Julius Sumner Miller Lesson 3: Newton's Second Law of Motion - The Elevator Problem

00:14:23
https://www.youtube.com/watch?v=_XJrY2sKfFQ

Resumen

TLDRJulia Sumner Miller explores Newton's Second Law of motion, famously encapsulated by the equation F = ma, but expounded with more complexity and experiments. The law indicates that a change in motion is proportional to the force applied and occurs along the direction of the force. This principle explains why objects with less mass accelerate more rapidly under the same force, and why in circumstances like free fall, a body is considered weightless as the scale reads zero. Miller demonstrates these theories using various practical experiments, such as analyzing the forces on carts of different masses, and, in a societal context, using elevators to visualize changes in perceived weight. Furthermore, connections are drawn between Newton's law and everyday experiences, emphasizing its foundational role in physics. Concepts like gravitational acceleration among objects of different masses are clarified, illustrating Galileo's findings that all objects in free fall accelerate equally, irrespective of mass, a principle rooted in Newton's law. Miller concludes with insights on the broader implications of physics in understanding the natural world.

Para llevar

  • 👨‍🔬 Newton's Second Law says F = ma, explaining force-motion relationships.
  • 🚗 Lighter objects accelerate more with the same force due to inverse mass ratio.
  • ⚖️ In free fall, scales read zero, as gravitational pull negates weight reading.
  • 🛗 Elevators illustrate perceived weight changes due to upward/downward acceleration.
  • 🌀 Gravitational acceleration is consistent across different mass objects, as Galileo noted.
  • 📖 Newton's insights have foundational implications for modern physics understanding.
  • 🤔 Equal forces in opposite directions don't sum or cancel on a scale; they read as one force.
  • 🚀 Physical laws like Newton's are reflected in daily phenomena such as driving and lifting.
  • 👶 Young Newton, as pictured, was a groundbreaking scholar who transformed science.
  • 🔬 Experiments solidify understanding of theoretical physics through practical application.

Cronología

  • 00:00:00 - 00:05:00

    Julia Sumner Miller introduces the focus on Newton's Second Law, noting the common understanding of it as F=MA. Through demonstrations with objects of different masses connected by a spring, she illustrates that with the same force applied, an object with less mass accelerates faster, emphasizing that acceleration is inversely proportional to mass. This demonstration serves as a foundation for later discussions on energy and momentum influenced by Newton's second law. Further, she discusses the weight and acceleration with a scale, showing that acceleration adds to the force read by the scale, and explains weightlessness during freefall.

  • 00:05:00 - 00:14:23

    Miller uses various examples and experiments to further explain Newton's Second Law. She talks about weightlessness by describing freefall and relates it to gravitational acceleration. Using different-sized objects, she proves that all objects have the same freefall acceleration, echoing Galileo's observations. She includes a cartoon scenario showing acceleration's effect on scale readings, demonstrating Newton's second law. Additionally, she explains through a pulley system that when a force is applied by one person, another gets a 'free ride.' Through these practical explanations and thought experiments, she simplifies the complex ideas of physics according to Newton's principles.

Mapa mental

Mind Map

Preguntas frecuentes

  • What is Newton's Second Law?

    Newton's Second Law states that change of motion is proportional to the force applied and occurs in the direction of the force, often summarized as F = ma.

  • Why does a smaller car accelerate faster than a larger one?

    According to Newton's Second Law, the smaller car accelerates faster because their acceleration is inversely proportional to their masses.

  • What does an upward acceleration do to the weight reading on a scale?

    When you accelerate upward, the scale reads more due to the added force required to accelerate the object, represented as F = mg + ma.

  • What happens to the reading on a scale during free fall?

    During free fall, the scale reads zero because the acceleration due to gravity equals the downward acceleration, effectively making one weightless.

  • Why do objects of different masses fall at the same acceleration?

    Because the force (weight) on them and their mass ratio remains consistent, leading to the same gravitational acceleration.

  • What occurs when two equal forces pull in opposite directions on a scale?

    The scale reads the weight of one of the forces, indicating it doesn't simply sum or negate the opposite forces.

  • How can an elevator's movement affect your perceived weight?

    Accelerating upward increases perceived weight due to added force (F = mg + ma), while downward acceleration decreases it (F = mg - ma).

  • Who was Isaac Newton and what did he contribute to physics?

    Isaac Newton was a 17th-century physicist whose work on motion and gravity laid the groundwork for classical mechanics.

  • Why do heavier and lighter spheres fall at the same rate?

    They both experience the same gravitational force relating to their masses, maintaining consistent acceleration.

  • Can Newton's Second Law apply to everyday phenomena?

    Yes, examples include the acceleration of vehicles, changes in weight perception in elevators, and free-falling objects.

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Desplazamiento automático:
  • 00:00:12
    how do you do ladies and gentlemen and
  • 00:00:14
    boys and girls I am Julia Sumner Miller
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    and physics is my business
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    and our special business today is
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    Newton's second law the second law now
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    in an earlier program we discussed the
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    first law and I showed you some dramatic
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    demonstrations on the first part a body
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    at rest and on the second part a body
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    moving uniformly wants to do that now we
  • 00:00:40
    come to Newton's second law this is a
  • 00:00:43
    staggering thing in its implications and
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    very very difficult really
  • 00:00:49
    but what students of physics learn
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    somewhere in their course is that
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    Newton's second law says F equals MA and
  • 00:00:58
    indeed that's what it says but that's
  • 00:01:01
    powerful
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    and not so easy let us see what Newton
  • 00:01:05
    said for his second law in the Latin
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    Utah ciona motors propulsion Allah Messi
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    Wiimote RIS e but the Latin is a little
  • 00:01:16
    old-fashioned so if we look at the
  • 00:01:18
    English here it is change of motion is
  • 00:01:22
    proportional to force applied and takes
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    place in the direction of the straight
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    line in which the force acts so let me
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    demonstrate Newton's second law here I
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    have two cops a heavy one a massive one
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    and a less massive one and they are
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    connected with a pseudo spring an array
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    of rubber bands which are called elastic
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    bands but which incidentally are
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    inelastic now they are on wheels so that
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    they move rather freely but we learned
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    earlier that this one has less inertia
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    than this one now when I pull them apart
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    and stretch the spring between them the
  • 00:02:10
    same force acts on both and let us see
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    if we cannot at once predict what will
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    happen if we apply Newton's second law
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    to the forces acting on these cars
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    clearly the big car will have a little
  • 00:02:26
    acceleration and the little car will
  • 00:02:29
    have a big acceleration that's an
  • 00:02:31
    obvious thing to to speculate on watch
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    it I'm going to pull them apart there is
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    one in the same force acting on both
  • 00:02:40
    cars and you will observe that the
  • 00:02:43
    smaller one gets going the fastest
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    sooner of course and so here is an
  • 00:02:50
    expression mathematically that describes
  • 00:02:53
    this and what can we learn from that
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    remark we learn that the accelerations
  • 00:03:00
    are inversely proportional to the masses
  • 00:03:02
    the bigger the mass the less the
  • 00:03:04
    acceleration now this experiment with
  • 00:03:07
    the two cars very important for our
  • 00:03:10
    concern later because we will talk in
  • 00:03:13
    subsequent programs about the energy
  • 00:03:16
    possessed by each car and about the
  • 00:03:19
    momentum possessed by each car and we
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    shall learn then that Newton's second
  • 00:03:24
    law has enormous implications for later
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    work in physics now more about the
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    second law here is a scale on which I
  • 00:03:35
    hang a weight and I don't care what the
  • 00:03:38
    scale reads it reads something we say it
  • 00:03:40
    reads the weight of the body but I
  • 00:03:43
    really don't know what that means
  • 00:03:45
    nor did Newton because as we believed
  • 00:03:48
    gravitational forces the earth pulls on
  • 00:03:51
    this stretches the scale but remember
  • 00:03:54
    even Newton said I offer no hypothesis
  • 00:03:58
    concerning gravitation not do we
  • 00:04:00
    understand it today but anyway this
  • 00:04:03
    scale reads the weight of this so I'm
  • 00:04:06
    going to write Newton's second law
  • 00:04:08
    saying that very fact here it is F
  • 00:04:12
    equals mg where mg is the weight of the
  • 00:04:17
    body now I'm going to accelerate this
  • 00:04:21
    system upward and I want you to see what
  • 00:04:24
    the scale does watch it now the scale
  • 00:04:28
    read more and so I have to add here MA
  • 00:04:33
    in other words the scale reads
  • 00:04:36
    not only the rest mass of the body but
  • 00:04:39
    an additional force which was required
  • 00:04:41
    to accelerate it upward
  • 00:04:43
    let me now start again in the zero
  • 00:04:47
    position the system at rest the scale
  • 00:04:50
    reading the so called weight of the body
  • 00:04:52
    and let me accelerate downward watch it
  • 00:04:55
    the scale reads less and so I write
  • 00:04:59
    minus M a mg minus M a and this tells us
  • 00:05:04
    a wonderful thing because if I work to
  • 00:05:07
    go to the edge of my roof and hold this
  • 00:05:10
    like this and then let go of it here and
  • 00:05:13
    the whole thing fell down toward the
  • 00:05:14
    earth a good question to ask is what
  • 00:05:17
    would the scale read during the falling
  • 00:05:20
    and the answer is obvious since the
  • 00:05:23
    acceleration downward would be that of a
  • 00:05:26
    freely falling body the scale would read
  • 00:05:28
    zero so if I should jump off from my
  • 00:05:31
    tabletop while I am in flight toward the
  • 00:05:33
    earth I way I am weightless I'm
  • 00:05:36
    weightless now this second law bears on
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    the first one which I showed in an
  • 00:05:44
    earlier program you remember that I had
  • 00:05:47
    an enormous weight here which on which I
  • 00:05:51
    pull gently with a string and the string
  • 00:05:53
    held it but when I gave the system a
  • 00:05:56
    sudden acceleration upward the string
  • 00:06:00
    cannot endure it and I said then that
  • 00:06:03
    the body wishes to remain at rest I now
  • 00:06:06
    add an additional fact that the string
  • 00:06:10
    must exert a force not only equal to the
  • 00:06:12
    weight of the body but an additional one
  • 00:06:14
    to accelerate it which it may not be
  • 00:06:17
    able to do no it couldn't do it
  • 00:06:19
    now what is the meaning of this for
  • 00:06:24
    other things supposing I had an enormous
  • 00:06:28
    sphere such as I have here a steel
  • 00:06:31
    sphere two inches in diameter and then a
  • 00:06:36
    teeny weensy one and I want to show you
  • 00:06:39
    that I want to show you that in fact
  • 00:06:41
    here I have several of different sizes
  • 00:06:43
    there's one there's one very good now I
  • 00:06:48
    have one
  • 00:06:49
    yeah that is so tiny in fact that I
  • 00:06:52
    can't see it without my glasses that
  • 00:06:56
    shows you how tiny it is and I wonder if
  • 00:06:59
    I get the other debris out of the way
  • 00:07:01
    can the camera get that into one right
  • 00:07:06
    right well it's there
  • 00:07:09
    I assert it is there even though you
  • 00:07:12
    cannot see it
  • 00:07:13
    oh yeah it's awful tiny and what am I
  • 00:07:16
    going to say about it
  • 00:07:18
    supposing I hold these two I won't hold
  • 00:07:21
    the tiny one cos you can't see it
  • 00:07:23
    supposing I hold these two at the same
  • 00:07:25
    horizontal level above the level of the
  • 00:07:28
    earth equally and I let them go they
  • 00:07:32
    fall with the same acceleration proof
  • 00:07:35
    Newton's second law
  • 00:07:37
    proof F equals MA is the generic
  • 00:07:42
    expression for Newton's second law now
  • 00:07:45
    what is the F acting on this body the F
  • 00:07:48
    acting on that body is its weight and
  • 00:07:51
    when I let it go what is its
  • 00:07:54
    acceleration it has a certain Assam its
  • 00:07:57
    acceleration is G so these two equations
  • 00:08:00
    you see this the generic one F equals MA
  • 00:08:04
    all over the universe so we think and W
  • 00:08:06
    equals mg for earth-dwelling creatures
  • 00:08:08
    who wish to look at the weight of a body
  • 00:08:10
    so you can see that if I double the mass
  • 00:08:14
    of anybody I would once double its
  • 00:08:17
    weight and its acceleration remains
  • 00:08:19
    unaltered which is a sort of explanation
  • 00:08:23
    why all bodies have the same freefall
  • 00:08:26
    acceleration as Galileo showed in the
  • 00:08:30
    17th century now this is quite
  • 00:08:33
    remarkable because one is led to think
  • 00:08:36
    why I can't believe that this one will
  • 00:08:40
    not fall faster than this one and this
  • 00:08:42
    subject is taken up very excellently by
  • 00:08:45
    Galileo in his dialogues concerning two
  • 00:08:47
    Sciences where I urge you to read the
  • 00:08:51
    discussion between segredo and Salvati
  • 00:08:54
    and simply keo now there are some
  • 00:08:59
    further implications of the second law
  • 00:09:02
    which
  • 00:09:03
    have some levity I like physics in
  • 00:09:08
    cartoons and here is a cartoon that I
  • 00:09:11
    recently saw here is a little boy and
  • 00:09:15
    there is a bathroom scale and here is
  • 00:09:19
    another little boy and they way by all
  • 00:09:23
    looks of things about 70 pounds now it's
  • 00:09:27
    obvious what has happened this one jumps
  • 00:09:30
    down onto the scale and what is the
  • 00:09:33
    caption under the picture Wow he says
  • 00:09:36
    Wow
  • 00:09:37
    a hundred and forty you can see that
  • 00:09:40
    this is Newton's second law F equals mg
  • 00:09:44
    plus MA because of the force delivered
  • 00:09:48
    through his acceleration to the scale
  • 00:09:50
    and I think that's terrific
  • 00:09:53
    let's consider another such problem here
  • 00:09:58
    is a smooth pulley fix a - a solid beam
  • 00:10:02
    up there and here is a rope over the
  • 00:10:05
    pulley and here one man stands holding
  • 00:10:08
    the rope and here an identical weighted
  • 00:10:10
    man stands holding this rope and they
  • 00:10:14
    are both on the ground question the man
  • 00:10:17
    a climbs the rope B just holds on he
  • 00:10:23
    just stays there question what happens
  • 00:10:26
    to be answer B gets a free ride for
  • 00:10:31
    whatever a does is felt by the rope and
  • 00:10:34
    in turn by the man and so this is really
  • 00:10:39
    Newton's second law
  • 00:10:41
    two men on a pulley now a more dramatic
  • 00:10:45
    event much more dramatic here is a scale
  • 00:10:50
    which reads from 0 to 2,000 grams and I
  • 00:10:53
    put a thousand on it and clearly the
  • 00:10:55
    scale reads a thousand if I put two
  • 00:10:58
    thousand on it at rest remember at rest
  • 00:11:02
    the scale reads two thousand now what am
  • 00:11:05
    I going to do I am going to put the
  • 00:11:08
    scale on a horizontal plane on that
  • 00:11:10
    board in such a fashion with a pulley
  • 00:11:14
    here and a rope and a pulley
  • 00:11:16
    here and a rope and I'm going to put a
  • 00:11:18
    thousand there and a thousand right
  • 00:11:21
    there so that I have a thousand pulling
  • 00:11:24
    to the right and a thousand pulling to
  • 00:11:26
    the left I'm going to do that right now
  • 00:11:28
    there's a thousand on the right and I've
  • 00:11:32
    got to hold that now I get over here and
  • 00:11:34
    I put a thousand on the left and then I
  • 00:11:37
    cover it over as I like to say for my
  • 00:11:39
    students so that evil eyes do not see it
  • 00:11:42
    and remember now we asked the classic
  • 00:11:46
    question
  • 00:11:46
    hmm when I had a thousand on the scale
  • 00:11:49
    in the vertical line it read a thousand
  • 00:11:51
    when I put two thousand on it in a
  • 00:11:53
    vertical line that read two thousand we
  • 00:11:55
    want to know what does the scale now
  • 00:11:57
    read thousand pulling to the right
  • 00:11:59
    thousand pulling to left several answers
  • 00:12:01
    one all says somebody it reads zero
  • 00:12:04
    since the forces are null each other
  • 00:12:07
    no no says somebody else a thousand to
  • 00:12:10
    the right a thousand left and reach two
  • 00:12:12
    thousand and I must tell you that
  • 00:12:16
    whatsoever your point of view these are
  • 00:12:18
    both wrong so I could leave it as an
  • 00:12:22
    exercise for you to do but since I have
  • 00:12:26
    a kind heart I will tell you that the
  • 00:12:29
    scale reads 1,000 grams but having told
  • 00:12:32
    you this I urge you very seriously to
  • 00:12:36
    explore why that is so one further
  • 00:12:40
    little comment oh I want you to see
  • 00:12:43
    another picture of Newton I showed an
  • 00:12:46
    earlier photograph in his later years
  • 00:12:48
    and here is one as a young man 17 years
  • 00:12:53
    old when he entered Trinity College in
  • 00:12:56
    Cambridge a genius the light of which
  • 00:12:59
    the human race has not yet again seen
  • 00:13:03
    one last experiment Newton's second law
  • 00:13:07
    here I am going into an elevator on the
  • 00:13:12
    ground floor the push of the floor of
  • 00:13:15
    the elevator when at rest is my weight
  • 00:13:17
    plus the weight of the bag now the
  • 00:13:18
    elevator accelerates upward you know
  • 00:13:21
    what happens your knees buckle and the
  • 00:13:24
    load is pulled out of your hand no no no
  • 00:13:26
    not pulled it wanted to stay at rest it
  • 00:13:29
    wasn't rest and that's what
  • 00:13:30
    tried to do but what is the explanation
  • 00:13:33
    of the added tension in my arm and the
  • 00:13:36
    bending of my knees answer f equals mg
  • 00:13:39
    plus MA now the elevators on an
  • 00:13:43
    uppermost floor and starts down you know
  • 00:13:45
    what happens your belly feels empty f
  • 00:13:48
    equals mg minus MA and so we have a
  • 00:13:52
    better understanding of the laws that
  • 00:13:56
    envelop us by applying the laws of
  • 00:14:00
    Newton and I thank you for your
  • 00:14:02
    attention
  • 00:14:09
    you
  • 00:14:20
    you
Etiquetas
  • Newton's Second Law
  • Physics
  • F=ma
  • Acceleration
  • Force
  • Mass
  • Weightlessness
  • Gravitational Force
  • Isaac Newton
  • Free Fall