Simple math question proportions

Shjanzey

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Jun 30, 2012
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  1. Medical Student
    Lets say you have:

    KE = 1/2mv^2 and then you double KE. The velocity increases by a factor of square root 2. Can someone show the algebraic steps to this. Thank you

    The equation for KE is K = (1/2)*mv^2

    So you solve for v

    v1 = sqrt(2K/m)

    Now double K (kinetic energy) to see what happens

    v2 = sqrt((2*2K)/m) --> sqrt(4K/m)

    If you compare the two, v2 has increased by sqrt(2).
     

    gettheleadout

    MD
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      I would think about it like this:

      You can't increase mass, so you must increase velocity, right? We want the total KE doubled, so:

      KE = (1/2)*m*(v)^2

      needs to become

      KE = 2*(1/2)*m*(v)^2

      This means we need to put something into the parentheses that contain "v" that, when squared (and thus pulled out from the parentheses under the exponent), will give us a coefficient of 2. What can we put in as a coefficient of "v" that will be squared to yield 2? The square root of 2 of course.
       
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      Hemorrage

      Ambrose
      7+ Year Member
      Sep 4, 2011
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      1. Medical Student
        I would think about it like this:

        You can't increase mass, so you must increase velocity, right? We want the total KE doubled, so:

        KE = (1/2)*m*(v)^2

        needs to become

        KE = 2*(1/2)*m*(v)^2

        This means we need to put something into the parentheses that contain "v" that, when squared (and thus pulled out from the parentheses under the exponent), will give us a coefficient of 2. What can we put in as a coefficient of "v" that will be squared to yield 2? The square root of 2 of course.

        Very intuitive method
         

        MD9

        New Member
        Jan 27, 2013
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          Hopefully this is what you're looking for. If you need any more explanation, please let me know!

          ZltsWv8.jpg


          You can see that instead of doubling the K.E., if we generalize and say we multiply it by some number n, then the result will be that the new velocity, v2, is equal to the initial velocity, v1, multiplied by the square root of n (i.e. just replace "2" in "2K.E." with the variable "n" to get n*K.E. and the result should be v2=sqrt(n)*v1).
           
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