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    I am stuck with this


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    Your help is valued and appreciated ...
    comoving_frame
    constellarknight
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    Here's my solution
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    Why am I never on here when these are posted lol

    Anyway I'll give it a go tonight. Looks on the approachable side of your questions I must say

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    (Original post by A Slice of Pi)
    Here's my solution
    I got as far as deriving the eqns of motion before I saw your full solution (you work too fast :-)) so I won't bother to finish off - my approach was a little different though, since you can work in terms of v(x) from the start

    \displaystyle v(x)= \frac{dx}{dt} \Rightarrow dI = F dt = F \frac{dx}{v}

    Then we have by the usual argument:

    \displaystyle m dv + v dm = F \frac{dx}{v} \Rightarrow m v \frac{dv}{dx} + v^2 \frac{dm}{dx} = F

    and since m(x)=M(\lambda x+1) \Rightarrow \frac{dm}{dx} =M\lambda and the external force is the weight, acting in the negative sense to x, then

    \displaystyle M(\lambda x+1) v \frac{dv}{dx} + v^2 M\lambda = -M(\lambda x+1)g \Rightarrow v \frac{dv}{dx} + \frac{\lambda v^2}{\lambda x+1} = -g
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    (Original post by atsruser)
    I got as far as deriving the eqns of motion before I saw your full solution (you work too fast :-)) so I won't bother to finish off - my approach was a little different though, since you can work in terms of v(x) from the start

    \displaystyle v(x)= \frac{dx}{dt} \Rightarrow dI = F dt = F \frac{dx}{v}

    Then we have by the usual argument:

    \displaystyle m dv + v dm = F \frac{dx}{v} \Rightarrow m v \frac{dv}{dx} + v^2 \frac{dm}{dx} = F

    and since m(x)=M(\lambda x+1) \Rightarrow \frac{dm}{dx} =M\lambda and the external force is the weight, acting in the negative sense to x, then

    \displaystyle M(\lambda x+1) v \frac{dv}{dx} + v^2 M\lambda = -M(\lambda x+1)g \Rightarrow v \frac{dv}{dx} + \frac{\lambda v^2}{\lambda x+1} = -g
    that is my approach but the ODE will be tough for most students to solve ...
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    (Original post by TeeEm)
    that is my approach but the ODE will be tough for most students to solve ...
    From which we can see that "A Slice of Pi" is not like most students.
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    (Original post by atsruser)
    From which we can see that "A Slice of Pi" is not like most students.
    his mechanics definitely is amazing ....
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    (Original post by TeeEm)
    I am stuck with this


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    Your help is valued and appreciated ...
    comoving_frame
    constellarknight
    Honoured that you'd ask but I don't do mechanics. Anyway shouldn't you be fixing all the mistakes in your practice papers and topic booklets?
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    (Original post by constellarknight)
    Honoured that you'd ask but I don't do mechanics. Anyway shouldn't you be fixing all the mistakes in your practice papers and topic booklets?



    As they are free I do not think so ...
    Besides anybody with half a molecule of brain should be able to deal with any typos/errors by cross referencing between the typed question and the worked solution.
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    (Original post by A Slice of Pi)
    Here's my solution
    That was what I did!!

    Though TeeEm, did you really not know how to do this? Or is it just to get people to try it?
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    (Original post by gagafacea1)
    That was what I did!!

    Though TeeEm, did you really not know how to do this? Or is it just to get people to try it?
    I hope I know how to do it ... but I feel better to "be one of us" and struggle to do it ...
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    (Original post by TeeEm)
    As they are free I do not think so ...
    Besides anybody with half a molecule of brain should be able to deal with any typos/errors by cross referencing between the typed question and the worked solution.
    Linux is free but that doesn't mean the maintainers fix bugs only out of grace: they do so because they know that if they behave in an arrogant and sanctimonious manner, people will eventually have had enough and will fork the project.

    Similarly I have already begun creating competition to your resources with my Advanced Mathematics Extension Paper:
    http://www.thestudentroom.co.uk/show....php?t=3905787. You think that you're so clever, and beautiful, and whatever, because you have 18,000 posts, which actually doesn't mean ****.
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    (Original post by TeeEm)
    I hope I know how to do it ... but I feel better to "be one of us" and struggle to do it ...
    You hope, as in you don't know.
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    (Original post by constellarknight)
    Linux is free but that doesn't mean the maintainers fix bugs only out of grace: they do so because they know that if they behave in an arrogant and sanctimonious manner, people will eventually have had enough and will fork the project.

    Similarly I have already begun creating competition to your resources with my Advanced Mathematics Extension Paper:
    http://www.thestudentroom.co.uk/show....php?t=3905787. You think that you're so clever, and beautiful, and whatever, because you have 18,000 posts, which actually doesn't mean ****.
    have you taken your medication today?
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    (Original post by TeeEm)
    have you taken your medication today?
    What medication? Again you are libelling me.
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    (Original post by constellarknight)
    What medication? Again you are libelling me.
    I would love to talk to you kid but I am a bit busy .... Maybe tomorrow ...
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    (Original post by TeeEm)
    I would love to talk to you kid but I am a bit busy .... Maybe tomorrow ...
    Why would you want to talk to me? You clearly have nothing non-frivolous and non-libellous to say.
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    (Original post by constellarknight)
    Why would you want to talk to me? You clearly have nothing non-frivolous and non-libellous to say.
    If you have nothing relevant to the question to add to this thread, then why even bother to post?
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    (Original post by A Slice of Pi)
    If you have nothing relevant to the question to add to this thread, then why even bother to post?
    To express the fact that a tort has been committed against me, and the tortfeasor TeeEm must be held responsible.
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    This is my solution
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