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Dimensional Analysis and Uncertainty - Example 2

In physics, dimensional analysis is the study of the relationships between different fundamental physical quantities. It is a method of checking the consistency of the basic physical quantities used to describe a system, and to discover possible errors in a set of derived units.


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Video Transcript

Welcome to our second review video on dimensional analysis. And this is an example video. Um, in this video we're gonna look at, how do you solve problems with dimensional analysis? Oftentimes, in physics classes, you'll have an introductory section that we'll talk about in dimensional analysis, and you might get a problem that goes something like, um, Terry eats three candy bars. Each candy bar has 2000 jewels of energy in it. If Terry gets 65% of this energy, how much energy did Terry get by eating the candy bars? So we want to keep track of all the numbers given here. So Terry eats three candy bars. So we write that down. We know that there are 2000 jewels in one candy bar, so we make a note of that as well, and we know that he gets 65 not 60 65% of the total energy. So what's the final amount of energy that Terry gains? So we're just gonna do dimensional analysis, So we say three candy bars times in one candy bar. Sure, there are 2000 jewels, so that's equal to 6000 total jewels. That could come from the candy bars, but we only get 65% so we have to multiply it by the correct ratio. In order to get the total amount of energy that Terry would gain 0.65 or their their 0.65 multiplied by 6000 jewels, eso the other type of problems that we might have could involve something like, say, Oh, there are 10 gallons of water that air passing over a waterfall every minute we'll say it's a small waterfall, so 10 gallons of water every minute after an hour, How much weight of water has come over the fall? So after one hour, what's the total weight of water that's passed over the falls? So and this problem, we have to do a little bit more of a conversion because we also know that it's going to last for one hour and we want the total weight. So what we need is how many pounds are in a gallon of water, so looking up that on mine, we know there are 8.34 pounds per gallon, and then we've got ours here in one hour, so we know there are 60 minutes in an hour. So what I'm gonna do is I'm gonna say Okay, I've got 10 gallons per minute going to convert the end of weight. So I'm going to say there are £8.34 in one gallon. Now, I have pounds per minute, and now I want to multiply it by the total amount of time. So I'm going to say I'm gonna multiply this times one hour, But I need that to be in minutes so it will cancel with the minutes here. So I'm going to say, Well, I know in one hour there's 60 minutes. So now the minutes cancels and I get a total amount of weight. It'll be 10 times 8.34 times 60 is gonna be our final answer. So that'll be 83.4 times 60 pounds of water. Ah, quick note here. Um, pounds and kilograms are not the same type of unit. Ah, Pound is actually a measure of force, which we would use Newton's for that and are s I units. So that and Newton instead of a kilogram. So make sure that you keep track of that difference if they ask for a weight, then they're looking for something in terms of Newton's or pounds. If they ask for a mass, then they're looking for something in terms of kilograms. So make sure you watch those differences between the S I C system of units and the standard system of units that you've probably learned growing up.