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Newton second law involving a gallon of water

  1. Nov 9, 2011 #1
    1. The problem statement, all variables and given/known data
    a box filled of water is over at the beginning of a incline plane of 30 degree, it has a mass of 1 kg,from the bottom of the plane to the top is 10m, the gallon is pushed with a force of 10N to the top, and the gallon is leaking 0.01kg per second

    what is the final velocity?
    2. Relevant equations

    f=ma

    3. The attempt at a solution
    analyzing this problem each since the force doesnt change, the mass decrease each second so the acceleration increase each second. i really dont know how to solve this problem when involving a gallon of water leaking.
     
    Last edited: Nov 10, 2011
  2. jcsd
  3. Nov 9, 2011 #2
    Only when the mass remains constant does Newton's Second Law of motion reduce to
    [tex]\vec{F}=m\vec{a}[/tex]
    When dealing with variable mass, use
    [tex]\vec{F}=\frac{d}{dt}(m\vec{v})[/tex]
     
  4. Nov 9, 2011 #3
    Last edited: Nov 9, 2011
  5. Nov 9, 2011 #4
    so it means the mass is constant, it only changes the velocity
     
  6. Nov 9, 2011 #5
    No, the mass is not constant. It is changing with time. Also, did you copy the question down fully, and properly?
     
  7. Nov 9, 2011 #6
    well if you dont understand my question u can ask me
     
  8. Nov 9, 2011 #7
    as far i understand time is changing as well as mass and velocity
     
  9. Nov 9, 2011 #8

    Ray Vickson

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    This equation is known to be incorrect in general, although it is true in some cases. Correct classical variable-mass equations of motion were finally well established in the 1990s! Before that, many incorrect results appeared in the published literature. Google 'variable-mass dynamics' for relevant papers.

    RGV
     
  10. Nov 9, 2011 #9
    so... this is harder now, can u help me?
     
  11. Nov 10, 2011 #10

    PeterO

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    A couple of questions:

    Is this a gallon of water or a kilgram of water? A litre of water has a mass of 1 kg.
    If this is a gallon, is this a US gallon [8 lb] or an imperial gallon [10 lb],

    EDIT: I ask about which gallon as I don't know where you are posting from.
     
    Last edited: Nov 10, 2011
  12. Nov 10, 2011 #11
    Interesting to know.. Especially considering this was in my Calculus textbook from January 2009.
     
  13. Nov 10, 2011 #12
    actually is not really a gallon of water....is just a box or tank filled with water which leak every second.
     
  14. Nov 10, 2011 #13
    i'm pretty sure that the volume isn't important just the change in mass
     
  15. Nov 14, 2011 #14

    PeterO

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    If the box was not leaking, it would take only about 2 seconds to reach the top, arriving with a velocity of about 10 m/s.

    In two seconds, the mass will have reduced from 1.00 kg to 0.98 kg - a very small change, so the final velocity won't be much bigger.
    Since data was given to one specific figure only, the answer should be 1 x 101 regardless.
     
  16. Nov 14, 2011 #15
    i already solved it
     
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