Dimensional Analysis

Goals

• Use dimensional analysis to solve conversion problems.

Examples

1. 38, page 466

   I have 105 miles
   I want km.
   
   1.6 km = 1 mile,
   
                 1.6 km
   105 miles x ---------  = 105*1.6 km = 168km
                 1 mile
      

2. 42, page 466

   I have 80 kph
   I want mph
   
   80 km     1 mile      80  miles
   ------  x  ------ =  ---  -----  =  50 mph
   1 hour    1.6 km     1.6  hour
      

3. 44, page 466

   I have gal
   I want kl
   
   1 gal = 3.8 l
   1 kl = 1000 l
   
                3.8 l    1 kl     12,500 x 3.8 kl
   12,500 gal x ----- x ------ = ----------------- = 47.5 kl
                1 gal   1000 l         1000
   

4. 46, page 466

   I have mi2
   I want km2
                 1.6 km   1.6 km     
     1189 mi2 x ------- x ------  =  1189x 1.6 x 1.6 km2 = 3043.84 km2
                   mi      mi 
    

Homework