This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Dimensions and Units Every expression you write down that tries to describe something about the real world has to be dimensionally consistent. After all, what does the expression 5 mi hr + 3 ft mean? Or an equation such as 6 sec 2 km = 4 kg? Or the statement that the distance from here to downtown Miami is 8? Answer: Nothing! (Well, maybe in the last case there is a context, and you know that the speaker meant eight miles , but often you don’t know this, and it means there’s a mistake.) You can figure out correct units for something just by solving a little algebra. In the equation x = vt , if x = 50 meters and t = 2 seconds, you can solve for the units of v by straight algebra: v = x t = 50 meters 2 seconds = 25 meters second . If, a few lines later, you see an expression such as x = vt 2 / 2, where x , v , and t are supposed to mean the same thing as before, you can immediately see that this makes no sense. The units would be x = 1 2 v t 2 = ⇒ meter = meter second · second 2 , or meter = meter · second , and that’s nonsense. Notice the the factor of 1/2 didn’t play any role in this; it has no units, so (for this purpose) you can ignore it. In the equation, p + ρv 2 / 2 + ρgh = C , I tell you some of the units: ρ : kg / m 3 , v : m / s , h : m , What are all the rest? (You don’t even need to know what all the terms in this expression mean. You’ll encounter it in a much later chapter.) All the terms must have the same units, so just write them down: p + kg m 3 · m s 2 + kg m 3 · g · m = C. p , and g , and C don’t have any units specified, so multiply all the units to get p + kg m · s 2 + kg m 2 · g + C. This means that p and C both must have units of kg (m s 2 ). I can solve for the units of g by g = kg (ms 2 ) kg m 2 = kg · m 2 kg · m s 2 = m s 2 ....
View
Full
Document
This note was uploaded on 01/08/2012 for the course PHYSICS 205 taught by Professor Galeazzi during the Fall '11 term at University of Miami.
 Fall '11
 Galeazzi

Click to edit the document details