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Balloon Full of Mercury

1 pointrobocat6 comments

Does a solid metal object thrown into the air have net downwards force by the air (a negative buoyancy force?).

A Balloon full of Helium clearly has net positive buoyancy: the air pushes up on the balloon more than the balloon’s weight pushes down. A balloon full of air at room temperature is close to neutral buoyancy.

I am asking because the internet says the answer for the following Force Concept Inventory[1] question is B.

  An empty office chair is at rest on a floor. Consider the following forces:
  1. A downward force of gravity.
  2. An upward force exerted by the floor.
  3. A net downward force exerted by the air.

  Which of the forces is (are) acting on the office chair?
  (A) 1 only.
  (B) 1 and 2.
  (C) 2 and 3.
  (D) 1, 2, and 3.
  (E) none of the forces. (Since the chair is at rest there are no forces acting upon it.)

Disclosure: I have no investments in mercury commodity futures and I haven’t done physics for decades and I laugh at the various pronunciation discrepancies for the word buoyancy.

[1] part of talk about lecturing: https://youtube.com/watch?v=WwslBPj8GgI

Buoyant force is always up and equal to the weight of the displaced fluid (air here).

https://en.m.wikipedia.org/wiki/Buoyancy

That makes sense.

The error I am implicitly making is thinking in relative differences rather than absolute differences (an error I have made in the past about pressure differences because we are standing at the pressurised bottom of an ocean of air).

Buoyancy is always there in air just like in water. However the weight of most objects dominates the upwards buoyancy force.

I think the buoyancy force is equivalent to about 1.2 grams per litre of object volume. Or for a person ≈1.2 grams upwards force per kilogram of weight: you would weigh ≈1/1000th more if you were in a vacuum? We do slightly float in our atmosphere!

Interestingly, it needs to be accounted for when doing precise measurements: https://chem.libretexts.org/Bookshelves/Analytical_Chemistry...

Buoyancy is an effect of gravity. Gravity pulls down on the chair harder than on the air, that's why the chair sinks to the floor.

Since air is a fluid, it pushes equally hard on every square inch of the chair, including the ones facing upward (on the bottom). So I think that's why they would say there is no net force exerted by the air.

But that is technically slightly wrong, since there are small spots where the legs or wheels of the chair are touching the floor and not the air. So the net effect from the air would be just a little bit downward.

> Gravity pulls down on the chair harder than on the air

That is usually not the way to express what you mean? Drop a feather and a brick on the moon and they take the same time to fall because gravity pulls down on them the same amount. But yeah, the actual forces on a brick and feather are different.

There is a pressure gradient from the top of the atmosphere to the bottom. So voluminous objects have more pressure pushing up on the bottom of an object than they do pushing down from the top - causing buoyancy (assuming the object is mostly surrounded by air). The buoyancy in this case is offset by gravity pulling down on the mass of the chair.

I think the question is a kind of trick question because it ignores buoyancy as a force, but the forces definitely exist. There is definitely a downward force by the air column above the chair, and there is definitely an upward force by the air below the chair (and also on the sides, but that nets out equally). 101kPa is significant!

The trick is that I think technically “A net downward force exerted by the air” on the chair exists as a negative number. But the question is not asking as though a physicist is answering precisely, even though it is asking precise questions about forces in physics. Annoying question with a trick - the worst kind - the kind of test question where you have to answer it “correctly”, not correctly.

Any of the above could be wrong or poorly explained, but that is what I think after reading the comments and thinking about it a little more.

minus 3. A net upward force exerted by the air.

The answer B includes forces 1 and 2, but not force 3.

The extended answer is 1, 2 and minus 3 (that is a fake item I just added here).

I think your intuition is right, but you are misinterpreting what B means.

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