The Science of Physics Chapter 1: Factor-Label and Dimensional Analysis

The Science of Physics

The Science of PhysicsChapter 1: Factor-Label and Dimensional Analysis

Factor Label MethodWhy unit conversions?Want all numbers to have like units before performing calculationsMay want to represent number differently

Factor Label MethodNeed conversion factorConversion factor is equal to 1 so doesnt change amount of what you have

Example: convert 32 inches to feetConversion factor: 1 foot = 12 inches or 1 ft/12 inConvert 32 inches x (1 ft/12 inches) = 2.7 ftNot 3 ft and not 2.6667 ft !

Factor Label Practice Handout

Dimensional AnalysisDimensional Analysis is a tool to see if youve set up your equation correctly.For instance, say you want to know how long it will take you to travel to Iowa City which is about 75 miles away and you know you will be travelling at an average speed of 50 miles per hour.

How to solve problem using dimensional analysis1. Identify equation to use:D= s x tD= distance travelled, milesS = speed, miles per hourt = time travelled, hours2. Rearrange equation such that unknown is isolated on one side:

t = D/s3. Substitute values with units and solve:

t = 75 miles/ (50 miles/hour) = 75 miles x (hour/50 miles) = 1.5 hours

How to solve problem using dimensional analysisoops!1. Identify equation to use:D= s x tD= distance travelled, milesS = speed, miles per hourt = time travelled, hours2. Rearrange equation such that unknown is isolated on one side:

t = D x s3. Substitute values with units and solve:

t = 75 miles x (50 miles/hour) = 3750 miles2/hour