Young Modulus - Physics A-level Required Practical

00:07:27
https://www.youtube.com/watch?v=Eqjfw56tV1Q

概要

TLDRLa Sra. Wilkins ens guia a través d'un experiment pràctic per determinar el mòdul de Young d'un fil de coure. El mòdul de Young mesura l'elasticitat d'un material, rellevant per a l'enginyeria. Es presenten les mesures necessàries, com la longitud original del fil i el seu diàmetre, i es destaquen precaucions de seguretat per evitar accidents durant l'experiment. Aquest vídeo inclou el procés de mesurar extensions sota càrregues aplicades, el càlcul del gradient del gràfic resultant i la comparació dels valors obtinguts amb els coneguts per determinar el cop de percentatge d'error.

収穫

  • 🔍 El mòdul de Young mesura l'elasticitat d'un material.
  • ⚙️ La fórmula és E = (F * L) / (A * ΔL).
  • 📏 Es recomana fer diverses mesures del diàmetre.
  • 🧊 Mesurar amb un micròmetre per obtenir precisió.
  • 🔗 Cal comparar amb un altre fil per estabilitat de les lectures.
  • ⚠️ Utilitzar equips de seguretat per protegir-se.
  • 📈 El gradient del gràfic és clau per calcular E.
  • 📊 Les extensions s'han de convertir a metres per facilitar gràfiques.
  • 💡 L'error percentual es calcula comparant amb el valor teòric.
  • 👩‍🔬 El resultat obtingut va ser 1.39 x 10^11 pascals.

タイムライン

  • 00:00:00 - 00:07:27

    Benvinguts a la classe de ciència amb la senyora Wilkins, on aprendrem a determinar el mòdul de Young d'un material, en aquest cas un fil de coure. El mòdul de Young és una propietat clau en l'enginyeria, que ens indica com un material es deforma amb la tensió. Es defineix com la relació entre l'estrès i l'estrès, on l'estrès és la força aplicada per unitat d'àrea i l'estrès és l'extensió relativa a la longitud original. La configuració de l'experiment implica un fil de coure llarg, amb precaucions de seguretat per evitar lesions si el fil es trenca. Es prendran mesures crucials com la mida del fil i la longitud original, usant un micròmetre per assegurar-vos que les lectures siguin precises. Finalment, es mesurarà l'extensió del fil sota una càrrega i es grafiaran els resultats per calcular el mòdul de Young.

マインドマップ

ビデオQ&A

  • Què és el mòdul de Young?

    El mòdul de Young és la relació entre l'estrès i l'estrès, que indica com de fàcilment un material s'estira o es deforma.

  • Com es calcula el mòdul de Young?

    E = (F * L) / (A * ΔL), on F és la força aplicada, L és la longitud original, A és l'àrea de secció transversal i ΔL és l'extensió.

  • Quines mesures són necessàries per a l'experiment?

    Cal mesurar el diàmetre del fil, la seva longitud original, i l'extensió sota diferents càrregues.

  • Quines precaucions de seguretat s'han de considerar?

    Portar ulleres de seguretat i evitar estar sota les masses que es poden caure.

  • Quina és la importància de comparar amb un altre fil?

    Permet tenir un punt de referència per detectar canvis en l'extensió que podrien ser causats per factors ambientals.

  • Per què és important mesurar el gradient del gràfic?

    El gradient del gràfic ha de calcular-se només a la part lineal per obtenir una mesura precisa del mòdul de Young.

  • Quin valor es va obtenir per al mòdul de Young del coure?

    Es va obtenir un valor de 1.39 x 10^11 pascals.

  • Quina és la importància de convertir les unitats a metres?

    Les extensions han de ser convertides a metres per a la correcta representació en el gràfic.

  • Com es pot calcular l'error percentual?

    Comparant el valor obtingut amb el valor teòric conegut del mòdul de Young i aplicant la fórmula d'error percentual.

  • Quin era l'error percentual en l'experiment?

    L'error percentual en el valor obtingut comparat amb el valor teòric era del 19%.

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  • 00:00:00
    hello i'm mrs wilkins and welcome to
  • 00:00:02
    marsbury science
  • 00:00:03
    today we're going to look at an a-level
  • 00:00:05
    physics-required practical how to
  • 00:00:07
    determine the young modulus of a
  • 00:00:08
    material and specifically a copper wire
  • 00:00:11
    the young modulus is a really important
  • 00:00:13
    property in engineering as it tells us
  • 00:00:15
    how easily a material will stretch or
  • 00:00:17
    deform the young modulus is defined as
  • 00:00:19
    the ratio of tensile stress to tensile
  • 00:00:22
    strain where stress is the force applied
  • 00:00:25
    per unit area and the strain is the
  • 00:00:27
    extension relative to original length
  • 00:00:30
    the young modulus is given the letter e
  • 00:00:32
    and this is equal to f l
  • 00:00:35
    over a delta l this is the setup that
  • 00:00:38
    we're going to use today we have taken a
  • 00:00:41
    fairly long piece of copper wire it is
  • 00:00:43
    over two meters because the extensions
  • 00:00:45
    are so small you do want fairly long
  • 00:00:47
    original length this is just one example
  • 00:00:50
    of a setup you can also hang some wires
  • 00:00:53
    sometimes steel is the best vertically
  • 00:00:56
    suspended from a beam but it depends if
  • 00:00:57
    your school laboratory has that sort of
  • 00:00:59
    infrastructure that enables you to do it
  • 00:01:01
    so this is the best option for us in
  • 00:01:03
    this investigation there are two safety
  • 00:01:05
    precautions to consider the first is
  • 00:01:08
    that if the wire breaks and it may well
  • 00:01:11
    do it could snap across the surface of
  • 00:01:14
    the eye causing damage so it is really
  • 00:01:17
    important to wear eye protection in the
  • 00:01:19
    form of safety goggles this second is
  • 00:01:22
    that if the wire snaps of course the
  • 00:01:24
    slot masses will force the ground
  • 00:01:26
    be careful not to have your foot or a
  • 00:01:28
    knee underneath the slot masses and
  • 00:01:31
    perhaps also place a carpet or a tray of
  • 00:01:33
    sand underneath the slot masses to
  • 00:01:35
    protect the floor when they fall so the
  • 00:01:38
    fourth applied is the tension that we
  • 00:01:40
    apply to the wire as you can see we have
  • 00:01:42
    clamped the wire at the far end of the
  • 00:01:44
    bench and then we've run the wire over a
  • 00:01:46
    pulley and attached it to a vernier
  • 00:01:49
    scale at the end of the vernier scale we
  • 00:01:50
    have the hanger and we are going to
  • 00:01:54
    attach slot masses in increments of 100
  • 00:01:56
    grams and that will provide the tension
  • 00:01:59
    which is mg you will notice that we
  • 00:02:01
    actually have two wires attached and
  • 00:02:03
    this is because it's important to have a
  • 00:02:05
    test wire that we apply the tension
  • 00:02:08
    force to and also a comparison wire this
  • 00:02:11
    allows us to give us a reference point
  • 00:02:13
    and also if there are any changes in the
  • 00:02:15
    ambient atmosphere for example if the
  • 00:02:17
    wire extends due to temperature it will
  • 00:02:19
    happen to both and we can find the
  • 00:02:21
    relative extension of the test wire the
  • 00:02:23
    next step is to find the diameter of the
  • 00:02:25
    wire and for this the best equipment is
  • 00:02:27
    a micrometer and this will give us a
  • 00:02:29
    resolution to a hundredth of a
  • 00:02:30
    millimeter the wire may not be perfectly
  • 00:02:33
    uniform throughout and so it's a good
  • 00:02:35
    idea to take the diameter measure the
  • 00:02:36
    diameter at three separate points and
  • 00:02:39
    then calculate the mean i'm going to
  • 00:02:41
    take it here
  • 00:02:42
    you
  • 00:02:43
    turn the small dial until you hear the
  • 00:02:45
    first click
  • 00:02:47
    and i can see the reading
  • 00:02:48
    to be
  • 00:02:51
    0.28 millimeters i then measured the
  • 00:02:54
    diameter in the middle of the wire and
  • 00:02:56
    at the far end of the wire
  • 00:02:58
    the first two readings were the same the
  • 00:03:00
    diameter was 0.28 millimeters but the
  • 00:03:02
    third was 0.27 millimeters however when
  • 00:03:05
    i calculated the mean you still have to
  • 00:03:07
    give the final result to two significant
  • 00:03:10
    figures and so it still averages out
  • 00:03:12
    2.28 millimeters cross sectional area
  • 00:03:14
    equals pi d squared over four the next
  • 00:03:17
    measurement we require is the original
  • 00:03:19
    length of the wire and for this we used
  • 00:03:22
    a series of meter rules and found the
  • 00:03:24
    original length to be 2.46 meters we
  • 00:03:27
    have of course already applied a small
  • 00:03:29
    tension to the wire to ensure that the
  • 00:03:31
    wire is taught when we took the readings
  • 00:03:33
    of diameter and original length and this
  • 00:03:35
    was supplied by the hangers already
  • 00:03:37
    attached to the vernier scale
  • 00:03:39
    however before we add the additional 100
  • 00:03:42
    grams we have to make sure that our
  • 00:03:44
    vernier scale is perfectly zeroed so if
  • 00:03:47
    we go back to our original equation e
  • 00:03:49
    equals f l over a delta l we've
  • 00:03:52
    accounted for the force we've measured
  • 00:03:53
    the original length we've calculated the
  • 00:03:55
    cross-sectional area by measuring the
  • 00:03:57
    diameter so now we can start to measure
  • 00:03:59
    the extension under an applied force by
  • 00:04:02
    attaching the slot masses and we will
  • 00:04:06
    measure the extension on the vernier
  • 00:04:07
    scale so i'm going to start by adding my
  • 00:04:10
    first 100 grams because this is our
  • 00:04:12
    reference point of zero as i mentioned
  • 00:04:14
    before the extensions are very small and
  • 00:04:17
    so far i have not seen a significant
  • 00:04:19
    extension so i'm going to add another
  • 00:04:21
    100 grams i've taken a few readings now
  • 00:04:24
    and i can see that adding 500 grams is
  • 00:04:28
    now ascended by 1.4 millimeters if
  • 00:04:32
    you're not sure how to read vernier
  • 00:04:33
    scales remember that there are two
  • 00:04:34
    scales the first reading you see where
  • 00:04:37
    the zero on the sliding scale where it's
  • 00:04:40
    between on the fixed scale so i can see
  • 00:04:42
    it's between one and two millimeters so
  • 00:04:44
    i know it's one point something
  • 00:04:46
    millimeters i then get the next decimal
  • 00:04:49
    point by seeing which is the first line
  • 00:04:52
    that lines up with a line on the fixed
  • 00:04:54
    scale and i can see here that the fourth
  • 00:04:57
    line lines up with the fixed scale and
  • 00:05:00
    therefore i can say it's 1.4 millimeters
  • 00:05:02
    in this investigation although we're
  • 00:05:04
    interested in extension in meters our
  • 00:05:06
    vernier scale gives us an extension in
  • 00:05:08
    millimeters so don't forget to convert
  • 00:05:10
    it to meters when plotting your graph
  • 00:05:12
    when you have a full set of data we can
  • 00:05:15
    now plot the graph there are various
  • 00:05:17
    ways of plotting the graph and you could
  • 00:05:18
    plot the stress versus the strain but
  • 00:05:20
    this is quite a complicated way of doing
  • 00:05:22
    it it's more standard to plot the force
  • 00:05:25
    against extension however plotting a
  • 00:05:27
    force when you have to times the mass by
  • 00:05:29
    g 9.81 the values aren't particularly
  • 00:05:32
    easy to plot on a graph so we're going
  • 00:05:34
    to stick with the mass and the extension
  • 00:05:37
    our preferred method is to plot the mass
  • 00:05:39
    on the y-axis and the extension on the
  • 00:05:42
    x-axis because this gives us quite a
  • 00:05:44
    typical stress-strain curve that you'd
  • 00:05:47
    be familiar with if you plot the
  • 00:05:50
    extension on the y-axis and the mass on
  • 00:05:52
    the x-axis which you may also see it
  • 00:05:54
    does of course give you the inverse for
  • 00:05:56
    the gradient plotting it this way our
  • 00:05:59
    gradient gives us the mass divided by
  • 00:06:01
    delta l we can then say that the young
  • 00:06:04
    modulus e is equal to the gradient
  • 00:06:07
    times g times the original length
  • 00:06:10
    divided by the cross-sectional area
  • 00:06:12
    when measuring the gradient it's really
  • 00:06:14
    important that you take the gradient
  • 00:06:16
    from the linear part of the graph
  • 00:06:19
    your graph may show a linear part and
  • 00:06:21
    then it may curve off in which case
  • 00:06:23
    that's great because you've shown that
  • 00:06:25
    the wire behaves elastically and then
  • 00:06:28
    starts to behave plastically
  • 00:06:30
    however for determining young modulus
  • 00:06:32
    it's really important to only take the
  • 00:06:34
    gradient in the linear part and not
  • 00:06:37
    include the part after it's gone beyond
  • 00:06:39
    the limit of proportionality it's also
  • 00:06:41
    important on your graph to plot the mass
  • 00:06:43
    in kilograms our gradient is 357
  • 00:06:46
    kilograms per meter times that by g 9.81
  • 00:06:51
    times it by our original length which
  • 00:06:52
    was 2.46 meters and divided by our
  • 00:06:55
    cross-sectional area which was 6.2 times
  • 00:06:58
    10 to the minus 8 meter squared and we
  • 00:07:00
    get a value for the young's modulus e of
  • 00:07:03
    1.39 x 10 to the 11 pascals
  • 00:07:07
    or 139 giga pascals we can compare this
  • 00:07:11
    to the known value of the young modulus
  • 00:07:13
    of copper which is
  • 00:07:15
    gigapascals we can now take a percentage
  • 00:07:18
    error in our value compared to the
  • 00:07:20
    theoretical value which gives us a
  • 00:07:22
    percentage error of 19 percent
タグ
  • mòdul de Young
  • coure
  • experiment de física
  • tensió
  • seguretat
  • mesura
  • extension
  • gràfic
  • error percentual
  • enginyeria