked Question

  • Quels sont les principes de base de la chute libre ?

    Tous les objets, indépendamment de leur masse, tombent à la même vitesse lorsqu'ils sont en chute libre conformément à la seconde loi de Newton.

  • Quels facteurs peuvent influencer le mouvement des objets en chute libre dans la vie réelle ?

    Dans la réalité, la viscosité, la friction et d'autres interactions avec l'atmosphère peuvent influencer le mouvement des objets en chute libre.

  • Qui a découvert que les objets décrivent une parabole lorsqu'ils sont projetés ?

    Galileo Galilei a découvert que le mouvement d'un projectile forme une parabole.

  • Comment démontrer que tous les objets en chute libre touchent le sol en même temps ?

    Exploiter une expérience avec un ressort pour projeter horizontalement une bille pendant qu'une autre tombe verticalement démontre qu'elles touchent le sol simultanément.

  • Quelle est l'indépendance des mouvements horizontal et vertical ?

    Le mouvement horizontal est indépendant du mouvement vertical, chaque composante se réalisant sans interférence de l'autre.

  • Quelle est l'importance de la découverte de Galilée sur les distances parcourues par un corps en chute libre ?

    Galilée a découvert que les distances parcourues forment une progression arithmétique liée aux nombres impairs : 1, 3, 5.

  • Comment le placement des balles sur une corde démontre-t-il la progression de la chute libre ?

    Les intervalles entre les balles sont plus serrés vers le bas et s'élargissent vers le haut, illustrant la progression géométrique des distances parcourues en chute libre.

  • Quel est le rôle de la gravité sur un projectile tiré horizontalement ?

    La gravité provoque une chute du projectile dès son émergence, ce qui empêche de toucher une cible en ligne droite.

  • Quel dispositif permet de prouver le mouvement parabolique des projectiles ?

    Un mécanisme avec une bille et une voiture montre que la bille est rattrapée par la voiture même lorsqu'elle est projetée verticalement.

  • Pourquoi les viseurs de fusils doivent-ils être ajustés ?

    Les viseurs sont ajustés pour compenser la chute du projectile due à la gravité et permettent de viser juste.

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  • 00:00:00
    [Music]
  • 00:00:14
    how do you do ladies and gentlemen and
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    boys and girls I am juliia Suna Miller
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    and physics is my business and our very
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    special business today is the subject of
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    freely falling bodies and bodies which
  • 00:00:27
    are projected projectile motion and I
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    would remind you of things already
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    learned in earlier lessons such as for
  • 00:00:35
    example a body of small Mass a body of
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    enormous Mass released to fall freely
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    released simultaneously to fall freely
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    and what is their behavior they fall at
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    the same rate and you remember it is
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    Newton's second law that tells us that
  • 00:00:53
    namely that f equals ma or for freely
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    falling bodies W equal m
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    J now what is the action of a body
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    falling
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    freely of course it Encounters in real
  • 00:01:07
    life some viscosity and friction and
  • 00:01:09
    trouble with the atmosphere so what we
  • 00:01:11
    can do is large a heavy body and a light
  • 00:01:14
    one say a coin and a piece of paper in a
  • 00:01:17
    tube and then with a vacuum pump take
  • 00:01:19
    out as much air as we can and then do as
  • 00:01:23
    follows and we would see both bodies
  • 00:01:26
    fall at the same rate I had this tube
  • 00:01:29
    originally evacuated but there has been
  • 00:01:31
    a leak so the experiment as some would
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    say has failed but I remind you I have
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    not provided nature with her
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    requirements to show the simultaneity of
  • 00:01:41
    fall of both bodies in free space now
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    when we study a falling body dropped so
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    like that we learn as follows supposing
  • 00:01:52
    it starts right there 1 second elapses
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    and we find it right there how far has
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    it Fallen 16 ft
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    now we let another second elapse and I'm
  • 00:02:02
    not drawing this to scale and how far
  • 00:02:05
    would it fall in the second second
  • 00:02:07
    during the second second it would fall
  • 00:02:10
    48 ft now let it fall for a third second
  • 00:02:14
    and how far would it fall during the
  • 00:02:16
    third second and we find 80 ft and these
  • 00:02:19
    numbers have some mathematical
  • 00:02:22
    enchantment because 16 divided by 16 48
  • 00:02:26
    divided by 16 80 divided by 16 and we
  • 00:02:30
    see that the numbers are the odd numbers
  • 00:02:33
    beginning with unity which is a
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    discovery that Galileo made in the 16th
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    century now further than that you see
  • 00:02:42
    that first the first two seconds is
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    64t the first second is 16 ft the first
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    3 seconds is
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    144t and look at these numbers
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    16 16 into 64 is 4 that's 2^ squar 16
  • 00:03:01
    into 144 is 9 that's 3 squar so the
  • 00:03:05
    distances all fallen during the
  • 00:03:08
    succeeding seconds are in the order 1
  • 00:03:12
    three uh uh 1 149 you see 149 1 squar 2
  • 00:03:17
    squ 3 squar now when we study a freely
  • 00:03:21
    falling body it is too far to measure in
  • 00:03:24
    real life so what do we do we have a
  • 00:03:27
    machine which records a falling body and
  • 00:03:31
    where it is every 60th of a second and
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    here is a tape which I have run and the
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    point to be noticed is that the
  • 00:03:39
    distances as we go down increase in the
  • 00:03:43
    order I have described a discovery made
  • 00:03:46
    by Galileo now there is another exciting
  • 00:03:49
    Adventure regarding falling bodies
  • 00:03:52
    another very exciting Adventure suppose
  • 00:03:55
    and I had a body a and a body B on the
  • 00:03:58
    same horizontal level
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    with respect to the
  • 00:04:01
    ground and what am I going to do I'm
  • 00:04:04
    going to allow a to fall freely and B
  • 00:04:08
    I'm going to project horizontally like
  • 00:04:10
    that now you know the path it takes is a
  • 00:04:13
    parabola indeed this was discovered also
  • 00:04:17
    by Galileo in the 16th century and the
  • 00:04:20
    question that's enchanting is this how
  • 00:04:23
    about their times of arrival at the
  • 00:04:25
    ground the impulsive notion is well this
  • 00:04:28
    is going much farther and hint should
  • 00:04:30
    take longer but that is not true the
  • 00:04:32
    time of fall for a to the ground and B
  • 00:04:36
    to the ground are one in the same why
  • 00:04:39
    because the horizontal velocity of B
  • 00:04:41
    remains unaltered and the vertical
  • 00:04:44
    velocity is taken care of by
  • 00:04:46
    gravitational forces the same in both
  • 00:04:49
    cases and here we have an experiment a
  • 00:04:52
    demonstration to show that here is a
  • 00:04:55
    device with a
  • 00:04:56
    spring which permits me to shoot a ball
  • 00:05:00
    horizontally as in the case of B and
  • 00:05:03
    here is one that I can release to fall
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    freely as a in the picture and we will
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    rely on our senses hearing and sight to
  • 00:05:12
    verify what happens watch it
  • 00:05:16
    simultaneity of
  • 00:05:17
    impact now this is not a proof but it is
  • 00:05:21
    a suggestion of the reliability of the
  • 00:05:23
    law of falling bodies and projectiles
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    consider now another one this one has
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    absolute
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    enchantment let me put a ball in a car
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    on a
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    spring and now I will put the spring in
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    compression drive the car away from me
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    the spring will be released and project
  • 00:05:49
    the ball vertically and the car will go
  • 00:05:52
    horizontally and it does no longer have
  • 00:05:55
    the ball in it pretty soon the car is
  • 00:05:58
    over here and what do we discover we
  • 00:06:01
    discover an amazing and wonderful thing
  • 00:06:03
    that the ball is caught by the car and
  • 00:06:07
    I'm going to show you that first let us
  • 00:06:09
    take a look at the mechanism here is the
  • 00:06:12
    cart there is the ball and I have
  • 00:06:16
    compressed the spring and it is held by
  • 00:06:19
    a pin below so when I pull a string
  • 00:06:22
    which releases the spring the ball will
  • 00:06:26
    be shot up let's get over to this table
  • 00:06:29
    and take a look at it I'll put something
  • 00:06:31
    down out of the way
  • 00:06:34
    here let us take a look at
  • 00:06:38
    it watch now watch I am going to drive
  • 00:06:42
    the car
  • 00:06:43
    away so pull the pin up goes the ball
  • 00:06:48
    the car keeps going and Zoe the ball is
  • 00:06:51
    caught by the car watch it
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    now there it is now I did not go so very
  • 00:06:58
    high and perhaps I should do that again
  • 00:07:00
    to show you what a wonderful thing it is
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    to witness watch it watch it oh this
  • 00:07:07
    is there it is and I say this is
  • 00:07:11
    enchanting to
  • 00:07:13
    witness which suggests a very important
  • 00:07:16
    piece of physics the horizontal motion
  • 00:07:18
    of the car which we would refer to as
  • 00:07:21
    the horizontal the horizontal velocity
  • 00:07:24
    is independent of the vertical
  • 00:07:27
    velocity each goes its own way without
  • 00:07:30
    interference by the
  • 00:07:32
    other now here is an
  • 00:07:36
    experiment that I wish to talk about but
  • 00:07:39
    will not show you and I suggest you try
  • 00:07:42
    to make the apparatus yourself I call it
  • 00:07:45
    the monkey and Hunter here it is let us
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    take a tube say of lucite such as I have
  • 00:07:55
    here and let us bore sight
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    on a monkey here that's why I call it a
  • 00:08:01
    monkey and Honda now what is the monkey
  • 00:08:03
    going to be the monkey is going to be a
  • 00:08:05
    tin can held up by an
  • 00:08:08
    electromagnet now what am I going to do
  • 00:08:11
    I'm going to put a light say a loose
  • 00:08:13
    sight ball in this place here in the
  • 00:08:16
    chamber of the gun and I'm going to have
  • 00:08:19
    two little wires across the end of this
  • 00:08:21
    tube such as I have right here if you
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    look carefully I'll take that stopper
  • 00:08:27
    out now what happen
  • 00:08:31
    when these two wires are crossed the
  • 00:08:33
    electromagnetic circuit is closed and
  • 00:08:36
    the tin can is held up now I put my
  • 00:08:39
    mouth to this end in this fashion and I
  • 00:08:43
    blow now you know what happens the
  • 00:08:46
    projectile emerges here as it emerges it
  • 00:08:49
    opens the two little wires the
  • 00:08:52
    electromagnet loses its magnetic hold
  • 00:08:55
    and the monkey falls down there's the
  • 00:08:58
    monkey now let's say say the monkey
  • 00:09:00
    Falls to there in a certain time and
  • 00:09:03
    what do we expect we ex expect the
  • 00:09:05
    projectile to hit him and here is a very
  • 00:09:09
    important detail the monkey can never be
  • 00:09:13
    hit at that place if he stays there why
  • 00:09:17
    because the moment the projectile
  • 00:09:19
    emerges it is taken down by
  • 00:09:21
    gravitational forces and can never hit
  • 00:09:24
    the monkey that is to
  • 00:09:26
    say looking at it in another view that
  • 00:09:30
    if we had a gun aimed absolutely
  • 00:09:34
    horizontally absolutely
  • 00:09:37
    horizontally at a Target on the
  • 00:09:41
    nose and we fired the gun absolutely
  • 00:09:45
    horizontally and the projectile emerged
  • 00:09:47
    there we could never hit the bullseye
  • 00:09:52
    never why because the instant the
  • 00:09:55
    projectile emerges it is taken down like
  • 00:09:57
    that and as an illustration of numbers
  • 00:10:01
    supposing the muzzle velocity of the gun
  • 00:10:03
    was 1,000 ft per second 1,000 ft per
  • 00:10:07
    second supposing this was 1,000 ft and
  • 00:10:10
    supposing under ideal conditions the
  • 00:10:13
    horizontal velocity of the projectile
  • 00:10:15
    remains unaltered it would take one
  • 00:10:17
    second for the projectile to reach the
  • 00:10:20
    target but in one second how far does do
  • 00:10:23
    gravitational forces take the projectile
  • 00:10:26
    as we discovered 16 ft
  • 00:10:29
    now somebody says look here Professor I
  • 00:10:32
    shoot guns and I hit targets of course
  • 00:10:35
    you do because what is really done is
  • 00:10:38
    this the sight on the gun is such as to
  • 00:10:43
    compensate for this fall due to
  • 00:10:45
    gravitational forces and so the
  • 00:10:47
    projectile is hit so remember it is
  • 00:10:50
    Newton and Galileo very important very
  • 00:10:54
    important in the case of falling bodies
  • 00:10:57
    and projectile motion now here is
  • 00:11:00
    another experiment that you can
  • 00:11:02
    do did we not say that when a body falls
  • 00:11:07
    from rest it falls successively farther
  • 00:11:11
    and the distance is 16 ft 48 ft 80 ft
  • 00:11:15
    and so on I have here another experiment
  • 00:11:19
    that you can do and we need to take a
  • 00:11:21
    look at an apparatus which you can make
  • 00:11:23
    at
  • 00:11:24
    home it consists of a string to which
  • 00:11:28
    are attach ATT some spheres and I have
  • 00:11:31
    used billiard balls and now since this
  • 00:11:34
    is pretty high I will show you that at
  • 00:11:38
    the
  • 00:11:39
    bottom the separation is
  • 00:11:43
    closer and farther apart as we get
  • 00:11:46
    higher so the picture I have drawn on
  • 00:11:48
    the Blackboard is turned upside down now
  • 00:11:52
    supposing we released the whole string
  • 00:11:54
    of things from the very top would not
  • 00:11:58
    the successive impacts of these balls on
  • 00:12:01
    the ground be in arithmetic progression
  • 00:12:05
    every second let us say one would hit or
  • 00:12:08
    every certain part of a second but the
  • 00:12:11
    distances are clearly in geometric
  • 00:12:14
    proportion as you see from what I have
  • 00:12:17
    done on the
  • 00:12:18
    Blackboard very exciting adventures and
  • 00:12:21
    I must say again this business of one
  • 00:12:25
    three
  • 00:12:26
    five uncovered by galile
  • 00:12:30
    and remember this distance is 16 ft in
  • 00:12:33
    the first second in the first 2 seconds
  • 00:12:36
    64 ft in the first 3 seconds 144 ft and
  • 00:12:41
    I wish to point out again because this
  • 00:12:43
    is enchanting to
  • 00:12:45
    follow this number if we divide by 16 is
  • 00:12:49
    one if we divide by 16 is four if we
  • 00:12:52
    divide by 16 is nine and you see 1 is 1
  • 00:12:56
    squared and four is 2 squared and nine
  • 00:12:59
    is 3^ squ so to quote
  • 00:13:02
    Galileo the distances passed over by a
  • 00:13:05
    falling
  • 00:13:06
    body beginning at zero time are in the
  • 00:13:10
    ratio of the odd numbers beginning with
  • 00:13:12
    one 1 3 5 but the total distances passed
  • 00:13:16
    over 16 64 144 are in the ratio of the
  • 00:13:22
    integers beginning with one squared 1
  • 00:13:25
    squar 2 squar 3 squar and so the next
  • 00:13:28
    must be of course four squ and so on and
  • 00:13:31
    since I have spoken about Galileo we
  • 00:13:34
    should take a look at this wondrous
  • 00:13:36
    gentleman of Florence and
  • 00:13:39
    Pisa and Rome and Padua and here is
  • 00:13:45
    Galileo
  • 00:13:47
    1564
  • 00:13:49
    1642 and I thank you for attending to
  • 00:13:52
    our business
  • 00:13:55
    [Music]
Tags
  • chute libre
  • mouvement projectile
  • Newton
  • Galilée
  • physique
  • gravité
  • expériences
  • progression arithmétique
  • parabole
  • vitesse