NOM :

Travaux
pratiques n°12
Objectifs :
La chute des corps sur la Terre… Et sur la Lune !
Seconde – L'Univers
étudier et analyser la chute des corps sur la Lune et sur la Terre à l’aide de vidéos pour en déduire les
paramètres ayant une influence sur ce phénomène.
A. Quelques expériences sur la chute des corps.
A.1. Expérience n°1.
 Lâcher simultanément une plume (ou une feuille de papier en forme de plume) et une bille de la même hauteur.
 Noter vos observations.
A.2. Expérience n°2.
 Ouvrir la vidéo intitulée « Expérience Apollo 15» située dans le dossier « 2em13 $ sur ’srv01’(S:) », puis « sujets »
et ensuite « Physique-Chimie ».
 Visionner la vidéo (voir page suivante pour la transcription des dialogues).
 Noter vos observations.
A.3. Premières conclusions.
A.3.1. Comparer les observations des deux expériences précédentes. Est-ce surprenant ?
A.3.2. Comment expliquer la différence entre ces deux expériences ?
A.3.3. Quelles premières conclusions peut-on tirer de ces expériences concernant les lois générales de la chute des
corps ?
B. Étude détaillée de la chute des corps sur Terre.
B.1. Mesures.
On se propose de faire l'étude expérimentale de la chute de deux billes de masse m1 égale à 6,88 g (bille 1) et de
masse m2 égale à 35,8 g (bille 2) à l'aide d'enregistrements vidéo.
 Ouvrir le logiciel Généris5+ dans le sous-dossier Physique du dossier Logiciels spécifiques. Cliquer sur l’icône
vidéo :
, puis sur l’onglet à gauche : Traitement manuel.
 Ouvrir la vidéo intitulée « Bille_1_air .avi» en ouvrant le dossier « 2em13 $ sur ’srv01’(S:) », puis « sujets » et
ensuite « Physique-Chimie » en cliquant sur l’icône choix du fichier.
 Réglage de l’onglet « Étalonnage » :
 cliquer au centre de la bille de l’image 0 pour définir
les axes et leur origine (pour mieux visualiser la bille
en cliquer sur la loupe à gauche et choisir 2,0 et
utiliser la fonction zoom en maintenant enfoncé le
bouton droit de la souris). Orienter l’axe des
ordonnées vers le bas en double-cliquant sur
l’extrémité possédant la flèche. Cocher la case à
gauche : « l’image choisie associée au repère
constitue l’origine des dates ».
 Étalonner l’axe vertical en effectuant un click-glissé
sur la règle de 0,507 m.
 Lancer le traitement en cliquant sur :
.
 Se mettre en zoom 4. Cliquer sur le centre de bille (pour
l’image n°0 avoir les coordonnées x : 0,000 m et y : 0,000 m)
jusqu’à ce qu’elle soit en bas (image n°11), puis arrêter le traitement :
 Enregistrer votre travail dans « Mes documents » sous : TP n°12-L’Univers.
. Soyez précis !
B.2. Exploitation des mesures.
Dans cette partie on va étudier la vitesse de la bille en fonction de la durée de sa chute.
 Cliquer sur l’onglet Tableau. Double-cliquer sur la colonne D pour définir la grandeur
vitesse (voir ci-contre).
 Entrer ensuite la valeur de la vitesse à l’instant initial t1 égal à 0 s dans la cellule D1.
 Pour calculer la vitesse à l’instant t2 égal à 0,0333 s entrer la formule : ( 3
1 ) (t 3
t 1 ) dans la cellule
D2. Inutile d’écrire 3 , il suffit de cliquer sur la cellule C3. Il en est de même pour les autres cellules.
 Pour compléter automatiquement la colonne D se placer sur la cellule D2 et tirer vers le bas la croix située en bas à
droite de la cellule.
 Cliquer sur l’onglet Graphique et afficher le graphe de la courbe d’équation : v f(t).
Choisir des plus pour les points (voir ci-contre).
B.2.1. À quelle type de courbe s’apparente le nuage de points formé par les valeurs
expérimentales de la vitesse en fonction du temps ?
 On va utiliser les fonctionnalités du logiciel pour en déduire l’équation numérique de la
courbe obtenue par modélisation, notée v (t).
TP n°12 – Thème n°1 – L'Univers – Seconde
Pour cela cliquer sur l’icône :
, puis l’onglet à gauche Modélisation. Choisir alors la
courbe voulue. Puis compléter les paramètres comme indiqué ci-contre. Modéliser.
B.2.2. Écrire la relation numérique qui lie les grandeurs v et t. Quelle remarque pouvezvous faire sur le coefficient liant ces deux grandeurs sachant que sa valeur est
donnée à cinq dixièmes d’unité près ?
 Refaire les mêmes mesures et exploitations pour la bille 2 de masse m2 égale à 35,8 g.
B.2.3. Que constatez-vous ?
B.3. Conclusions.
B.3.1. De quel(s) paramètre(s) dépend la chute des corps sur la Terre ?
B.3.2. Quel (s) est(sont) le(s) paramètre(s) qui n’a(ont) aucune influence ?
B.3.3. Ces conclusions sont-elles toujours valables ?
C.
Étude de la chute des corps sur la Lune.
C.1. Peut-on appliquer les conclusions précédentes pour la chute des corps sur la Lune ? Justifier votre réponse.
 À l’aide du tableau de valeur ci-dessous tracer le graphe de la courbe d’équation : v f(t) sur le quadrillage cidessous.
t en s
v en m.s-1
0
0
0,8
1,3
1,5
2,4
2,0
3,3
2,6
4,2
3,1
5,1
Représentation graphique de l’évolution temporelle de la vitesse de chute d’un corps sur la Lune
0
0
C.2. Déduire du graphique la valeur de l’intensité de la pesanteur sur la Lune.
C.3. Sur la vidéo de l’expérience d’Apollo 15 le marteau et la plume chute en 1,2 s. En déduire la hauteur h de chute des
deux objets, sachant que cette hauteur h est liée à leur vitesse de chute v par la relation : v
2 g h.
Sources :


http://www.astrosurf.com/luxorion/galilee-hommage5.htm
http://www.hq.nasa.gov/office/pao/History/alsj/a15/a15.clsout3.html#1672158
TP n°12 – Thème n°1 – L'Univers – Seconde
Transcription du dialogue entre les deux astronautes
167:22:06 Scott: Well, in my left hand, I have a feather; in my right
hand, a hammer. And I guess one of the reasons we got here today
was because of a gentleman named Galileo, a long time ago, who
made a rather significant discovery about falling objects in gravity
fields. And we thought where would be a better place to confirm his
findings than on the Moon.
[Fendell zooms in on the hammer and feather but then pulls back to
watch the action.]
167:22:28 Scott: And so we thought we'd try it here for you. The
feather happens to be, appropriately, a falcon feather for our Falcon.
And I'll drop the two of them here and, hopefully, they'll hit the
ground at the same time. (Pause)
[Dave is holding the feather and hammer between the thumb and
forefinger of his left and right hands, respectively, and has his
elbows up and out the side. He releases the hammer and feather
simultaneously and pulls his hands out of the way. The hammer and
feather fall side by side and hit the ground at virtually the same
time.]
167:22:43 Scott: How about that!
167:22:45 Allen: How about that! (Applause in Houston)
167:22:46 Scott: Which proves that Mr. Galileo was correct in his
findings. (Pause)
167:22:58 Allen: Superb.
[Jones - "That is a beautiful piece of theater. What can you tell me
about the origins of the experiment?"]
[Scott - "The basic idea was Joe Allen's. It was another thing from
sitting in the crew quarters at night, trying to figure out interesting
things to do - that were useful, too. And I guess we had a lot of ideas.
But Joe came up with the hammer and feather idea, and we decided
where to get a feather. I had a friend who was a professor at the Air
Force Academy. Their mascot's the Falcon. And we had the (LM)
Falcon. So that was indeed, a falcon feather from an Air Force
Academy bird. In fact, I had two of them. I was going to try it, first, to
see if it worked - because of static charge and all that stuff it might
have stuck to my glove. Didn't have time (for the trial run), so we
just winged it. And it worked!"]
[The accompanying photo shows Al Worden (left), Dave Scott, and
Jim Irwin at the U.S. Air Force Academy in Colorado Springs with
one of the Academy's falcon mascots on Dave's gloved arm.]
[Jones - "Brought the feather out in the ETB?"]
[Scott - "No, I think the feather was in my pocket. I think I had two
feathers in my pocket. I don't even know where the other feather is.
That one we just left there."]
[Dave had four readily available pockets: one on each sleeve just
below the shoulder ( 150k ) and one strapped to each thigh ( 219k
).]
[Jones - "So the feather's just sitting there, some ways away from
the Descent Stage because of the launch exhaust."]
[Scott - "It was a fun little trick."]
[Jones - "Agreed. Actually, it's one of the great moments of Apollo."]
[Scott - "I think a lot of kids still see this in school. When I was at
Edwards (after leaving the Astronaut Corps), some company came
out there and filmed me dropping a hammer and a feather on the
lake bed. To show the difference. And, of course, the feather floats
down, because of the air. I don't know where that went, either. Some
production outfit went to a lot of effort to do that. It is an interesting
demonstration for the kids, on the effects of gravity and the air."]
["There were a lot of ideas on what do you do to have a zinger.
Shepard hit a golf ball. Purportedly hit a golf ball. Was it on the
TV?"]
[Jones - "Yeah, it is. But it didn't go miles and miles. It went about as
far as the javelin. Ed showed a picture to me that shows both the
javelin and one of the golf balls in a crater not too terribly far
away."]
[Scott - "Well, he hit it, and that's what counts. Everybody tries to do
a little something to have a little levity. Doesn't cost anybody
anything and it's a nice visual image."]
[Jones - "Yours was a class act."]
[Scott - "Yeah, and you know Fendell did good getting the camera on
it, too. I'm wondering if Joe cued him in, 'cause nobody knew we
were going to do this, except Joe. Well, there were some people who
knew but, in general, the people in the MOCR didn't know about it. I
don't think Fendell knew that."]
[Jones - "But you guys pointed the camera..."]
[Scott - "But he zoomed in and then zoomed back so he could see the
ground. It's absolutely perfect framing. I thought that was pretty
clever of Fendell 'cause, had he not framed me correctly, you would
not have seen the hammer or the feather hit the ground."]
[We looked at the TV.]
[Scott - "Joe knows, but I'll bet Fendell doesn't know what we're
doing."]
[Jones - "Where's Fendell sitting?"]
[Scott - "Along the row with Allen."]
[We watch the sequence where Fendell starts to zoom in on the
hammer and feather but then pulls back.]
[Scott - "See, if he doesn't back up now, you're not going to see it.
And he's got a 3-second lag, plus the lag of the lens. So I've often
wondered if Joe told him to back up, or whatever. Because he got
back just barely in time"]
[We watch the sequence at 'appropriately a falcon feather'.]
[Jones - "Now he's backing off. Joe's got to be telling him. It's just
perfect camera work."]
[Scott - "Perfect. And without the framing, it would have lost it's
effect."]
[On a historical note, while reading Christopher Hibbert's George
III: A Personal History (p. 194) during the Christmas 2000 holidays,
I learned that the King, known for his personal interest in the
sciences, was shown a demonstration of the simultaneous fall of a
feather and a one guinea coin in an evacuated tube (p. 194). The
demonstration was performed in 1761 by one John Miller, assistant
to His Majesty's Mathematical Instrument Maker, George Adams.
The experiment is known as the Guinea and the Feather and has
been seen by countless physics students over the centuries. The
Adams Guinea-and-Feather apparatus is on display at the Science
Museum of London along with the Adams air pump with which it
was evacuated. Photos by Mick Hyde.]
[AFJ Editor David Woods calls our attention to the following from
the Apollo 15 Preliminary Science Report: "During the final minutes
of the third extravehicular activity, a short demonstration
experiment was conducted. A heavy object (a 1.32-kg aluminum
geological hammer) and a light object (a 0.03-kg falcon feather)
were released simultaneously from approximately the same height
(approximately 1.6 m) and were allowed to fall to the surface.
Within the accuracy of the simultaneous release, the objects were
observed to undergo the same acceleration and strike the lunar
surface simultaneously, which was a result predicted by wellestablished theory, but a result nonetheless reassuring considering
both the number of viewers that witnessed the experiment and the
fact that the homeward journey was based critically on the validity
of the particular theory being tested."]
[Journal Contributor Joonas Helminen notes that the estimated
height - 1.6 meters - from which the hammer and feather were
dropped is in error. Although the important part of the experiment
is the fact that these two objects of very different weight
experienced the same motion, for completeness we offer the
following. If we concentrate on the hammer, Helminen has stepped
through the mpeg clip and finds that the time between Dave's
release of the hammer and its impact is 36 frames. The framing rate
is 30 frames per second, giving a fall time of 1.2 seconds. We have
two separate estimates of the height. Helminen estimates the height
as 120 cm and writes, "My estimation was simply from thinking
how far you would bend forward with the PLSS on your back and
from noticing how Dave did not hold his arms straight out parallel
to the ground. I am just below 180cm tall and, when put myself in
the same posture, 120 cm was a close estimate of the height of the
bottom of the hammer head." An independent estimate is provided
by the known length of the hammer, which is 39 cm. By noting the
point on the ground where the hammer hits, a measurement can be
made on the image of the initial height of 2.9 hammer lengths or
113 cm. We can use these estimates to calculate the strength of
lunar gravity (grav = 2 * height / time squared). A height of 120 cm
gives 167 cm per second squared and a height of 113 cm gives 157
cm per second squared. Because of likely errors, particularly the
height estimates, both are consistent with the actual value of 163
cm per second squared.]
TP n°12 – Thème n°1 – L'Univers – Seconde