Docsity
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Docsity AI
Docsity AI
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search for your university

Find the specific documents for your university's exams

Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

Dimensional Analysis: A Practical Guide to Unit Conversions, Schemes and Mind Maps of Dimensional Analysis

University of California - Los Angeles (UCLA)Dimensional Analysis

The critical thing to note is that the units behave like numbers do when you multiply fractions. That is, the inches (or foot) on top and.

Typology: Schemes and Mind Maps

2022/2023

Uploaded on 02/28/2023

alfred67
alfred67 🇺🇸

4.9

(20)

328 documents

1 / 13

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
Dimensional Analysis
•In order to perform any conversion, you need a
conversion factor.
•How does dimensional analysis work?
•It will involve some easy math (Multiplication & Division)
•Conversion factors are made from any two terms
that describe the same or equivalent “amounts”
of what we are interested in.
For example, we know that:
1 inch = 2.54 centimeters
1 dozen = 12
pf3
pf4
pf5
pf8
pf9
pfa
pfd

Partial preview of the text

Download Dimensional Analysis: A Practical Guide to Unit Conversions and more Schemes and Mind Maps Dimensional Analysis in PDF only on Docsity!

Dimensional Analysis

  • In order to perform any conversion, you need a conversion factor.
  • How does dimensional analysis work?
  • It will involve some easy math (Multiplication & Division)
  • Conversion factors are made from any two terms that describe the same or equivalent “amounts” of what we are interested in. For example, we know that: 1 inch = 2.54 centimeters 1 dozen = 12

Conversion Factors

  • In mathematics, the expression to the left of the equal sign is equal to the expression to the right. They are equal expressions.
  • So, conversion factors are nothing more than equalities or ratios that equal to each other. In “math-talk” they are equal to one. or
  • For Example 12 inches = 1 foot Written as an “equality” or “ratio” it looks like = 1 (^) = 1

Example Problem

  • How many feet are in 60 inches? Solve using dimensional analysis.
  • All dimensional analysis problems are set up the same way. They follow this same pattern: What units you have x What units you want = What units you want What units you have The number & units you start with The conversion factor (The equality that looks like a fraction) The units you want to end with
  • Remember 12 inches = 1 foot Written as an “equality” or “ratio” it looks like 60 inches

Example Problem #1 (cont)

  • You need a conversion factor. Something that will change inches into feet. What units you have x What units you want = What units you want What units you have x (^) = 5 feet (Mathematically all you do is: 60 x 1  12 = 5)

Dimensional Analysis

  • The hardest part about dimensional analysis is knowing which conversion factors to use.
  • Some are obvious, like 12 inches = 1 foot, while others are not. Like how many feet are in a mile.

Example Problem

  • You need to put gas in the car. Let's assume that gasoline costs $3.35 per gallon and you've got a twenty dollar bill. How many gallons of gas can you get with that twenty? Try it!
  • $ 20.00 1 gallon = 5.97 gallons $ 3. (Mathematically all you do is: 20 x 1  3.35 = 5.97)

Example Problem

  • There's another way to do the previous two problems. Instead of chopping it up into separate pieces, build it as one problem. Not all problems lend themselves to working them this way but many of them do. It's a nice, elegant way to minimize the number of calculations you have to do. Let's reintroduce the problem.
  • $ 20.00 1 gallon 24 miles = 143.28 miles $ 3.35 1 gallon

Example Problem #3 (cont)

  • You have a twenty dollar bill and you need to get gas for your car. If gas is $3.35 a gallon and your car gets 24 miles per gallon, how many miles will you be able to drive your car on twenty dollars? Try it! (Mathematically all you do is: 20 x 1  3.35 x 24  1 = 143.28 )

Example Problem #4 (cont)

  • $ 20.00 1 gallon 24 miles 1 day 1 week $ 3.35 1 gallon 7.1 miles 7 days = 2.88 weeks (Mathematically : 20 x 1  3.35 x 24  1 x 1  7.1 x 1  7 = 2.88 )