Why is my weight at 2600 meters of altitude 10 pounds less that at sea level?

Question

I recently visited Bogota located at 2,600 meters above sea level and after checking my weight in several scales I found that I weighed 10 pounds less than my normal weight. Is there a reason why that is so?

Answer 1

Don't know...10 lbs less sounds high if was simply due to the increased distance between you, m, and the center of the Earth's mass M.

Your sea level weight W = mg = GmM/r^2; where r is the distance between you and the center of Earth's mass M. So if R > r; where r is sea level and R is you at 2,600 meters above sea level, you can easily see that w = GmM/R^2 < GmM/r^2 = W

That is, because you are a bit farther away from the Earth's center of mass, your weight on the mountain top should be less than your "normal" weight at sea level. You can go on the web and find M, G, and r. And you can calculate your m = W/g; where W is your normal weight and g = 32.2 ft/sec^2.

When you find r, you find R = r + 2,600 meters. Work the numbers to find w according to w = GmM/R^2 to see how much less w < W is. It will be less, but I'm guessing not ten pounds less than your normal weight.

Answer 2

This is explained by basic physics. When you are at sea level you are x meters above the center of the earth spinning in a circle. When you are in Bogota you are x+2600 meters above the center of the earth and you are spinning at the same speed as at sea level. Since you are farther our from the center of the earth you are traveling faster than you were when you were at sea level. This speed counteracts gravity a small amount, this combined with gravity being a very tiny amount weaker at higher altitudes makes you 10 lbs. lighter.

Answer 3

Weight is indicated as a force measured in units of newtons.
What we measure on a scale is really a mass measurement either in pounds or kilograms units.
When you say you were 10 pounds less than at sea level ,you are stating that you have lost ten pounds of mass. It is impossible, you cannot lose by climbing in an airplane one and a half miles up and lose 10 pounds of body of mass. Unless you ate too much and could not hold it.

Answer 4

My best guess is that you lost some weight during your trip, or you did not have an accurate scale (either at the start of the trip to measure your baseline or during the trip to measure the 10 lb loss).

Since your measuring in lbs, and the Colombian scales are no doubt calibrated in kgs, are you sure you're performing the conversion correctly? (1 kg = 2.2 lbs)

Answer 5

The force of gravity goes down like one over r^2 (F = GMm/r^2), but that shouldn't make as big a difference as ten pounds, since the radius of the earth is so large to begin with compared to a change of 2.6 km. Maybe you were dehydrated.

PS: The centripetal force goes up like r (F = omega^2 r), but that's small to begin with compared to your weight, so it isn't going to make that kind of difference either.

Answer 6

I can't understand this question. Presumably "ride" is a misprint for "rise". But even so, it doesn't make sense. "If every rise 100 meters" doesn't mean anything. And what is "it" in the last sentence? I get the impression that you have tried to shorten the question to save time, and have mangled it in the process. If you really want help with this I suggest you start again, and this time type out the question exactly as you have it in front of you.

Answer 7

Because Colombians have their scales fixed.
Bogota is the nest of mafia.

Answer 8

Because the acceleration of gravity, g, is smaller at that altitude. It decreases as you increase your height above the surface.