Dimensional Analysis Example 1

by Jules Bruno
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Here are example states a ta King. Great for Simon's per hour. If each assignment has 12 questions, how many questions can the th grade and 130 minutes? All right, So if we're gonna approach a question like this, let's look at our steps. If present, start with the given amount. That is not a conversion factor, remember, are given. Amount is when we have a single unit by itself that isn't tied toe another. We're going to stay within this question are 130 minutes is are given amount to identify the end amount. You want toe isolate for your unknown. So we're going to say, here, this is our given amount. We have to figure out what our end amount will be. So our end amount is over here. They're asking us how many questions How many questions. So questions will be our UN amount. Ah, step to write down all the conversion factors. So all our conversion factors Let's see, we have four assignments per hour. Remember, per is the word that connects different units together. So one is four assignments every per hour. So that's four assignments for every one hour they tell me. Also, each assignment has 12 questions, so that means one assignment is 12 questions. Okay, so 12 questions now this last part find the connection between the given amount and the conversion factors in orderto isolate the end amount. Okay, so let's look at the given amount given amount has minutes within it. But neither one of the conversion factors has minutes involved. What we do have is ours. That tells me there's a conversion factor that's even before either one of these two. So conversion factor one actually involves us first changing minutes into hours. So we have minutes here on the bottom hours here on top. One hour is 60 minutes minutes. Cancel out this way, and the reason we're doing that is because now that we have ours, we can connect it to the hours here within this conversion factor. So that will be my second conversion factor bringing the one hour for every four assignments. Now that we have ours lined up, they cancel out. Now we have assignments and we need to get the questions. Here is our last conversion factor. Now it has assignments and questions within it, but we need assignments to cancel out. So assignments need to be here on the bottom, right? And then we need questions. Questions go here on top and it is one assignment is 12 questions. Remember? One of the first things we said is that conversion factors we can flip them. They could be presented in two different ways. Here, we had to flip the initial conversion factor so that assignments can cancel one another out. They have to be on opposite levels to be able to do that. So in conversion factor three, what I'll have left at the end is questions. So what we do now is we're going to multiply times four times 12, divided by 60. So when we do all of that, we're gonna get here. Ah, 130 actually, 930. We're gonna get here as our final answer. Ah, 104 questions. So we have 104 questions as our end amount. But remember, we need to worry about significant figures. 1 30 has to sick fix four has won six fig 12 has to sick figs, 60 has won six fig. So we need to go and have only one sick thick as our final answer. So we say roughly about 100 questions is what the TA could do within the 130 minutes, which is a lot of questions. All right, so now that we've done this example where we've set up the basic principles behind dimensional analysis, let's continue onward and do some practice questions.