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Math Help - [SOLVED] A sailboat of mass

  1. #1
    paulina
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    Question [SOLVED] A sailboat of mass

    A sailboat of mass m is moving with a momentum p. which of the following represents its kinetic energy?
    a) mp
    b) p2/2m
    c) mp/3
    d) 1/2 mp2
    c) mp/2
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  2. #2
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    Quote Originally Posted by paulina
    A sailboat of mass m is moving with a momentum p. which of the following represents its kinetic energy?
    a) mp
    b) p2/2m
    c) mp/3
    d) 1/2 mp2
    c) mp/2
    Hello, paulina,

    p=m\cdot v\ \Longrightarrow\ v=\frac{p}{m}

    The kinetic energy is E_{kin}=\frac{1}{2}\cdot m\cdot v^2. Plug in v into E and you'll get:

    E_{kin}=\frac{1}{2}\cdot m\cdot \left(\frac{p}{m}\right)^2 = \frac{p^2}{2m}

    So it's answer b)

    Greetings

    EB
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by paulina
    A sailboat of mass m is moving with a momentum p. which of the following represents its kinetic energy?
    a) mp
    b) p2/2m
    c) mp/3
    d) 1/2 mp2
    c) mp/2
    Sloppy question \bold{p} is a vector quantity, KE is a scalar, but the wording seems to treat the two of them as if they are scalars

    Also what is meant by \bold{p}^2 is not specified, presumably it means |\bold{p}|^2.

    RonL
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by CaptainBlack
    Sloppy question \bold{p} is a vector quantity, KE is a scalar, but the wording seems to treat the two of them as if they are scalars

    Also what is meant by \bold{p}^2 is not specified, presumably it means |\bold{p}|^2.

    RonL
    In Physics, \bold{p}^2 is defined to be the Euclidean dot product (unless otherwise stated), thus there is no ambiguity.

    Note that the scalar vs. vector argument can be used to throw out answers a), c), and c) .

    -Dan
    Last edited by CaptainBlack; August 17th 2006 at 09:17 PM.
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