## View Poll Results: If 1 lbs of feathers and 1 lbs of bricks were taken to the top of a tall building, which would weigh

Voters
3. You may not vote on this poll
• Feathers weigh more

0 0%
• Bricks weigh more

0 0%
• Both weigh the same

3 100.00%

# Thread: Pound of feathers vs pound of bricks

1. With all the arguments about gravity, I thought this might be an interesting question to ask. Think about it for a while before answering.

(Mods, if you feel this should be in physics instead of math, feel free to move it. I put it here since I think the answer is going to require several integrals.)

2.

3. Depends how you define 1 lbs of something.

If you mean the quantity of feathers (or bricks) which weight exactly 1 lbs on the ground, in normal conditions, i.e. surrounded by air, then, once taken "upstairs", the feathers will weigh more than the bricks because they are greater in volume and so the loss of buoyancy in air is greater.

If you mean the quantity of feathers (or bricks) that has exactly the mass of 1 lbs, then feathers will consistently weigh less than bricks, because the buoyancy of feathers at any level is greater than that of the bricks. But the difference will be smaller on the roof than on the ground.

The proportion by which gravity is reduced due to moving away from the Earth is the same for both.

Note that, in any case, the differences will be so small they will be almost impossible to measure.

Hope this helps,
Leszek.

4. By 1 lbs of something, I did mean something that weighs 1 lbs at ground level, but I forgot about bouyancy. Still, even in a vacuum the answer isn't straight forward. (Though I agree than in anything near real world conditions, the difference is going to be almost unmeasurable.)

I wonder if I shouldn't reword the poll to include a vacuum, since it's complicated enough without worrying about bouyancy?

5. Originally Posted by MagiMaster
By 1 lbs of something, I did mean something that weighs 1 lbs at ground level, but I forgot about bouyancy. Still, even in a vacuum the answer isn't straight forward. (Though I agree than in anything near real world conditions, the difference is going to be almost unmeasurable.)

I wonder if I shouldn't reword the poll to include a vacuum, since it's complicated enough without worrying about bouyancy?
If it's in a vacuum, and no additional forces are involved besides gravity (no magnetism or electrostatic attraction/repulsion for example), then any two things that weigh the same on the ground will weigh the same on the roof.

The weight of an object is its mass times the local intensity of the gravitational field. That's it. The volume does not enter into the equation.

Or doesn't it? Not volume perhaps but height (size in the vertical direction). But mind you, I am picking very tiny nits now. Any physical body has some nonzero dimensions. Assuming your bag of feathers and your sack of bricks are the same shape, say spherical, the radius of the ball of feathers will be greater. The feathers which are closer to Earth will weigh more than those at the center, and those above it will weigh less. But these two differences will not balance each other out - the additional pull at the lower feathers will be greater than the reduction of weight experienced by the upper ones.

So a ball of feathers which weighs exactly (with unimaginable precision) 1 lbs on the ground will have less mass than a ball of bricks that weighs the same, given that a ball of bricks is more compact and thus less affected by the inhomogeneity of the gravity field.

On the roof, where the inhomogeneity is smaller and the size of each ball becomes "more negligible" compared to the (now greater) distance from the center of the Earth, the truth will prevail and the "pound" of feathers will be lighter.

Note: all this passage coloured in green is about differences in weight which are so subtle that I doubt any existing instruments could detect them. Way smaller than the buoyancy in the air of a pound of bricks.

Is it simple enough now? :P

6. Like Leszek, I think it's pretty simple - theyre the same. I don't know why an integral would be required, but maybe MagiMaster has something up his sleeve.

7. Actually, the trick is, it does depend on the shape of the object.

I did the math with a 1 cm x 1 cm x Y cm stick of various densities at various heights (sitting vertically), which all weighed 1 lbs (4.448 newtons) at the average equatorial radius. It turns out that the less dense stick weighs less (IIRC) at a higher altitude. Working out the full equation for the weight of a stick of a given height and density at altitude isn't easy. I haven't done the opposite shape, which would be a Y cm x Y cm x 1 cm sheet, but I expect I'd get the opposite result.

The equations showed a measurable difference in weight between a 1 g/cc and a 100 g/cc stick at 10 km. I also expect that cubes and spheres would show a lot less change. It'd be interesting to see what shape showed no change.

As best I could gather, feathers are 0.0025 g/cc and bricks are 1.84 g/cc. The most natural shape for the two would be a pile and a cuboid respectively, but since a pile isn't exactly amenable to a mathematical analysis, either individual feathers or a sphere or hemisphere would be better. If one were to grind through all the math for all that, I really have no idea what the analysis would show, other than that building aren't really tall enough to check this IRL.

Edit: Oh yeah, for anyone who cares, my math showed that a stick with a cross section of 1 cm x 1 cm would have to be cm tall. is the gravitational constant, is the mass of the earth, is the height from the center of the earth, is the density of the stick and is the weight of the stick. Be careful of units on that though. I converted all units to grams, centimeters and seconds before doing any math.

8. It's probably not legit to make assumptions about the shape of the quantity of feathers, or assume that the brick is not stood on end, etc.

Consider a pound mass of feathers woven into a flat rug, vs a one pound mass brick stood on one end.

9. True, but considering the particulars of the math I used, my results were just "it depends." The taller you make it, the more weight it loses as it's elevated.

10. I'm not convinced. So you are saying that if you have a pound of brick, it really doesn't weigh a pound. A bit contradictary, don't you think?

11. I'm saying that a pound of bricks at sea level doesn't weigh as much when elevated. I'm also saying that the shape of the object matters when determining how much its weight changes.

12. I'll acknowledge that weight changes with respect to elevation, but if the center of mass of two objects are at the same exact elevation, the shape should not matter I think. The gravitational pull on both objects should still be the same.

If you are saying that by elongating an object, you are dropping the center of mass towards or away from Earth, then yes, the gravitational pull changes, but not acording to the shape. The gravitational pull changes becase the center of mass changes.

13. Well, I didn't calculate it based on the center of mass. I calculated it based on the bottom. I'd have to go back and redo my math to see with effect that'd have.

14. I believe technically a pound is a unit of force, not mass (which is why a foot-pound is a unit of energy). So by definition a pound is the apparent weight that an object would actually register on a scale after any buoyancy issues etc.

 Bookmarks
##### Bookmarks
 Posting Permissions
 You may not post new threads You may not post replies You may not post attachments You may not edit your posts   BB code is On Smilies are On [IMG] code is On [VIDEO] code is On HTML code is Off Trackbacks are Off Pingbacks are Off Refbacks are On Terms of Use Agreement