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Dot product or cross product?

  1. Dec 27, 2009 #1
    In the equation v^2 = u^2 + 2aS , What kind of products are v^2 , u^2 , and aS ?
    Cross product or dot product?
     
  2. jcsd
  3. Dec 27, 2009 #2
    Please correct me if i am wrong, but i believe they will be dot products, cross products will have a change in directions as well.
     
  4. Dec 27, 2009 #3
    Definitely dot products.
    When you cross a vector with itself, you get the zero vector, which is absolutely meaningless.
     
  5. Dec 27, 2009 #4
    OK . So v^2 and u^2 are dot products ...but what about aS?
     
  6. Dec 27, 2009 #5
    Going from just a shallow point of view (without analyzing the meaning of the equation whatsoever) it must be a dot product as well as v^2 and u^2 are both scalars, which necessarily requires the product aS to yield a scalar as well.
     
  7. Dec 27, 2009 #6

    D H

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    Unless of course a and S are already scalars.
     
  8. Dec 27, 2009 #7
    I think it is important to not just guess what the products might be, but rather prove the law anew. It might be none of the products. So let's do that
    [tex]\Delta E_\text{kin}=\int\vec{F}\cdot\mathrm{d}\vec{s}[/tex]
    [tex]\therefore m|v|^2-m|u|^2=2\vec{F}\cdot\Delta\vec{s}[/tex]
    if the force is a constant
    [tex]\therefore |v|^2=|u|^2+2\vec{a}\cdot\Delta\vec{s}[/tex]
    or if you wish
    [tex]\therefore \vec{v}\cdot\vec{v}=\vec{v}_0\cdot\vec{v}_0+2\vec{a}\cdot(\vec{s}-\vec{s}_0)[/tex]

    Note that all this assumes that the force/acceleration is constant.
     
  9. Dec 27, 2009 #8

    Redbelly98

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    [nitpick]

    Just to clarify, Gerenuk means that force and acceleration are both constant.

    [tex]\frac{force}{acceleration}[/itex] is the same as the mass, which is always constant (at nonrelativistic speeds)

    :smile:
    [/nitpick]
     
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