1. Proportion

2. Galileo Was unable to measure the acceleration of gravity accurately. a = g = 9.80 m/s² Discovered Change in velocity is proportional to the time elapsed. Δv ~ t

3. Proportion When I was growing up Little girls played with dolls 1959 ! Barbie Proportion Head to height – Baby 1:3 – Adult woman 1:7 A Proportion Equal Ratios Head Height Adult 9" 63" Barbie 2" 14" Prob Set 1Q

4. It’s about the Relationship The greater the force, the greater the stretch Force ~ Stretch F ~ x or F α x F = k ∙ x F 1 /x 1 = k = F 2 /x 2 F 1 /x 1 = F 2 /x 2 x 2 /x 1 = F 2 /F 1 x 2 is to x 1 as F 2 is to F 1 Blue is to pale blue as red is to __________ The Stretch is Proportional to the Force

5. We can use Any Units F 1 /x 1 = F 2 /x 2 20 pounds is to 4 inches as 10 pounds is to 2 inches 20 lbs : 4" :: 10 lbs : 2" F 2 /F 1 = x 2 /x 1 20 lbs is to 10 lbs as 4 inches is to 2 inches 20 lbs : 10 lbs = 4" : 2“ = 2 pure number Prob Set 14B

6. Pressure and Volume are Inversely Related When the volume goes down, the pressure goes up Pressure is inversely proportional to volume P ~ 1 / V P = k / V P 1 V 1 = k = P 2 V 2 P 1 V 1 = P 2 V 2 P 1 /P 2 = V 2 /V 1 Direct: F 1 /x 1 = F 2 /x 2 Inverse: P 1 V 1 = P 2 V 2 or: P 1 /P 2 = V 2 /V 1 Prob Set 14G

7. A Scale Drawing is in Proportion 4" x 10" 6" x 15" Both Ratios are 2 : 5