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Math Help - Vector problem

  1. #1
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    Vector problem

    A particle collides with a surface, at velocity vector v. The normal vector for the point at which is collides is vector n. \hat v and \hat n are the unit vectors for v and a respectively.

    1) Using the fact that angle of incident = angle of reflection, what is the new vector o, which represents the outgoing velocity, assuming there is no loss of energy.

    2) Given a coefficient of restitution, c, how would the vector o differ?
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  2. #2
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    Part c) If friction, with coefficient f, is introduced, how would this affect the outgoing vector, o?
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  3. #3
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    Quote Originally Posted by scorpion007 View Post
    A particle collides with a surface, at velocity vector v. The normal vector for the point at which is collides is vector n. \hat v and \hat n are the unit vectors for v and a respectively.

    1) Using the fact that angle of incident = angle of reflection, what is the new vector o, which represents the outgoing velocity, assuming there is no loss of energy.
    The component of \bold{v} normal to the surface has
    its sign reversed:

    <br />
\bold{o}=\bold{v}-2 (\bold{v}.\bold{\hat{u}}) \bold{\hat{u}}<br />

    RonL
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  4. #4
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    Quote Originally Posted by scorpion007 View Post
    A particle collides with a surface, at velocity vector v. The normal vector for the point at which is collides is vector n. \hat v and \hat n are the unit vectors for v and a respectively.

    2) Given a coefficient of restitution, c, how would the vector o differ?
    Remove component of \bold{v} normal to the surface and replace with -c times it:

    <br />
\bold{o}=\bold{v}-(1+c) (\bold{v}.\bold{\hat{u}}) \bold{\hat{u}}<br />

    RonL
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by scorpion007 View Post
    Part c) If friction, with coefficient f, is introduced, how would this affect the outgoing vector, o?
    It would apply an additional change in component parallel to the surface
    proportional to f\ dt where dt is the duration of
    contact. The constant of proportionality would depend on factors we are not
    told (or a definition of coefficient of friction of which I am unaware).

    RonL
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