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How do I identify the unit from the question?

  1. May 6, 2014 #1
    EXAMPLE QUESTION:
    Calculate the mass per unit length of the wire, μ, given by
    μ = g /(2fG)^2
    where g = 9.81 N kg–1 and f = 50 Hz.

    For example here is it mass per unit length and so would it be kg/m? It kg/m the same as kgm^-1. But then how do I identify the units like kgm^-2 like how would they be written, mass per squared unit length? I'm a bit confused.

    Also, if the result was
    0.0072 kg/m
    Could I say it is 7.2 x10^-3 kg/m or can I convert it to something like g/m?
     
  2. jcsd
  3. May 6, 2014 #2

    BvU

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    Hello tangent,

    Yes, mass per length is kg per m, or kg/m also written as ## {{\rm kg}\over {\rm m}} ## or ## {\rm kg}\, {\rm m}^{-1} ##. Ropes and chains have mass per length as a characteristic.

    And ## {\rm kg}\, {\rm m}^{-2} ## is what you get when you divide mass by area. Tiles and floorboards have that. If a tile of 0.3 m x 0.3 m weighs 0.81 kg, the mass per area is 0.81 kg / (0.3 m x 0.3 m) = 0.81 / (0.3 x 0.3 ) kg / (m x m) = 9 kg/m2.

    Water weighs approximately 1000 kg/m3.


    Converting is easy, for example the tiles: 0.81 kg / (0.3 m x 0.3 m) = 0.81 kg x (1000 g/kg)/ (0.3 m x 0.3 m) = 9000 g/m2.
    Or 0.81 kg / (0.3 m x 0.3 m) = 0.81 kg / (0.3 m x 100 cm/m x 0.3 m x 100 cm/m) = 9 x 10 -4 kg/cm2.

    So, in your example: 0.0072 kg/m is indeed 7.2 x10-3 kg/m, and multiplying by 1 (namely 1 = 1000 g/kg) gives 0.0072 kg/m x 1000 g/kg = 7.2 kg/m x g/kg = 7.2 g/m.
     
  4. May 6, 2014 #3

    CWatters

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    As BvU said.. m2 is "square meters" which is a unit of area, so m-2 is "per square meter".

    mS-1 is "meters per second" which is a velocity so
    mS-2 is "meters per second squared" which is an acceleration
     
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