[Physics/Applied maths] Centre of mass (calculus, continuous mass distribution - physics of continuous matter lautrup pdf
The question is, any help would be very grateful, I am a part of the answer, but I'm not sure how to proceed:
The air density at height z above the Earth's surface is proportional to e ^ (-Z), where a is a constant greater than zero.
Find the center of mass of the infinite cylinder of air on a small flat on the surface of the earth .....
I know that the center of mass by a member of (DMZ / M), where z is the height and POS dm = where p is the density exists, and dv = pi (r ^ 2) dz
I joined the expression relating z to the height, but I think I support made mistakes, and a step in the integration process and the resulting expression would be a great help to you!
Physics Of Continuous Matter Lautrup Pdf [Physics/Applied Maths] Centre Of Mass (calculus, Continuous Mass Distribution
1 comments:
♠ density with height is D (z) = D0 * exp (-AZ), we find the center of mass z0 column of air above the surface of the earth, as the case for example, T1 = T2,
T1 = ∫ D0 * exp (-z) * (z0-z) * dz (z = 0 to z0); some background;
D0 * T2 = ∫ exp (-z) * (z-z0) * dz (z = z0) to infinity, is a pair from the top of the column in a unit square base;
Thus, T = T1-T2 = ∫ exp (-z) * (z0-z) * dz (z = 0 to ∞) = 0;
♣ ∫ exp (-Z) * z0 * dz = (-z0 / a) exp (-z) (z = 0 to ∞) = z0 / a;
♣ ∫ exp (-Z) * z * dz = () = Split
= (-Z / A) * exp (-z) + (-1 / a ^ 2) * exp (-) z) (z = 0 = ∞
= 1 / a ^ 2;
T = z0 / a -1 / a ^ 2 = 0, ie, z0 = 1 / a QED;;
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