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    Variable Mass Problem ...
    Name:  Mechanics Variable Mass.jpg
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    Only minutes old ...
    I have not even written the solution yet.
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    (Original post by TeeEm)
    Variable Mass Problem ...
    Name:  Mechanics Variable Mass.jpg
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    Only minutes old ...
    I have not even written the solution yet.
    I get 1/k * ln 2 but I haven't checked just yet.
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    (Original post by A Slice of Pi)
    I get 1/k * ln 2 but I haven't checked just yet.
    one of the two answers is
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    (Original post by TeeEm)
    one of the two answers is
    Didn't see the last bit aha, I'll work it out now
    Edit: I get x = \frac{g}{k^2}(\ln 2 - 0.5)
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    (Original post by A Slice of Pi)
    I get 1/k * ln 2 but I haven't checked just yet.
    Bloody hell, how are you so good at mechanics?!
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    (Original post by Zacken)
    Bloody hell, how are you so good at mechanics?!
    I was thinking the same thing..
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    (Original post by TeeEm)
    one of the two answers is
    I get \frac{1}{k}\ln 2 as well, but I don't see where another answer is going to come from, so maybe I've just fluked it. I derived the eqns of motion from scratch though, so perhaps I screwed up. Roughly, for the raindrop, assuming infinitesimal changes of mass and velocity dm, dv over time dt:

    dI  = p_f-p_i=F dt \Rightarrow \\ \\ (m+dm)(v+dv)-mv = mg dt \Rightarrow m\frac{dv}{dt}+v\frac{dm}{dt}=mg

    But m(t) = Me^{kt} \Rightarrow m\frac{dv}{dt}+kvm=mg \Rightarrow \frac{dv}{dt}+kv=g

    Thereafter it's just integration and initial conditions so I'm not sure what I've missed.
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    (Original post by atsruser)
    I get \frac{1}{k}\ln 2 as well, but I don't see where another answer is going to come from, so maybe I've just fluked it. I derived the eqns of motion from scratch though, so perhaps I screwed up. Roughly, for the raindrop, assuming infinitesimal changes of mass and velocity dm, dv over time dt:

    dI  = p_f-p_i=F dt \Rightarrow \\ \\ (m+dm)(v+dv)-mv = mg dt \Rightarrow m\frac{dv}{dt}+v\frac{dm}{dt}=mg

    But m(t) = Me^{kt} \Rightarrow m\frac{dv}{dt}+kvm=mg \Rightarrow \frac{dv}{dt}+kv=g

    Thereafter it's just integration and initial conditions so I'm not sure what I've missed.
    clearly too tired

    the same equation
    2 solutions

    one as
    a = dv/dt
    the other
    a = v dv/dx
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    (Original post by TeeEm)
    clearly too tired

    the same equation
    2 solutions

    one as
    a = dv/dt
    the other
    a = v dv/dx
    OK, perhaps I'm being really dense but I have no idea what you are saying here. We can only get one time from that equation, AFAICS.

    [edit: eff it. There's another question - sorry didn't see it]
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    (Original post by atsruser)
    OK, perhaps I'm being really dense but I have no idea what you are saying here. We can only get one time from that equation, AFAICS.
    the equation of motion should be after simplification

    dv/dt = g - kv

    solving this as it is gives you your answer.

    you can also solve the same ODE as

    v dv/dx = g - kv

    to get v as a function of x
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    (Original post by A Slice of Pi)
    Didn't see the last bit aha, I'll work it out now
    Edit: I get x = \frac{g}{k^2}(\ln 2 - 0.5)
    yes that is the other solution
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    (Original post by TeeEm)
    the equation of motion should be after simplification

    dv/dt = g - kv

    solving this as it is gives you your answer.

    you can also solve the same ODE as

    v dv/dx = g - kv

    to get v as a function of x
    Yes - see my edited answer above. You hid the second question too well. This is a pretty standard variable mass question though. Got any harder ones?
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    (Original post by Zacken)
    Bloody hell, how are you so good at mechanics?!
    (Original post by Student403)
    I was thinking the same thing..
    he is the governor !!!
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    (Original post by atsruser)
    Yes - see my edited answer above. You hid the second question too well. This is a pretty standard variable mass question though. Got any harder ones?
    Yes very standard ... good practice for the students here

    I have written 3 more, 2 slightly harder, the other very hard.

    I have written the solutions but they need typing
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