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Basic Physics: Conversions help

  1. Mar 30, 2012 #1
    Does anyone know a good website or other source for practicing conversions and really just units in general? I'm having trouble with them, I'll give you an example problem I did to illustrate my problem...

    What is the pressure at a depth of 5 meters in alcohol? (The specific gravity of alcohol is .8)

    Pressure in water = weight density*depth
    Sg=mass density/ mass density of water -> .8 = mass density/ 1 = .8g/ccm (cubic centimeter)
    weight= mass*9.8 (force of gravity on Earth.) = .8*9.8=7.84 Newtons
    depth= 5 meters
    Pressure= 7.84N*5 meters = 39.2N/m

    The book answers are

    Mass density of Alcohol= 800 kilograms per cubit meter
    Weight density of Alcohol= 7840 Newtons per cubic meter
    Pressure at 5 meters deep in alcohol= 39,200 Newtons per square meter= 3.92 Netwons per square centimeter.

    What was the correct way of doing that problem? I know I did the math right, it's the units that are troubling me.
     
  2. jcsd
  3. Mar 30, 2012 #2
  4. Mar 30, 2012 #3

    K^2

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    Science Advisor

    What you did wrong is not convert properly between meters and centimeters. Keep the units as part of your computation, and you won't have these problems. Watch. I'm going to just multiply all the numbers together, as you did, but I'll keep units going all the way through.

    (9.8 m/s²) * (0.8 g/cm³) * (5 m) = 39.2 m*g*m/(s²*cm³) = 39.2 g*m²/(cm³ * s²)

    That's actually the correct answer, but the units of that answer are not pretty. So we look for things to simplify. First, you notice that you have meters at the top and centimeters at the bottom. You can do some cancellation using the fact that m/cm = 100.

    39.2 g*m²/(cm³ * s²) = 39.2 * (m/cm) * g * m/(cm² * s²) = 39.2 * 100 * g * m/(cm² * s²) = 39.2 * 100 * 100 g/(cm*s²) = 392,000 g/(cm * s²).

    That's better, but the units turned out to be CGS, and it'd be nicer to have the result in SI. Now, m/cm = 100 as we established, so 100cm / m = 1, and we can always multiply by 1. Lets do that.

    392,000 g/(cm * s²) * 1 = 392,000 g/(cm * s²) * (100 cm/m) = 39,200,000 g/(m * s²)

    Now we want to get rid of grams. 1kg / 1g = 1000, so 1 = 1kg/(1000 g)

    39,200,000 g/(m * s²) * 1kg / (1000g) = 39,200 kg/(m * s²)

    That's SI already. Final trick is to realize that what you are looking for is pressure, which is in N/m². Lets see if we can get it to that form. 1N = 1kg * m / s². Or 1 = 1N * s² / (kg * m). Lets multiply by 1 again.

    39,200 kg/(m * s²) * (1N * s² / (kg * m)) = 39,200 N/m².

    You can leave it like this, or convert this to Pa, using 1Pa = 1N/m², or to kPa, using 1kPa = 1000Pa. But you always do the same thing. You multiply and divide units as if they were variables expressed in terms of other units.

    Once you have enough practice working with units, you won't need to carry out such long chains of computations. You'll be able to use many shortcuts. But while you are feeling uncertain, carry out each step explicitly to avoid making mistakes.
     
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