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balandron [24]
4 years ago
15

Coughing forces the trachea to contract, which affects the velocity v of the air passing through the trachea. Suppose the veloci

ty of the air during coughing is v = k(R-r)r2 where k and R are constants, R is the normal radius of the trachea, and r is the radius during coughing. What radius will produce the maximum air velocity?
Physics
1 answer:
Katyanochek1 [597]4 years ago
7 0
The normal radius of the trachea does not change so you can view R as a constant as well. 


Find v ' and solve v ' = 0. 

v ' = k(R-r)(2r) + k(-1)(r^2) 

v ' = 2rk(R-r) + -kr^2 

v ' = 2rkR - 2kr^2 - kr^2 

v ' = 2rkR - 3kr^2 


Set v ' = 0 and solve for r. 


0 = 2rkR - 3kr^2 

0 = rk(2R - 3r) 

rk = 0 or 2R - 3r = 0 

r = 0 or 2R = 3r 

r = 0 or r = 2R/3 


Plug 0 and 2R/3 for the orginal v and the larger value is the maximum. 


If r = 0, then v = k(R - 0)(0^2) = 0 

If r = 2R/3, then v = k(R - 2R/3)(2R/3)^2 


v = k(R/3)(4R^2 / 9) 

v = 4kR^3 / 27 


<span>Therefore, the radius of 2R/3 will produce the maximum air velocity of 4kR^3 / 27.</span>
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Answer:

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3 years ago
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a)  Total mass form, density and axis of rotation location are  True

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From these two equations we can see that the moment of inertia depends on mass, density and distance

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Explanation:

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From the question given above, the following data were obtained:

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