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Earth's atmospheric pressure is produced by the mass of the air in the atmosphere, most of which exists in the lowest 50km of the atmosphere. Earth's atmosphere at ground level produces a pressure of 101000Pa. You want to test a hypothesis that the density of air decreases exponentially to 0.1% of the sea level value by 48.6km altitude. Thus, the density would be parametrized as p(z) = Poe-z/a, where z is the altitude, and a is a decay constant. The total mass of the atmosphere above a rectangle of area A can be solved via: m = pAdz Zi If considering the entire atmosphere, then, the integration bounds are 0 to oo: 00 -z/adz | Apoe m = What is the value of a in the parametrization? km What is the force produced on a 1m2 area the atmosphere? N Assuming that the gravitational constant, g = 9.8m/s², does not change appreciably with altitude, what is the total mass of air that produces this pressure? (Note: By the time g has changed much, there is hardly any air density anyways, so it is a reasonable approximation to make for these purposes.) kg

Earth's atmospheric pressure is produced by the mass of the air in the atmosphere, most of which exists in the lowest 50km of the atmosphere. Earth's atmosphere at ground level produces a pressure of 101000Pa. You want to test a hypothesis that the density of air decreases exponentially to 0.1% of the sea level value by 48.6km altitude. Thus, the density would be parametrized as p(z) = Poe-z/a, where z is the altitude, and a is a decay constant. The total mass of the atmosphere above a rectangle of area A can be solved via: m = pAdz Zi If considering the entire atmosphere, then, the integration bounds are 0 to oo: 00 -z/adz | Apoe m = What is the value of a in the parametrization? km What is the force produced on a 1m2 area the atmosphere? N Assuming that the gravitational constant, g = 9.8m/s², does not change appreciably with altitude, what is the total mass of air that produces this pressure? (Note: By the time g has changed much, there is hardly any air density anyways, so it is a reasonable approximation to make for these purposes.) kg

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Earth's atmospheric pressure is produced by the mass of the air in the atmosphere, most of which exists in the lowest 50km of the atmosphere. Earth's atmosphere at ground level produces a pressure of 101000PA. You want to test a hypothesis that the density of air decreases exponentially to 0.1% of the sea level value by 48.6km altitude. Thus, the density would be parametrized as p(z) = Poe¯z/a, where z is the altitude, and a is a decay constant. The total mass of the atmosphere above a rectangle of area A can be solved via: zf т — pAdz If considering the entire atmosphere, then, the integration bounds are 0 to oo: =| Ap,e=/ªdz What is the value of a in the parametrization? km What is the force produced on a 1m² area by the atmosphere? Assuming that the gravitational constant, g = 9.8m/s², does not change appreciably with altitude, what is the total mass of air that produces this pressure? (Note: By the time g has changed much, there is hardly any air density anyways, so it is a reasonable approximation to make for these purposes.) kg What is the value of p, in the parametrization? kg/m³
Transcribed Image Text:Earth's atmospheric pressure is produced by the mass of the air in the atmosphere, most of which exists in the lowest 50km of the atmosphere. Earth's atmosphere at ground level produces a pressure of 101000PA. You want to test a hypothesis that the density of air decreases exponentially to 0.1% of the sea level value by 48.6km altitude. Thus, the density would be parametrized as p(z) = Poe¯z/a, where z is the altitude, and a is a decay constant. The total mass of the atmosphere above a rectangle of area A can be solved via: zf т — pAdz If considering the entire atmosphere, then, the integration bounds are 0 to oo: =| Ap,e=/ªdz What is the value of a in the parametrization? km What is the force produced on a 1m² area by the atmosphere? Assuming that the gravitational constant, g = 9.8m/s², does not change appreciably with altitude, what is the total mass of air that produces this pressure? (Note: By the time g has changed much, there is hardly any air density anyways, so it is a reasonable approximation to make for these purposes.) kg What is the value of p, in the parametrization? kg/m³
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