Transcript ProportionA

Proportion
Proportion
• When I was growing up
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Little girls played with dolls
1959 !
Barbie
Proportion
Head to height
– Baby
1:3
– Adult woman 1:7
Head Height
Adult
9"
63"
Barbie 2"
14"
• A Proportion
Equal Ratios
Prob Set 1Q
It’s about the Relationship
The Stretch is Proportional to the Force
• The greater the force, the greater
the stretch
• Force ~ Stretch
A Particular Measurement
F1 = k ∙ x1
• F ~ x
F1/x1 = k
• F = k∙x
• F1/x1 = k = F2/x2 A Different Measurement
F2 = k ∙ x2
• F1/x1 = F2/x2
F2/x2 = k
Blue is to pale blue as
• x2/x1 = F2/F1
red is to __________
• x2 is to x1 as F2 is to F1
We can use Any Units
F1/x1 = F2/x2
Prob Set 14B
20 pounds is to 4 inches as 10 pounds is to 2 inches
20 lbs : 4" :: 10 lbs : 2"
20 lbs is to 10 lbs as 4 inches is to 2 inches
20 lbs : 10 lbs = 4" : 2"
= 2 pure number
Pressure and Volume are
Inversely Related
• When the volume goes down,
the pressure goes up
• Pressure is inversely
proportional to volume
• P ~ 1/V
Direct: F1/x1 = F2/x2
• P=k/V
Inverse: P1V1 = P2V2
• P1V1 = k = P2V2
Prob Set 14G
• P1V1 = P2V2
A Scale Drawing is in Proportion
4" x 10"
Both Ratios are
2:5
6" x 15"