Weight at different elevations in a tall building

In summary, the person would weigh 48.8 kg on the roof of a building 6400 km high, rather than 200 pounds on the floor.
  • #1
elissadi
10
0
I have done most of the work on the problem written below, but the more I look at it, the more I am not sure whether I should leave the pounds as they are instead of converting them to kilograms. If I leave it as 200 lbs, are the number plug-ins going to be wrong?
I am using the formula
g = 6.67x10^-11 x 6 x 10^24 / (2 x 6.40 x 10^3)^2 = 2.44 m/s^2 then W=mg which I have calculated at 20 x 2.44 = 48.8 N
A building is 6400 km high. On the bottom floor a person weighs 200 pounds when stepping on a spring scale. How much would the person weigh on the same scale if she were standing on the top floor?
I know that 6400 km is also the radius of the Earth so that the top floor is 2R from the Earth's center.

thanks!
 
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  • #2
If you are going to "plug in" numbers in a formula like W = mg, then you surely better use mass and not weight!

But for this problem you should be able to get the answer using ratios without plugging any numbers in. By what factor does the gravitational force change when the object goes from 1R to 2R?
 
  • #3
so, I should divide 200/9.8m/s^2 to get the mass which would be 20 kgs. Or should I convert 200 lbs to kilograms first?
 
  • #4
Let F represent the weight of the person on the floor
Let F' represent his weight on the roof
Let m represent his mass
Let M represent the Earth's mass
Let R represent the Earth's radius
Let G represent the gravitational constant

F = GmM/R²
F' = GmM/(2R)²

you have 2 equations and 2 unknowns (F' and m). Don't touch any numbers. Do the algebraic manipulations first, then plug in F = 200 lbs (you will never need to touch the numbers like G, M, or R -- although you did need to know that 6400 km = R -- nor will you need to convert any units). So what answer are you getting?
 
  • #5
elissadi said:
so, I should divide 200/9.8m/s^2 to get the mass which would be 20 kgs. Or should I convert 200 lbs to kilograms first?
You should convert the 200 lb to kilograms first.

You could divide 200 lb by 32 f/s to convert to mass in slugs, but you'd still be in the wrong units. You'd then have to convert slugs to kilograms. Pounds, feet, and slugs are measurements in the 'English' system and kilograms, meters, and Newtons are in the 'metric' system.

What the others are trying to tell you is that, in this particular problem, there's a better way to solve the problem than just plugging numbers into a memorized formula.
 
  • #6
AKG said:
Let F represent the weight of the person on the floor
Let F' represent his weight on the roof
Let m represent his mass
Let M represent the Earth's mass
Let R represent the Earth's radius
Let G represent the gravitational constant

F = GmM/R²
F' = GmM/(2R)²

you have 2 equations and 2 unknowns (F' and m). Don't touch any numbers. Do the algebraic manipulations first, then plug in F = 200 lbs (you will never need to touch the numbers like G, M, or R -- although you did need to know that 6400 km = R -- nor will you need to convert any units). So what answer are you getting?
I like this advice! Nice approach. You know that the force of gravity is not directly proportional to the distance between the objects. Rather it is...some other proportion :tongue:
 
  • #7
Thank you all! I think all this advice will help greatly! I will work on this when I get back from class :)
 

What is the effect of elevation on weight in a tall building?

The effect of elevation on weight in a tall building is minimal. While gravity is slightly weaker at higher elevations, the difference is so small that it does not significantly impact the weight of objects or people.

Why do people feel lighter at higher elevations in a tall building?

People may feel lighter at higher elevations in a tall building because there is less air pushing down on them. At higher elevations, there is less air pressure, which can make people feel like they are floating or lighter on their feet.

Does the weight of an object change as you move up or down in a tall building?

No, the weight of an object does not change as you move up or down in a tall building. The weight of an object is determined by its mass and the force of gravity, which remains constant throughout the building.

How does weight change in a tall building with multiple elevations?

The weight of an object will not change as you move between different elevations in a tall building. However, the perceived weight may change due to changes in air pressure or the tilt of the building.

Is there a difference in weight between the top and bottom floors of a tall building?

There is no significant difference in weight between the top and bottom floors of a tall building. While there may be slight variations due to air pressure and the tilt of the building, the difference is negligible and would not be noticeable to most people.

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