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Homework Help: Confused about units

  1. Oct 13, 2018 #1
    1. The problem statement, all variables and given/known data

    I've an equation here: h = 3270 Pa / 1,0 g/cm^3 × 9,81 m/s^2 = 33 cm

    How did those units cancel out to make it cm? That's something I don't get.

    2. Relevant equations

    Given above.

    3. The attempt at a solution

    I've tried to cancel them out by looking at the same unit in the numerator and denominator such as, for example m / m , so m cancels out and so on but I don't get it. Does anyone know or can anyone explain why the answer is in centimeters? How do the units cancel out in the given equation? Thank you
     
  2. jcsd
  3. Oct 13, 2018 #2

    Orodruin

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    Forum rules require you to show your attempt so you need to actually show your attempt at cancelling out the units.

    Technically you could put your answer in any length unit.
     
  4. Oct 13, 2018 #3
    If we count it:

    h = 3270 Pa / 1,0 g/cm^3 × 9,81 m/s^2 = 333 m

    It should be 333 meters. How that becomes centimeters? As for your statement, there really isn't much to show. I can't / don't know how to cancel them out but above I explained the idea of canceling out, so I've proved that I know it.
     
  5. Oct 13, 2018 #4

    Orodruin

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    You cannot put in different units and just assume that the answer will be in SI units. If you did the cancellation correctly, there would be a lot to show. Note that your density is in g/cm^3, not in kg/m^3!

    As a hint: How many grams are there in 1 kg? What is (1 kg)/(1 g)?
     
  6. Oct 13, 2018 #5
    There are 1000 grams in 1 kg. I still don't get it.
     
  7. Oct 13, 2018 #6

    Orodruin

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    So how many kg/m^3 are there in 1 g/cm^3?
     
  8. Oct 13, 2018 #7
    Well, 1 kg/m^3 = 0,001 g/cm^3 --> did you mean it vice versa? If so, then 1 g/cm^3 is 1000 kg/m^3
     
  9. Oct 13, 2018 #8

    Orodruin

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    No, this is wrong. 1 m^3 is not the same as 1 cm^3.
     
  10. Oct 13, 2018 #9
    That's right but 1 m^3 can be converted into cm^3, for example. I'd just like to let you know that I still haven't got the idea.
     
  11. Oct 13, 2018 #10

    Orodruin

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    Yes it can, just like 1 g can be converted into kilograms, the point is that you didn't do that. Hence your answer actually has the units cm^3 kg / (m^2 g).
     
  12. Oct 13, 2018 #11
    How can I solve this problem?
     
  13. Oct 13, 2018 #12

    Orodruin

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    How did you solve the problem of figuring out how many grams are in a kilogram? How would you solve the problem of figuring out what 30 km/h would be in m/s?
     
  14. Oct 13, 2018 #13
    1 kg = 1000 g

    kg hg dag g , so
    1 0 0 0

    30 km/h can be converted into m/s by dividing it by 3,6 , so it'd be 8,333333... m/s

    However, I don't still get the idea in this specific instance.
     
  15. Oct 13, 2018 #14

    Orodruin

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    You are missing the point entirely.
    The point was not what is the actual factor, the point is how you obtain that factor.
     
  16. Oct 13, 2018 #15
    Well 1 km = 1000 meters and 1 hour is 3600 seconds. That gives me the factor.
     
  17. Oct 13, 2018 #16

    Orodruin

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    So what is cm^3 kg / (m^2 g) in cm? The procedure is exactly the same.
     
  18. Oct 13, 2018 #17
    I've got no idea.
     
  19. Oct 13, 2018 #18

    Orodruin

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    Yes you do, you did it when you converted km/h to m/s.
     
  20. Oct 13, 2018 #19
    cm^2 * kg / m^2 * g

    m^2 / m = m

    kg / g = 1000 g => cm * 1000 ?
     
  21. Oct 13, 2018 #20

    Orodruin

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    Where did this come from? The length units you have are cm^3/m^2 = cm (cm/m)^2.
     
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