How far above the surface of the earth would you have to be before your weight is reduced by 13.52%?
To find the altitude above the surface of the Earth where your weight is reduced by 13.52%, you need to understand the concept of gravitational force and its relationship with altitude.
First, let's establish the basic understanding that your weight on Earth is the force with which Earth's gravity pulls you towards its center. The weight can be calculated using the equation:
Weight = mass × acceleration due to gravity
Now, the acceleration due to gravity decreases as you move farther away from the Earth's surface. The relationship between the acceleration due to gravity (g) and altitude (h) can be defined by the formula:
g’ = g × (R / (R + h))^2
Where:
g' = the new value of the acceleration due to gravity at altitude h
g = the acceleration due to gravity at the Earth's surface (approximately 9.81 m/s^2)
R = the radius of the Earth (approximately 6,371 km)
Now, we can set up an equation using the weight reduction percentage:
Weight at altitude h = (1 - weight reduction percentage) × Weight on Earth
Using the weight equation, we can write:
(Weight on Earth) × (g / g') = (1 - weight reduction percentage) × (Weight on Earth)
Simplifying the equation:
g / g' = (1 - weight reduction percentage)
Now, plug in the values and solve for h (altitude):
9.81 m/s^2 / (g' m/s^2) = 1 - 0.1352
Solving for g':
g' = 9.81 m/s^2 / (1 - 0.1352)
Finally, to find the altitude (h) above the Earth's surface, we can use the formula for g' mentioned earlier:
h = (g' / g) × R - R
Substituting the values into the equation:
h = (9.81 m/s^2 / (1 - 0.1352)) / 9.81 m/s^2 × 6,371 km - 6,371 km
Calculating the equation will give you the altitude above the surface of the Earth where your weight is reduced by 13.52%.
I'm not a physics geek, but I did find a problem on google (use it!) that is close to yours. Use it as a template.
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