# How big is 1 kg of feathers

## What is actually heavier, a kilogram of lead or a kilogram of feathers?

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by Klaus Kohl

Who doesn't know this joke question?
Intuitively one wants to say 'the lead' and yet knows that it is a joke question, both are equally difficult.
You know it, but is it also true?

Martin Wagenschein would have turned 100 on December 3, 1996; he died eight years ago. Honorary doctor, multiple award winner, he was and is revered, interpreted, misunderstood, insulted.
For decades he fought well into old age to make mathematics and physics lessons more understandable, to clear out bogus knowledge: "Understanding what is understandable is a human right" - "Teaching understanding" - "Save the phenomena" were often the title and content of his numerous lectures and publications. In his teacher training seminars, he worked on individual topics, such as the hexagonal construction in a circle, the spherical shape of the earth, sucking in lemonade in a straw, from the apparently self-evident habit to the question, yes to the tricky problem and then to his own self- to lead certain knowledge. He has mostly marked his pedagogical guidelines with the keywords genetic-Socratic-exemplary.

The following "miniature" happened - I can only call it that - at the Ecole d'Humanité in Goldern (Switzerland) with a group of five students (15-16 years old). With its question-and-answer game, I deliberately kept it in the teasing question form of the Socrates described by Plato (e.g. Meno - an ignorant slave recognizes the method of doubling the square; one of the favorite subjects of Wagenschein from an early age).
Nevertheless, it is not a "car license piece". Firstly, this sophistic question was not an issue for him; secondly, as a teacher, he would have spoken much less (!). It may serve as a later thank you from one of his guest students.

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M. What is actually heavier, a kilogram of lead or a kilogram of feathers?

Student: A kilo is a kilo!

L: That's right.

S: The springs just need more space.

L: Yes, that is also true.

L: Yes, but that's not what I mean. Does it weigh the same, does it weigh the same?

S: Try it out!

L: How?

S: We take 1 kilo of lead and 1 kilo of feathers ... (?) ----

L: ---

S: (pillow fights in thoughts, creative chaos that sinks into silence)

L: Let's make it a little more manageable, let's use wood instead of feathers. Is a kilo of lead as heavy as a kilo of wood? (He is as free, like the students, to occasionally say kilos instead of kilograms.)

S: Logo!

L: And a kilo of lead as heavy as a kilogram of stone?

S: Yes of course.

L: Try it out!

- He has got himself a stone and a block of lead with practically the same mass, - that both have only about 1 kg of mass is irrelevant - and places them on the scale opposite. -

S: See you!

L: Take them in your hand, are they equally heavy?

S: Yeah.

L: And now dip both hands in the water - are they equally heavy?

S: No, now the stone is lighter than the lead.

L: You see!

S: Yes, in the water, it's different. - Wood weighs nothing in the water, it even goes up. Like a balloon!

L: why?

S: Because it's lighter than water.

L: And the stone?

S: It is heavier than water, and lead is even heavier.

L: Remember, it's a kilogram of everything.

S: But they are of different sizes. - The density is different. - The buoyancy makes the stone and the wood lighter. - The lead too, but very little.

L: And outside?

S: There is no lift.

L: And the balloon?

S: Oh ...

L: If I inflate a balloon, or rather an empty plastic bag, with air, does it get heavier?

S: No.

L: Is there more in the full plastic bag than in the empty one?

S: (laughter)

L: So does the full plastic bag have a larger mass than the empty one?

S: Yes, a few grams. - But you can't weigh that. - Yes, where there is no air. - Water weighs nothing in water either. - Then the bag bursts! (What is meant is the air-filled bag in a vacuum).

L: Which is heavier, a gram of lead or a gram of air?

S: The air doesn't weigh anything.

L: What is heavier, 10 grams of lead or 10 grams of styrofoam?

S: Is there air in the styrofoam? - Yes. - I do not know. - Does not matter.

L: Why don't you care?

S: The air doesn't weigh anything. - How are you going to weigh the styrofoam correctly? - Without air. - How are you going to let the air out? - No, I mean in a vacuum. - Don't you chase them away then?

L: Try it out!

- A styrofoam ball with a diameter of approx. 10 cm is placed under the bell jar of the air pump. Then the glass is evacuated and the secretly anticipated catastrophe does not materialize. -

S: Can you weigh it?

L: In a vacuum?

S: yes. - But then also in the air.

- The experiment is carried out with a small bowl balance, small enough to fit under the bell jar, large enough to hold the ball. -

L: And what is the case now? Does the vacuum make it heavier or does it make the air lighter?

S: Vacuum is nothing, can't do anything! - It's wrong in the water, so it can't be right in the air either. - Not exactly, anyway.

L: So what is heavier, a kilogram of lead or a kilogram of feathers?

S: The lead, because it has less buoyancy in the air.

L: Are you sure?

S: Yes. - Logo, we don't live on the moon!