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Magnitude of the change in momentum equation

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  1. Sep 25, 2016 #1
    1. The problem statement, all variables and given/known data
    A single gas molecule of inertia m is trapped in a box and travels back and forth with constant speed v between opposite walls A and B a distance l apart. At each collision with a wall, the molecule reverses direction without changing speed.
    Write algebraic expressions for the magnitude of the change in momentum of the molecule as it collides with wall B.

    2. Relevant equations
    Δp

    3. The attempt at a solution
    i know i am looking for a change in momentum and tried answers such as p=mv. I know the the equation does not depend on l but i am unsure how you are suppose to figure out the answer
     
  2. jcsd
  3. Sep 25, 2016 #2

    Simon Bridge

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    The change in something is the final thing minus the initial thing.
    For all these momentum problems the start is the same:
    1. write a heading "before"
    1.1 draw a picture of the initial situation (here it is a particle headed to a wall, it has an arrow on it labelled "v" pointing towards the wall and the particle itself is labelled "m"
    1.2 write ##p_i=\cdots## whatever the total initial momentum is ... in this case ##p_i=mv##
    2. write the heading "after"
    2.1 as 1.1 but for the situation "after" the collision ... here the arrow points the opposite way but all the labels are the same: do you see why?
    2.2 write ##p_f=\cdots## whatever the final momentum comes to in terms of m and v etc ... remember that velocity is a vector.
    3. write the heading "change in momentum ##\Delta p = p_f-p_i##
    3.1 use the previous 2 sections to do the math.

    You seem to be having a lot of trouble with this section of your work because you do not know what many of the terms mean. You should review your coursework so far, paying particular attention to definitions.
     
  4. Sep 26, 2016 #3
    would that mean the the equation Δp=-mv-mv?
     
  5. Sep 26, 2016 #4

    PeroK

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    Yes, although since the collision take place at both end sof the box, I'd say you are looking for the maginitude of the change in momentum.
     
  6. Sep 26, 2016 #5
    so i will be using the equation p=mv?
     
  7. Sep 26, 2016 #6

    PeroK

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    You can always use that equation. It's how you interpret it. Do you understand what is happening to the momentum of the ball?
     
  8. Sep 26, 2016 #7
    i understand that before the collision its momentum is p=mv and after the collision, the momentum is the same only it is in the opposite direction so the equation after is p=-mv
     
  9. Sep 26, 2016 #8

    PeroK

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    You're right, but if you use an equation twice, you need to distinguish between, in this case, the two momenta. You should be writing:

    ##p_i = mv## and ##p_f = -mv##
     
  10. Sep 26, 2016 #9
    would the mean that the expression i am looking for be mv=-mv
     
  11. Sep 26, 2016 #10

    PeroK

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    Let's go back to post #3, where you nearly had the answer:

    I don't really understand why you didn't continue and write: ##\Delta p = -mv - mv = -2mv##

    Then, you just need to read the question and see that it wants the magnitude of the change in momentum.
     
  12. Sep 26, 2016 #11
    is this the equation for the change in momentum of the whole system or when it collides with both walls?
     
  13. Sep 26, 2016 #12

    PeroK

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    If ##\Delta p = -2mv## what is the magnitude of ##\Delta p##?
     
  14. Sep 26, 2016 #13
    2mv
     
  15. Sep 26, 2016 #14

    PeroK

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    And that's your answer!
     
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