Physics - Mechanics: Applications of Newton's Second Law (8 of 20)

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  • Опубликовано: 16 дек 2024

Комментарии • 146

  • @MichelvanBiezen
    @MichelvanBiezen  11 лет назад +8

    Thank you for the testimonial.
    Yes, the key to understanding any problem (or anything in science for that matter) is to pick out the fundamentals of what you know to be true and correct and then piece them together.

  • @MichelvanBiezen
    @MichelvanBiezen  10 лет назад +9

    Gareth,
    This is an algebra question. The key to working out algebra problems (as well as any mathematical problem) correctly they should always be in equation format. That way you can see what changes from line to line.
    In this case, the only change in the equation is that the a2 changed to (1/2)a1, which would imply that a2 = (1/2)a1.
    Thus I did not multiply by 2, but simply replaced one term by an equivalent term.

  • @Mango5389
    @Mango5389 9 лет назад +9

    I have a mechanics exam in two weeks time. I'd like to thank you for all the videos you have shared to the public to help us students out. You sir, are a genius :)

  • @joshspence6088
    @joshspence6088 7 лет назад +11

    my teacher went over this same exact situation on monday. didnt explain half of the things you did. made everything seem 100x more complicated than it actually is. i didnt even take notes on it because i hoped that you had a video on it which is 10000000x better than taking his notes. please adopt me.

  • @YogiliciousP
    @YogiliciousP 8 лет назад +5

    I don't know how, but you make what I initially expected to be a difficult problem easy-peasy...you're smthg special.

  • @Armada0500
    @Armada0500 7 лет назад +3

    For those who wonder why "m1g" is positive while "m1a" is negative thought the gravitational acceleration and "a" are both in the same direction, Fnet = ma. The forces which are acting on mass 1 are tension and gravity. If we take the acceleration direction as our positive direction, then the equation should be: +m1g - T = ma >> subtract "m1g" from both sides, multiply by -, and you should get the same equation as the video.

  • @completelystupid87
    @completelystupid87 9 лет назад +23

    This problem is hard, hopefully I'll see it on the test. I'm sure lots of ppl will be dead.

  • @menglongyouk167
    @menglongyouk167 8 лет назад +1

    You make physics exciting to learn, Sir. Thank you.

  • @petereziagor4604
    @petereziagor4604 2 года назад +3

    I also see why the relationship between the two acceleration is like that. From h = 1/2 at^2. The one moving down will always cover twice the distance of the one on the table and that's because of how the rope is connected in the pulley.
    Gracias 👍

    • @MichelvanBiezen
      @MichelvanBiezen  2 года назад +4

      That is correct. You understand the problem.

  • @camillehendricks9819
    @camillehendricks9819 7 лет назад

    I've never understood Newton this well... thank you so much!!!

  • @wishdoom
    @wishdoom Год назад +1

    at 6:39 you "factor out an a1" and it seems like you delete an "a1" out of the equation and just stop counting it... how could you do that ?

    • @MichelvanBiezen
      @MichelvanBiezen  Год назад +1

      I factured out the a1 and then divided both sides of the equation by m2 + 4 m1

  • @Snooperking
    @Snooperking 4 года назад +1

    You are the definition of Big Brain Time

  • @gregoryeastwood9068
    @gregoryeastwood9068 3 года назад +1

    This is why I love mechanical physics.....so Practical.

  • @maryanbumathy4833
    @maryanbumathy4833 7 лет назад +1

    simply superb professor.ur teaching is awsome

  • @jackellery5938
    @jackellery5938 8 лет назад +1

    This is really helpful! How would I factor in the Inertia of the pulley? For example if the moment of inertia, I, and the angular acceleration, alpha, need to be included in the question. How would this affect the tension in the rope?

    • @MichelvanBiezen
      @MichelvanBiezen  8 лет назад +1

      Yes the technique is very different. There are a number of examples in the CHAPTER 13.1 Playlist: Physics - Application of the Moment of Inertia (8 of 11) Acceleration=? When Pulley Has Mass (mu=0) ruclips.net/video/p6ZlBp_vQ6c/видео.html

    • @jackellery5938
      @jackellery5938 8 лет назад

      Michel van Biezen Thanks Michel! I will watch that video and many more of yours.

  • @kyliechesner8933
    @kyliechesner8933 10 лет назад +4

    how does T2 = 2 * T1 because if the masses are being accelerated, arent the pulleys then also being accelerated, meaning forces arent balanced ..?

    • @MichelvanBiezen
      @MichelvanBiezen  10 лет назад +7

      kylie,
      Good question.
      It is often difficult to comprehend or visualize what is actually going on and our intuition sometimes leads us astray.
      In this problem we are using and "ideal" pulley which means that it does not have mass.
      If the pulley does not have mass then there isn't an object to accelerate and when drawing the free body diagram around the pulley the forces on both sides must be equal.
      If the pulley had mass, then you would be correct.

    • @Svit.S
      @Svit.S 8 лет назад +2

      +Kylie Rose The pulleys here were massless and frictionless.

  • @ishikagupta5044
    @ishikagupta5044 8 лет назад +4

    i didnt understand the part where you say that the acceleration of m2 will be half of that of m1....why would it be like that ? i didnt get it through the pulley reference also...😞

    • @MichelvanBiezen
      @MichelvanBiezen  8 лет назад +2

      Since m2 is connected to the midpoint of the pulley, you have what we call a 2:1 mechanical advantage. You need 1/2 the force, but will require twice the pulling distance to move m2. It is the way pulleys work. If you have one, try it and see that it works that way.

    • @nandha0150
      @nandha0150 7 лет назад +1

      Simply put, if you draw the free body diagram for pulley 2, then you could clearly see, 2 tensions of T1 on the right-hand side and thus it must be T2 = 2 x T1 on the left-hand side.

    • @akshay1597
      @akshay1597 7 лет назад

      Nandha Kumar usne dusra question pucha tha..

  • @matthiasandersen3329
    @matthiasandersen3329 5 лет назад

    Hi Michel. Great video, but there is something I don't quite understand and it's why is T2=m2a2 not equal to T2-m2g=m2a2 at 4:22 in your video?

    • @MichelvanBiezen
      @MichelvanBiezen  5 лет назад +1

      Since m2 is sitting on the table, there is no tension component due to gravity, only to accelerate the block.

  • @TumwesigeDdavis
    @TumwesigeDdavis 11 месяцев назад +1

    Thanks i appreciate am now doing well in physics and math thanks so much for the great expectations

  • @garethm3171
    @garethm3171 10 лет назад +1

    Just a point of clarification Michael. If you're multiplying m2(1/2a1) by 2 in order to get rid of the 1/2a1 doesn't that give 2m2 a1? Because don't you multiply the whole expression by 2 i.e multiplying m2 x(1/2a1) by 2 so you get 2(m2 x 1/2a1) = 2m2 x a1

  • @alekseyov1350
    @alekseyov1350 10 лет назад +5

    Hi. Can You explain way T1=m1g-m1a (g and a same direction)

    • @MichelvanBiezen
      @MichelvanBiezen  10 лет назад +4

      Alexkey Ov,
      Vectors have both magnitude and direction. In the equation you reference, we just use the magnitude part and determine the sign by figuring out which way the block is moving.
      The best way to figure out the equation is this way:
      1) if the block is not moving the T1 = m1g
      2) if the block is accelerating upward you will need additional force to cause the acceleration T1 = m1g + m1a
      3) if the block is accelerating downward you don't need all of the force to hold it against gravity T1 = m1g - m1a

    • @alekseyov1350
      @alekseyov1350 10 лет назад +1

      Thanks for the answer. You are a very good teacher.

  • @idontknowyou1019
    @idontknowyou1019 8 лет назад

    Sir, You are simply Amazing!...

  • @adamwenicki6252
    @adamwenicki6252 4 года назад +1

    Could you pleas do similar problem,but on an inclined plane, what I mean is m2 hanging and m1 is one the plane inclined at an angel of 30. Thank you for all your help sir.

    • @MichelvanBiezen
      @MichelvanBiezen  4 года назад +2

      We have dozens of examples in all kinds of physical situations in the playlists on this topic.

    • @adamwenicki6252
      @adamwenicki6252 4 года назад

      @@MichelvanBiezen How would the equations change if the mass one the left was pulled to the left.

  • @josephnabil6744
    @josephnabil6744 7 лет назад +1

    Sir, Why is the direction of both T1 and T2 to the right? I think that the tension of the string below is to the left

    • @MichelvanBiezen
      @MichelvanBiezen  7 лет назад

      To find the direction of the tension in the string you must express it in terms of the object relative to. Note that every string has tension in both directions simultaneously.

  • @BAKER-zi3iw
    @BAKER-zi3iw 7 лет назад +1

    Wouldn't the tension of the t1 above the other t1 act towards the left not the right ? Thanks

    • @MichelvanBiezen
      @MichelvanBiezen  7 лет назад +1

      The direction of the tension only makes sense if you have a reference point. (tension relative to what?) Thus the tension T1 just above the 5 kg block is directed upward RELATIVE to the 5 kg block. But T1 on the top string is directed to the right relative to the left pulley and to the left relative to the right pulley.

    • @BAKER-zi3iw
      @BAKER-zi3iw 7 лет назад +1

      Michel van Biezen thank you for the explanation

  • @charlesbromberick4247
    @charlesbromberick4247 2 года назад +1

    nice problem - insightful solution

  • @musaabdelaziz9219
    @musaabdelaziz9219 4 года назад +1

    so for this problem, why couldn't you do m1g1 -m1a1 = m1a1. This is the F= ma but instead of T2 i just used T1. Using this formula you move m1a1 to the other side hence giving m1g1 = m1a1 + m1a1. Here you factor a out and move both m1 to the other side. This will give you (m1g1/m1+m1). Doing it this way also gave me 4.9. So is this way also acceptable for future problems?

    • @MichelvanBiezen
      @MichelvanBiezen  4 года назад +1

      If you draw a free body diagrams, then identify all the forces in and out of the diagram, and if they match your equation, you have the correct equation. (Better not use the "can this always be used")

  • @catherinexx00xx
    @catherinexx00xx 9 лет назад +1

    I have the same question as another commenter ... how does T2 = 2 * T1 because if the masses are being accelerated, arent the pulleys then also being accelerated, meaning forces aren't balanced?

    • @MichelvanBiezen
      @MichelvanBiezen  9 лет назад +1

      +Catherine Flynn
      Whenever you draw a free body diagram around an object (like the dashed line box around the pulley), the sum of the forces (added as vectors) must satisfy F = m * a Since the pulley is assumed not to have mass in this example, the sum of the forces must equal zero. Therefore 2 T1 = T2

    • @catherinexx00xx
      @catherinexx00xx 9 лет назад

      Ah I see, thanks so much! P.S. your videos are an amazing help!

  • @Nour-vk9md
    @Nour-vk9md 5 лет назад +1

    Please sir
    I cannot understand the idea of a2=0.5 a1 , though mass 1 is actually 25% of mass 2 , is not this a factor affects both the disatnce and acceleration ?
    Waiting for your reply 🤔🤔

    • @MichelvanBiezen
      @MichelvanBiezen  5 лет назад +1

      That is the result of the mechanical advantage of a pulley. The tension in the string connected to m2 is double the tension in the string connected to m1, and the velocity of m2 is half the velocity of m1. Hence the acceleration of m2 is also half of the acceleration of m1. See the sketch on the right side of the board.

    • @Nour-vk9md
      @Nour-vk9md 5 лет назад +1

      @@MichelvanBiezen so this means that the mass connected with rope doesnot affect the acceleration as I understand , it is about the mechanical advantage .
      I truely appreciate this , gratful for your help❤🌷

    • @hibazreik2228
      @hibazreik2228 3 года назад

      @@MichelvanBiezen my dr solved the same example but she considered a2=2a1 so this confused me can you please explain

    • @akinyelemorounfoluabdurahm5005
      @akinyelemorounfoluabdurahm5005 2 года назад

      @@hibazreik2228 maybe professors M¹ and M² are her M² and M¹ respectively

  • @dr.rajanikumari9673
    @dr.rajanikumari9673 6 лет назад

    Really nice and it will never go ebb of my mind

  • @petereziagor4604
    @petereziagor4604 2 года назад +1

    Amazing explanation

  • @favourefe2233
    @favourefe2233 6 дней назад

    Sir, can I use T2=2T1 ro prove why the acceleration a2= ½a1?

  • @pharaohtoon419
    @pharaohtoon419 6 лет назад +1

    what the book that you use???

    • @MichelvanBiezen
      @MichelvanBiezen  6 лет назад +2

      We use many books for reference and for my classes

    • @adityarajasekar1020
      @adityarajasekar1020 6 лет назад

      Ooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooooh.....

  • @esuresh107
    @esuresh107 4 года назад +1

    Is that correct??

  • @neworld2.073
    @neworld2.073 7 лет назад +1

    If T2=2T1 and T2=m2g=196N. Then can T1=T2/2= 98N. ? Then use T1=m1g-m1a1 to find a1? Which I found to be 9.8=[a1] ? then use a2=1/2 a1 to find a2. Which in this case would be 4.9 m/s^2? Am I wrong if I do this? Please respond?

    • @neworld2.073
      @neworld2.073 7 лет назад +1

      Never mind just found the mistake

    • @favourefe2233
      @favourefe2233 6 дней назад

      ​@@neworld2.073 which mistake please?

  • @iamyu
    @iamyu 7 лет назад

    i have question. i understand the diagram on the right where if we pull it upward for 1m, the distance will only be half at the end of the pulley. but i don't understand how we can use that length reference in an acceleration problem. is it possible for the pulley to "take" half of the acceleration as well?

    • @carultch
      @carultch 3 года назад

      You can prove mathematically that it has to work out this way, or you can do it by inspection as the professor did, simply reasoning through the proportions of changes in length. The changes in length are always proportional, which means time derivatives of any order of these changes in length will also be proportional. Below, I've written up how we know that, with a calculus proof.
      Define the position of block m1 to be distance y below the pulley.
      Define the position of block m2 to be distance -x from the pulley, such that x is a negative number when the block is to the left of the pulley. We assign a negative sign to this one, so that its acceleration can be a positive number, which you'll see later why this helps.
      The length of the string among the pulleys, the fixed point, and mass m1 is as follows (neglecting the diameter of the pulley, and the length of the string with tension T2):
      L = | 2*x | + y
      Since x is negative, replace the absolute value bars with a negation:
      L = -2*x + y
      Solve for y in terms of x:
      y = L + 2*x
      The acceleration is defined as the second derivative of each block's position, relative to time. Therefore:
      a2 = d^2/dt^2 x
      a1 = d^2/dt^2 y
      Substitute y = L + 2*x:
      a1 = d^2/dt^2 (L + 2*x)
      Since L is a constant, it's derivative is zero, and likewise, its second derivative is zero. The leading constant of 2, can be pulled out in front on the 2*x term:
      a1 = 2 * d^2/dt^2 x
      We recognize that this is the expression for a2 in this equation, which therefore means that:
      a1 = 2*a2
      And that concludes how we can prove that acceleration a1 has to equal 2*a2. It is based on the constraint that the length of the rope is a constant.

    • @akinyelemorounfoluabdurahm5005
      @akinyelemorounfoluabdurahm5005 2 года назад

      @@carultch wow,
      Mr Carl ,I just started a physics course , can I get you on WhatsApp maybe , I need your sort of help in my physics life 😔

  • @badreddine7187
    @badreddine7187 Год назад +1

    How do you know that blick (5kg) accelerate downward

    • @MichelvanBiezen
      @MichelvanBiezen  Год назад +1

      There are two choices. It either accelerated downward, or the friction between the table and the other block are sufficient to keep it from accelerating. Therefore assume the block accelerates and see what the acceleration is. If the answer is negative (compared to the assumed direction of the acceleration) then the block would not move.

  • @saimakhankhan2517
    @saimakhankhan2517 7 лет назад +1

    If T2 is equals to 2T1 then can we use (m1g-m1a)=2(m1g-m1a) to find a, instead of equating it to m2a2?

  • @nirdeshkunwar6285
    @nirdeshkunwar6285 7 лет назад +1

    Sir can you please tell me,
    -What is the condition for the tension to be equal?

    • @MichelvanBiezen
      @MichelvanBiezen  7 лет назад +1

      If you draw a free body diagram around the pulley on the left, you'll see that the one force to the left must be equal to the 2 forces on the right. Therefore both tensions on the left mus be equal and they must be half of the tension on the left side of the pulley.

    • @nirdeshkunwar6285
      @nirdeshkunwar6285 7 лет назад

      thank you sir...

  • @joeldesario9745
    @joeldesario9745 7 лет назад +1

    why is g not considered -9.8m/ss since it is a downward acceleration?

    • @MichelvanBiezen
      @MichelvanBiezen  7 лет назад +1

      Since we are only finding the magnitude of the acceleration.

  • @user_7865
    @user_7865 4 года назад

    oh my god man, thank you very much for explaining about the acceleration being halved.

  • @TheHarshit2
    @TheHarshit2 7 лет назад +2

    THANK YOU SO MUCH!

  • @dwightd3659
    @dwightd3659 8 лет назад +1

    Why would it be accelerating downward if the mass is 4 times heavier? It would be stationary

    • @MichelvanBiezen
      @MichelvanBiezen  8 лет назад +3

      +Dwight D
      Since there is no friction between the large mass and the table, there is no friction force, so how would the large mass keep the small mass from accelerating downward? Always go back to the F= ma equation and find all the forces aiding the acceleration and all the forces opposing the acceleration. If the forces causing the acceleration are greater, there will be an acceleration.

    • @akinyelemorounfoluabdurahm5005
      @akinyelemorounfoluabdurahm5005 2 года назад

      @@MichelvanBiezen nicely noted

  • @satyamkumar567
    @satyamkumar567 5 лет назад +1

    What will be a2 if m2 is at inclined plane??

    • @MichelvanBiezen
      @MichelvanBiezen  5 лет назад +1

      We have a number of examples with inclined planes and will make some more in the future.

    • @satyamkumar567
      @satyamkumar567 5 лет назад +1

      Sir please make videos on complex problem including inclined plane

  • @MultiShahem
    @MultiShahem 9 лет назад +4

    Oh sir you've Blown up my mind XD >>> But it's Enjoyable ! Thank you :)

  • @roshanaab116
    @roshanaab116 9 лет назад

    Sir how do you know the direction of both the T1?

    • @MichelvanBiezen
      @MichelvanBiezen  9 лет назад +1

      +Roshan Varghese
      I am not sure about the question but I'll try to answer it this way: Tension acts in both directions. (The string pulls on each object that it is connected to.)

  • @Said786ful
    @Said786ful Год назад +1

    Shouldnt T1= m1g+m1a ?

    • @MichelvanBiezen
      @MichelvanBiezen  Год назад +1

      No, it is T1 = m1g - m1a

    • @Said786ful
      @Said786ful Год назад +1

      @@MichelvanBiezen Thanks.
      But the directions of the two magnitudes are the same. Only tension has the direction.

    • @Said786ful
      @Said786ful Год назад +1

      I meant only tension has an opposite direction.

    • @MichelvanBiezen
      @MichelvanBiezen  Год назад +1

      The direction of the tension depends on the reference point.

    • @MichelvanBiezen
      @MichelvanBiezen  Год назад +1

      If you draw a free body diagram around m1 and use F = ma you get the following equation mg - T = ma Solve for T.

  • @directordissy2858
    @directordissy2858 5 лет назад +2

    Why does T2 = 2T1?
    I am also confused what T2 even does

    • @MichelvanBiezen
      @MichelvanBiezen  5 лет назад +1

      T2 is the tension in the rope that connects the 20 kg mass to the pulley on the left. It is T2 that accelerates the 20 kg mass to the right at acceleration = a2. If you draw a free body diagram around that pulley you have 3 forces contained within the free body diagram. T2 pulling to the left and 2 T1 forces pulling to the right (relative to the pulley). These forces must equal one another, thus T2 = 2 T1

  • @ajaygrewal5354
    @ajaygrewal5354 7 лет назад +1

    sir could you elaborate how T2=2*T1

    • @MichelvanBiezen
      @MichelvanBiezen  7 лет назад +4

      If you look at the free body diagram around the pulley then you can determine that the forces pulling to the left must equal to the forces pulling to the right. Thus T2 = T1 + T1

  • @yesheshchandra4044
    @yesheshchandra4044 9 лет назад

    sir can u please explain me the directions of T1

    • @carultch
      @carultch 3 года назад

      Tension means stretching force. A flexible rope, chain, cable, cord, or string has to carry a stretching force if it carries any force at all. If you attempt to push a rope, it will become slack, and be incapable of carrying any force.
      Therefore, the tension force has to point away from the object to which it is applied.

  • @petereziagor4604
    @petereziagor4604 2 года назад +1

    Thank you

  • @hanisahapendi4680
    @hanisahapendi4680 7 лет назад +1

    how is a2 is half of a1?

    • @MichelvanBiezen
      @MichelvanBiezen  7 лет назад +2

      Pulleys give you a 2:1 mechanical advantage which causes the distance you pull on one side to be twice the distance the pulley moves.

    • @hanisahapendi4680
      @hanisahapendi4680 7 лет назад +1

      Michel van Biezen thank you sir

  • @sovannaryvang8020
    @sovannaryvang8020 4 года назад +1

    Hello cher.
    Why T2=2T1

    • @carultch
      @carultch 2 года назад

      Because the pulley by mass M2 is treated as an idealized pulley, which means it has negligible mass and negligible friction. Forces acting on an object of negligible mass must add up to zero, otherwise it would have infinite acceleration.
      Two segments of the rope carrying tension T1, act on this pulley to the right. Both segments carry equal tension, because the pulley is idealized as massless and frictionless. The only remaining force acting on this pulley, is tension T2, which acts to the left. This means 2*T1 - T2 = 0, and we can solve for T2 = 2*T1.

  • @noluthandojili2696
    @noluthandojili2696 2 года назад +1

    Thanks a lot now iget the point

  • @ripperduck
    @ripperduck 5 лет назад

    It's impossible to read the text..,

  • @mennatallahmohamed8052
    @mennatallahmohamed8052 7 лет назад

    can you explain why T2=2*T1??

  • @armanko95
    @armanko95 11 лет назад

    thanks man

  • @obakengatom_sweetbrotherof1081
    @obakengatom_sweetbrotherof1081 7 лет назад +1

    WHY IS ACCELERATION OF M2 HALF

    • @MichelvanBiezen
      @MichelvanBiezen  7 лет назад

      Due to the mechanical advantage of a pulley. M2 is attached to the midpoint of the pulley. Therefore as the string is pulled on one end, the point where M2 is attached only moves half as far. (try it on a pulley and you will see). Mechanical efficiency requires that F1 * d1 = F2 * d2 (otherwise you create work and energy out of nothing).

    • @guydude3320
      @guydude3320 7 лет назад +1

      Obakeng Moribe differentiate displacement twice with respect to time

  • @takkisnassiopoulos9467
    @takkisnassiopoulos9467 9 лет назад

    why 1/2ΔL?

    • @MichelvanBiezen
      @MichelvanBiezen  9 лет назад

      takkis Nassiopoulos
      Think about it. How far does the other object move, if the first object moves 1 m?

  • @izzy_pk
    @izzy_pk Год назад +1

    I just said 5×9.8 is F and 25 is m and I found the a as 1.96... I dont understand why it is wrong

  • @esuresh107
    @esuresh107 4 года назад

    I bet

  • @sivaranjan9730
    @sivaranjan9730 7 лет назад

    That's awesome ;-)

  • @mayankchauhan4788
    @mayankchauhan4788 8 лет назад

    why∆l/2 sir

    • @MichelvanBiezen
      @MichelvanBiezen  8 лет назад

      Since the force required to lift up the object attached to the pulley is only half the weight of the object, you must pull twice the distance in order to accomplish the same amount of work. W = F * d = (1/2)F * 2d

    • @MichelvanBiezen
      @MichelvanBiezen  8 лет назад +1

      You can also try it yourself and you'll see that it is a two to one ratio

    • @mayankchauhan4788
      @mayankchauhan4788 8 лет назад

      thanx sir
      your videos are very helpful

  • @esuresh107
    @esuresh107 4 года назад

    Sir T1=m1g+m1a, u wrote wrong sir.

  • @JonLG490
    @JonLG490 7 лет назад +3

    gotdamn shawty

  • @adityarajasekar1020
    @adityarajasekar1020 6 лет назад +1

    This was actually easy. I understood how to solve it right before sir started to solve it.

    • @akinyelemorounfoluabdurahm5005
      @akinyelemorounfoluabdurahm5005 2 года назад

      Wow
      Could I get through to you on WhatsApp maybe , I just started a physics course ,and it's not that easy for me

  • @nanyscg2195
    @nanyscg2195 5 лет назад

    l like

  • @esuresh107
    @esuresh107 4 года назад

    I bet that what you wrote is wrong

  • @esuresh107
    @esuresh107 4 года назад

    I like ur lectures but the answer is wrong

  • @esuresh107
    @esuresh107 4 года назад

    It is not correct