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Please i want explanation of dimensional analysis

  1. Dec 11, 2011 #1
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Dec 11, 2011 #2

    PeterO

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    Homework Helper

    Dimensional analysis is considering the units of each part of an expression/formula and reducing them to the base references: kg, m, s or [MASS],[LEN],[TIME]

    eg F = ma
    we know the dimension of the m is [MASS]
    we know the dimensions of the a are [LEN][TIME]-2

    so hopefully the dimensions of force are: [MASS][LEN][TIME]-2
    [they are!]

    From there we can Work
    [Force * distance] → [MASS][LEN][TIME]-2*[LEN]
    Work → [MASS][LEN]2[TIME]-2

    Impulse: Force * time → [MASS][LEN][TIME]-2*[TIME]
    → [MASS][LEN][TIME]-1

    Momentum: mass*velocity → kg*m/s → [MASS][LEN][TIME]-1

    It is nice that Impulse and momentum have the same dimensions!!!

    EDIT: when a number appears in a formula - it has no dimension and is ignored. Take the perimeter of a square P = 4L both perimeter and side length have dimensions [LEN]; we don't have a 4 in there.
     
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