An industrial-strength fan creates the wind pattern indicated in this diagram. S
ID: 1523986 • Letter: A
Question
An industrial-strength fan creates the wind pattern indicated in this diagram. Someone holds a small kite at point A. Then the person holds a larger kite at that same point. In both cases, the kite directly faces the fan and therefore catches the wind.
1. In what sense is the wind stronger on the large kite than it is on the small kite?
2. In what sense is the wind equally strong at both kites?
3. A student says, The wind itself is equally strong at point A no matter which kite you hold there—or even if you don’t hold a kite there. The large kite feels more force than the small kite because it has more area and therefore catches more wind, not because the wind itself is stronger. Does this student agree with the answers you just gave? If not, do you think the student makes good points? In what ways do you disagree?
4. The smaller kite has cross-sectional area 0.50 m2. When held at point A, it feels a wind force of 3.0 N. The larger kite has exactly twice the cross-sectional area (1.0 m2) of the smaller kite. What wind force would you expect the larger kite to feel at point A? Explain.
5. Now a kite of cross-sectional area 2.0 m2 is held at point A. What wind force do you expect it to feel? Why?
6. Here’s the punch line. Each of the three kites from question (4) and (5) feels a different wind force at point A. But they should each feel the same wind field because the wind itself is the same at point A no matter which kite you hold there. Is there some number having to do with wind force and cross-sectional area that’s the same for all three kites and could therefore work as a definition of wind field? This is hard; try it for a while, and if you get stuck, move on to the next question.
7. Here are two proposed definitions of wind field: (i) wind field = wind force × cross-sectional area, or (ii) wind field = wind force ÷ cross-sectional area. Which of those definitions, if either, better captures the intuitive sense of what wind field is supposed to mean?
8. Let’s think more about the “better” definition of wind field from question (7). What are the units of that number?
9. Does the wind force depend on the fan, the kite, or both? What about the wind field? Briefly explain.
AExplanation / Answer
1.
The wind is stronger on larger kite in the sense that it strikes larger area in the care of larger kite as compared to smaller kite
2
the wind is equally strong at point A in the sense that the pressure applied is same at point A .
3.
yes the student agries with the answer
4.
Plarge = Psmall
Flarge/Alarge = Fsmall/Asmall
3/0.5 = Fsmall/1
Fsmall = 6
5.
F = 6/2= 3 N