How does an object's shape relate to its size? What does physics have to say about the problems objects encounter as they are scaled larger or smaller?
THE PHYSICS OF SCALING
There is a great deal of geometry involved...
A. First you should observe the surface of the small cube above. It takes 6 squares to create the closed cube. What is the area of one side of the cube? (Place the mouse over the numbers to see the answer.)
B. What is the total surface area of this cube? Remember that there are 6 sides. (Place the mouse over the numbers to see the answer,)
C. What is the volume of the cube? V = length x width x height (Place the mouse over the numbers to see the answer.)
D. What is the new surface area when each side is doubled (multiplied by 2)? (Place the mouse over the numbers to see the answer.)
E. What is the new volume when each side is doubled? (Place the mouse over the numbers to see the answer.)
F. When the each side doubles then the surface area is multiplied by __? ( Place the mouse over the numbers to see the answer.)
G. When the side doubles then the volume is multiplied by what number? ( Place the mouse over the numbers to see the answer.)
AS YOU SEE, THE VOLUME INCREASES MUCH MORE RAPIDLY THAN THE SURFACE AREA WHEN AN OBJECT IS SCALED LARGE R!
1. The mass of an object and therefore its weight.
2. The heat produced by the body--it's all in your "guts"!
1. The way your body cools off--your skin's surface area does this task.
2. The air resistance or drag as an object moves through the air or water. That's why a parachute slows down when open but falls rapidly when packed up.
3. Surface tension with water is based on the surface area touching the water. A razor blade will float lying flat on the water but sink when the sharp edge is dropped in first.
4. The strength of the bones of a skeleton depends on the cross sectional area of the bones.
VOLUME AFFECTS THE FOLLOWING:
SURFACE AREA AFFECTS THE FOLLOWING
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