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Homework Help: Resisted Motion

  1. Sep 18, 2008 #1
    1. The problem statement, all variables and given/known data

    A body of mass is projected with speed and moves under uniform gravity in a medium that exerts a resistance force of magnitude (i) mk*abs(v) or (ii) mK*(abs(v))^2 , where k and K are the positive constants and v is the velocity of the body. Gravity can be ignored. Determine the subsequent motion in each case . Verify motion the motion is bounded in case i , but not in case ii

    2. Relevant equations
    F=D+L



    3. The attempt at a solution


    for case i m*dv/dt= m*k*abs(v)

    applying seperation of variables, I get

    dv/abs(v)=kdt ==> ln(abs(v))=kt ===> v=Ce^-kt or v=Ce^kt , C being a constant and v depending on whether or not is positive or negative.

    for case two, my physical system is the quadratic resistance

    dv/dt=mk*(abs(v))^2

    applying once again the seperation of variables method I get:

    -1/K*1/v=t ==> v=-1/kt+C

    I don't understand how to verify that the body is bounded. I know that a body is bounded if it cannot overcome its gravitional potential energy. I don't understand how I can possibly ignore gravity , unless the body is completely immersed in a vacuum and that cannot be possible if a fluid force is exerting a force on the object.
     
  2. jcsd
  3. Sep 18, 2008 #2

    tiny-tim

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    Science Advisor
    Homework Helper

    Hi Benzoate! :smile:

    First … big mistake … resistance acceleration is negative, isn't it? :wink:

    (otherwise, your method is fine :smile:)

    As to gravity, I don't understand why they tell you that the gravity is uniform, and then tell you to ignore it! Well, ignore it anyway! :rolleyes:

    "Unbounded" means that the body goes infinitely far (in other words, x(∞) = ∞). To check that, put v = dx/dt, and integrate again to find x(∞). :smile:
     
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