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Homework Help: SI Unit analysis

  1. Jan 16, 2013 #1
    1. The problem statement, all variables and given/known data

    When an object falls through air, there is a drag force that depends on the product of the surface area, A (m2), and the square of the velocity, in (m/s). The equation is Fdrag = CAv2. The metric unit of force is the Newton, or (N). 1 N = 1 kg*m/s2. What are the units of the constant C?


    Given the equation F =kA, where F is a force, k is a constant, and A is area, use unit analysis to determine the units of k.

    2. Relevant equations

    3. The attempt at a solution

    Answer choices for the first:





    Answer choices for the second:

    N*m2, or kg*m3/s2

    N/m2, or kg/(m*s2)

    m2/N, or m*s2/kg

    N*m, or kg*m2/s2

    I'm just having trouble starting this class out, and I'm sure this stuff is simple but I'm being thrown off by the steps and my teacher is pretty disorganized but his explanations are confusing me. I would love information and steps on how to solve this.
  2. jcsd
  3. Jan 16, 2013 #2


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    Gold Member

    First step would be to rearrange each of your equations for the quantity you want the units for. What exactly is it you find difficult? Dimensional analysis is used so that the units on both sides of an eqn check out. (I.e think of it like 'you can only equate a vector with a vector'. Similarly, a force can only equal a force, etc.. so units on left = units on right)
  4. Jan 16, 2013 #3


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    Just rearrange the equation: F = CAv2; C = F/(Av2).
    Then substitute for F etc. using the units as though they were algebraic variables:
    C = (kg m s-2)/(m2 (m/s)2)
    and simplify.
  5. Jan 16, 2013 #4
    Wow.. for some reason I was forgetting to rearrange the equation which is the first step.. lol sorry I was just over thinking it.
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