Dimensional Analysis In dimensional analysis always ask three

Dimensional Analysis In dimensional analysis always ask three questions: • What data are we given? • What quantity do we need? • What conversion factors are available to take us from what we are given to what we need? Chapter 1 1

Dimensional Analysis Method of calculation using a conversion factor. * ALWAYS place the #1 in front of the largest unit. ! Chapter 1 2

Dimensional Analysis Example: We want to convert the distance 8 in. to feet. (12 in = 1 ft) Chapter 1 3

Dimensional Analysis Example: We want to convert the distance 8 in. to feet. (12 in = 1 ft) Chapter 1 4

Dimensional Analysis Convert the quantity from 2. 3 x 10 -8 cm to nanometers (nm) First we will need to determine the conversion factors Centimeter (cm) Meter (m) Nanometer (nm) Or 100 cm = 1 m 109 nm = 1 m Chapter 1 5

Dimensional Analysis Convert the quantity from 2. 3 x 10 -8 cm to nanometers (nm) 100 cm =1 m 1 x 109 nm = 1 m Now, we need to setup the equation where the cm cancels and nm is left. Chapter 1 6

Dimensional Analysis Convert the quantity from 2. 3 x 10 -8 cm to nanometers (nm) 1 cm = 0. 01 m 1 x 10 -9 m = 1 nm Now, fill-in the value that corresponds with the unit and solve the equation. Chapter 1 7

Dimensional Analysis Convert the quantity from 2. 3 x 10 -8 cm to nanometers (nm) Chapter 1 8

Dimensional Analysis Convert the quantity from 31, 820 mi 2 cm to square meters (m 2) First we will need to determine the conversion factors Mile (mi) Meter (m) kilometer (km) Or 1 mile = 1. 6 km 1000 m = 1 km Chapter 1 9

Dimensional Analysis Convert the quantity from 31, 820 mi 2 cm to square meters (m 2) Now, we need to setup the equation where the cm cancels and nm is left. 1 mile = 1. 6 km 1000 m = 1 km Chapter 1 10

Dimensional Analysis Convert the quantity from 31, 820 mi 2 cm to square meters (m 2) Now, we need to setup the equation where the cm cancels and nm is left. 1 mile = 1. 6 km 1000 m = 1 km Notice, that the units do not cancel, each conversion factor must be “squared”. Chapter 1 11

Dimensional Analysis Convert the quantity from 31, 820 mi 2 cm to square meters (m 2) Chapter 1 12

Dimensional Analysis Convert the quantity from 31, 820 mi 2 cm to square meters (m 2) Chapter 1 13

Dimensional Analysis Convert the quantity from 31, 820 mi 2 cm to square meters (m 2) Chapter 1 14

Dimensional Analysis Convert the quantity from 14 m/s cm to miles per hour (mi/hr). Determine the conversion factors Meter (m) Kilometer (km) Kilometer(km) Mile(mi) Seconds (s) Minutes (min) Minutes(min) Hours (hr) Or 1 mile = 1. 6 km 1000 m = 1 km 60 sec = 1 min 60 min = 1 hr Chapter 1 15

Dimensional Analysis Convert the quantity from 14 m/s cm to miles per hour (mi/hr). 1 mile = 1. 6093 km 1000 m = 1 km 60 sec = 1 min 60 min = 1 hr Chapter 1 16

Dimensional Analysis Convert the quantity from 14 m/s cm to miles per hour (mi/hr). 1 mile = 1. 6 km 60 sec = 1 min Chapter 1 1000 m = 1 km 60 min = 1 hr 17

Dimensional Analysis Convert the quantity from 14 m/s cm to miles per hour (mi/hr). 1 mile = 1. 6093 km 1000 m = 1 km 60 sec = 1 min 60 min = 1 hr Chapter 1 18