Answer to Question #259828 in Mechanical Engineering for Jool

Question

At 24° latitude, the gravitational acceleration as a function of elevation z above sea level is given by g=a-bz,

where a=9.807 m/s2 and b=3.32x10-6 s-2. Determine the height above sea where the weight of an object will decrease by 1 percent.

Answer 1

At a height above sea level, weight of object decreases by 1%

$\frac{g_o-g}{g_o}=\frac{1}{100}$

Given g=a-bz

At z=0, g_o=a-b(0)=a

g_o=9.807m/s²

$\frac{9.807-g}{9.807}=\frac{1}{100}=0.01$

9.807-g=0.01*9.807

9.807-g=0.09807

g=9.807-0.09807

=9.70893m/s²

g=a-bz

$z=\frac{a-g}{b}$

$=\frac{9.807-9.70893}{3.32*10^{-6}}$

=29539.156m