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Charged ball exiting a box....

  1. Jul 19, 2015 #1
    1. The problem statement, all variables and given/known data
    A small ball has mass 3.4x10^-8 kg and charge of 2.0x10^-5 C. It enters a box with initial speed 1.2x10^4 m/s. The point where the charge leaves the box is at a voltage 350kV higher than the entry point. Find the speed of the ball as it leaves the box.



    2. Relevant equations
    ΔE = E - E0

    ΔE = q(V)

    E = 1/2mv2

    3. The attempt at a solution

    E = 1/2 (3.4x10-8)(1.2x104)2 = 2.448 J
    ΔE = (2.0x10-5)(350000)= 7 J
    7J = E - 2.448J

    9.448J = 1/2(3.4x10-8)v2

    v = sqrt ((2(9.448))/(3.4x10-8)

    v = 23577 m/s

    Does this look right? Apparently the ball doesn't leave the box. But that doesn't make any sense to me.
     
    Last edited: Jul 19, 2015
  2. jcsd
  3. Jul 19, 2015 #2

    haruspex

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    Has it gained or lost electrostatic energy?
     
  4. Jul 19, 2015 #3

    haruspex

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    I assume the (2.0x10-5) is a typo.
     
  5. Jul 19, 2015 #4
    It's lost energy because the charge is positive, right?

    I don't believe it a typo. I'm helping someone with their homework. Their instructor said the ball doesn't leave the box. But that makes no sense to me.
     
  6. Jul 19, 2015 #5
    That is a typo. I just saw what I did wrong.
     
  7. Jul 19, 2015 #6
    But even with that 2.448 is correct. I put it in my calculator correctly but I typed it wrong.
     
  8. Jul 19, 2015 #7

    haruspex

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    Quite so. So what is the new KE?
     
  9. Jul 19, 2015 #8
    Should it have been 4.55 and not 9.44?
     
  10. Jul 20, 2015 #9

    haruspex

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    I'm sorry, I misremembered which way round I asked the question. I should have said that answer was wrong.
    It is a positive charge which has moved to a point at a higher potential. It has gained electrostatic energy.
     
  11. Jul 20, 2015 #10
    Ok. That doesn't help me though. I'm confused about what you're trying to get at.
     
  12. Jul 20, 2015 #11

    haruspex

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    If it started with 2.448J KE and gained 7J PE with no work being done on it, how much KE does it now have?
     
  13. Jul 20, 2015 #12
    -4.552J?
     
  14. Jul 20, 2015 #13

    haruspex

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    Right. What does that tell you?
     
  15. Jul 20, 2015 #14
    Does that mean that the ball stopped?
     
  16. Jul 20, 2015 #15

    haruspex

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    Is it possible for the ball to exit with negative KE?
     
  17. Jul 20, 2015 #16
    Wouldn't that mean the ball turned around. You can't have negative mass so it has to have negative direction.
     
  18. Jul 21, 2015 #17

    haruspex

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    Energy is a scalar. No matter which way it is moving it cannot have negative KE.
     
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