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B Collision between moving walls

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  1. Jun 16, 2017 #1
    https://www.physicsforums.com/attac...5/?temp_hash=f9f8d75085046fd530ad1071794d65c1

    I have problem with the solution given of the (b) part of the question.
    The given solution is :
    upload_2017-6-17_4-23-44.png

    I did not understand why the value of ##\Delta T = 2x/v## even when ##\Delta T \to 0## ?
    Since if the time taken for collision reduces so does the distance between the wall and the ball and since velocity is constant. The value should be ##0##. No ?
     
  2. jcsd
  3. Jun 16, 2017 #2

    jbriggs444

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    The value of what should be zero? And why do you expect velocity to be constant?
     
  4. Jun 16, 2017 #3
    Oh sorry, I mean the value of ##dv/dt## should be infinite.
    I expect the value to be constat because it is given in the question that the ball moves with a constant velocity.
     
  5. Jun 16, 2017 #4

    jbriggs444

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    As I read the question, no such thing is given. The speed increases with each bounce.
     
  6. Jun 16, 2017 #5
    If v was not constant then how does we got ##\Delta T = 2x/v## in the first place ?
     
  7. Jun 16, 2017 #6

    jbriggs444

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    Because V << v and because v is increasing, it is a good approximation that gets better and better.
     
  8. Jun 16, 2017 #7
    I am sorry, I did not follow how does velocity of wall has to do anything with the velocity of ball ? Can you elaborate on it please.
     
  9. Jun 16, 2017 #8

    jbriggs444

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    The velocity of the ball changes at each bounce from a moving wall. How much it changes depends on V.

    Also, how much x changes during a round trip depends on V.
     
  10. Jun 16, 2017 #9
    I can buy that explanation.
    If I wanted to find accelaration of ball without doing all this. Is it possible ?
     
  11. Jun 16, 2017 #10

    jbriggs444

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    I suspect that treating the ball as an ideal gas under adiabatic compression would work.
     
  12. Jun 16, 2017 #11
    I intended to ask if there is some more mathematically accurate way to do this using mechanics.

    Since you have mentioned, how should I go doing that ? I thought I will differentiate adiabatic work done but I don't know temperature, pressure and thing like that :((.
     
  13. Jun 18, 2017 #12

    sophiecentaur

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    All what? It's a simple elastic collision situation at each bounce. This is the sort of situation that is built on in deriving the simple theory for the Gas Equations so I think it would be much easier to keep to simple Mechanics, rather than getting into thermodynamics.
     
  14. Jun 18, 2017 #13
    I also don't like to use thermodynamics. But I want to know if there is a different way to solve this question using mechanics ?
     
  15. Jun 19, 2017 #14

    sophiecentaur

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    As I said before, the gas laws can be derived using exactly the same idea of elastic collisions against the walls of a box. What more could you ask for? See this link and do some more searching. The Web is seething with information about the.
     
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