if I weigh 141.2lbs at sea level what will I weigh 29,000ft above sea level

Guest Feb 19, 2015

#1**+5 **

**If I weigh 141.2lbs at sea level what will I weigh 29,000ft above sea level ?**

29000 ft = 8839.2 m

**Only Free-air correction:**

Accounts for the 1/r^2 decrease in gravity with the distance from the center of the Earth:

$$g_1=\boxed{g_{(\text{ see level })}=\dfrac{GM_E}{R_E^2}}$$

and in 8839.2 m

$$g_2=\boxed{g_{(\ 29000\ ft \text{ above sea level})}=\dfrac{GM_E}{( R_E +8.8392\ km )^2}}$$

$$F_2 = F_1\cdot \dfrac{g_2}{g_1}\cdot \dfrac{\not{m}}{\not{m}}$$

$$\small{\text{

$

F_2 = F_1\cdot \dfrac{R_E^2} {( R_E +8.8392\ km )^2}

=F_1\cdot \dfrac{6371^2} {( 6371 +8.8392\ km )^2}=F_1\cdot 0.99723094065

$

}}$$

So we have 141.2lbs * 0.99723094065 = 140.809008820 lbs

heureka
Feb 19, 2015

#1**+5 **

Best Answer

**If I weigh 141.2lbs at sea level what will I weigh 29,000ft above sea level ?**

29000 ft = 8839.2 m

**Only Free-air correction:**

Accounts for the 1/r^2 decrease in gravity with the distance from the center of the Earth:

$$g_1=\boxed{g_{(\text{ see level })}=\dfrac{GM_E}{R_E^2}}$$

and in 8839.2 m

$$g_2=\boxed{g_{(\ 29000\ ft \text{ above sea level})}=\dfrac{GM_E}{( R_E +8.8392\ km )^2}}$$

$$F_2 = F_1\cdot \dfrac{g_2}{g_1}\cdot \dfrac{\not{m}}{\not{m}}$$

$$\small{\text{

$

F_2 = F_1\cdot \dfrac{R_E^2} {( R_E +8.8392\ km )^2}

=F_1\cdot \dfrac{6371^2} {( 6371 +8.8392\ km )^2}=F_1\cdot 0.99723094065

$

}}$$

So we have 141.2lbs * 0.99723094065 = 140.809008820 lbs

heureka
Feb 19, 2015