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Calculate the net force on your 0.50-cm2 eardrum that air exerts on the inside and the outside after you drive from Denver, Colorado (elevation 1609 m) to the top of Pikes Peak (elevation 4301 m). Assume that the air pressure inside and out are balanced when you leave Denver, the pressure inside the eardrum does not change, and that the density of the air is constant and is equal to 0.80 kg/m3.

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Answer:

1.0563408 N

Explanation:

[tex]\rho[/tex] = Density of air = 0.8 kg/m³

g = Acceleration due to gravity = 9.81 m/s²

h = Altitude

A = Area = 0.5 cm²

Pressure

[tex]p=\rho gh\\\Rightarrow p=0.8\times 9.81\times (4301-1609)\\\Rightarrow p=21126.816\ Pa[/tex]

Pressure

[tex]p=\frac{F}{A}\\\Rightarrow F=pa\\\Rightarrow F=21126.816\times 0.5\times 10^{-4}\\\Rightarrow F=1.0563408\ N[/tex]

The net force on your ear is 1.0563408 N

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