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So I tried googling but unfortunately the world is filled with people who don't even get how to convert cm to m and I even found this gem.
Though that must be a troll or something.... I hope.
My question is about equations that involve conversion where making the conversion changes a number from say 7.5cm to .075m. I generally like to convert to SI units since that's what we're supposed to do in class and the formulas are all made using SI units so it seems like the obvious choice.
ie: The elastic potential energy equation (like for a spring) of U=(1/2)kx^2
I know this is basic but every time I do a problem I find myself having to play around to find the proper way and it'd be much easier if I just understood this.
Before you say ask a teacher. I will do it, micronesia answer plez!
The actual problem I just did was for finding the k value for.
25J=(1/2)k(7.5cm)^2
I know the answer is 89N/cm but I don't completely get the unit situation.
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Couldn't you just multiply the 25J by 100 since a J is just N x m?
edit: nevermind you get 88.88 repeating
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How does it not work?
It's 25J = (1/2) k (0.075m^2)
k = 8888N/M
or 89N/cm
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Don't you know the units for U? J = N*m = kg(m/s)^2
And do some cancelling/dimensional analysis...
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A joule is defined in MKS. (meters, kilograms, seconds) If you use centimeters for your length, you will have a term that is still an expression of energy, just not one that is standard or named.
You can mix and match units all you like, as long as you stay consistent.
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United States24771 Posts
The fact that the 7.5cm is squared doesn't matter when trying to convert the units. The easiest thing as already said is to convert the 7.5cm into m so you have m, N/m, and J, which are all consistent. Then solving the equation is pretty easy. If this doesn't answer your question then please clarify. As a ty can you tell me how to do a 10/15 gate? I've actually never seen/done it LOL
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look this... a square meter is 100cm X 100cm, thats 10000cm^2
So, when you have it like 7.5cms, the sqare is 66.9cm^2 ~ 0,0067m^2, you follow?
and the joule is (kg)(m^2)/(s^2)
So, now just do the maths
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On February 16 2010 12:53 micronesia wrote:
The fact that the 7.5cm is squared doesn't matter when trying to convert the units. The easiest thing as already said is to convert the 7.5cm into m so you have m, N/m, and J, which are all consistent. Then solving the equation is pretty easy. If this doesn't answer your question then please clarify. As a ty can you tell me how to do a 10/15 gate? I've actually never seen/done it LOL
Yea I guess I'll just remember to always convert then square. I don't get why exactly but this circumstance confuses me a bit.
Will you be on sc in 1.5 hours? I'll get on then for a bit! I actually have a lot of schoolwork this week so I won't be on a lot till the weekend unless I go skiing in which case I should still be online Sunday.
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The thing to remember is that these are just simple equations. Like any expression, you can freely multiply by 1 and the expression is still true.
So, what is 1? Here are various ways you can write 1:
12 inches = 1 ft
Therefore,
12 inches/1 ft = 1
likewise, these are true:
1 = 2.54 cm/1 inch
1 = 100 cm/1 m
1 = 1 inch/2.54 cm
1 = 1 J/(1 N*m)
and so on.
So by cleverly multiplying by 1 in the correct form, you can get certain units to cancel and you are left with new units. These are known as "conversion factors". All conversion factors are equal to 1. However they can change units for you.
One last thing. If you are converting square units like cm^2 into m^2, you can either use the 1 m/100 cm conversion factor twice, or you can square the conversion factor. This is because you need cm^2 to cancel out cm^2.
edit: this is what a squared conversion factor looks like explicitly:
(1 m/100 cm)^2 = 1 m^2/100^2 cm^2 = 1 m^2/10000 cm^2
Also realize that for my above conversion factors, you an invert them and they are the same. For example:
1 = 12 inches/1 ft = 1 ft/12 inches
because 1/1 = 1
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You can keep the units when you do the conversion, that might help you.
So for example, I want to convert BMI from empirical to SI units:
BMI = mass/(height)^2
x [lb / in^2] = x * [ lb * .454kg / lb ] * [ in^-2 * (inch / 0.0254 m) ^ 2 ]
notice in the first set of square brackets on RHS, [lb] cancels with [lb], you are left with [kg]
in the second set of sq brackets on RHS, [in^-2] cancels with [inch^2] and you are left with [m^-2]
simplify we get:
BMI = x * (0.454/(0.0254)^2) [ kg/m^2 ]
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