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What is actual heavier, a kilogram of lead or a kilogram of feathers?

by Klaus Kohl

Anyone here who does not know that joke?
Of course you might say "lead" but you know that it is a joke, as both are of the same weight
Of course you know - but are you right?

On December 3, 1996 Martin Wagenschein would have had his 100th birthday, he died eight years before. Doctor honoris causa, winner of several prizes, he was and is celebrated, interpreted, misunderstood, scolded.
By decades - until into highest age - he had struggled to make teaching comprehensible, especially math and physics, to clear it out from hollow knowledge: "Understanding the comprehensible is a human right" - "Teach to understand" - "Save the phenomena!" were often title and subject of his numerous publications and lectures. In his seminars to teach teaching he concentrated on themes like the hexagon in a circle, the earth globe, the suckling of lemonade by a straw, to show the way from the self-evident habit to a critical question which turns into a puzzling problem and after that the solution leads to a self-confident realization. He marked his pedagogical guidelines by the terms genetic, socratic, exemplary.

This "miniature" happened (I have no other word for it) at the Ecole d'Humanité in Goldern (Switzerland) with a group of five students, aged 15-16. The manner of asking and answering is deliberated guided along the manner of Socrates described by Platon (e.g. Menon - an ignorant slave detects a method to double a square; already in early times a preferred theme of Wagenschein).
Nevertheless this is not a "Wagenschein-piece". At first that sophistic question was no theme for him and by second: he as a teacher would have talked much(!) less. But as a late thank of one of his guest students it may serve.


Teacher: What is actual heavier, a kilogram of lead or a kilogram of feathers?

Students: A kilo is a kilo!

T: That's right.

S: The feathers need more room.

T: That's right, too.

S: Lead seems to be heavier.

T: Yes, but that is not what I mean. Is it the same, weighs it the same?

S: Try it!

T: How?

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

T: ---

S: (Cushion battles in mind, creative chaos, sinking into silence)

T: Lets do it a little more handsome. Let us take wood instead of feathers. Is a kilo of lead as heavy as a kilo of wood? (He is free enough to say -like his students- occasionally kilo instead of kilogram.)

S: Logo!

T: And a kilo lead as heavy as a kilogram stone?

S: Yes of course.

T: Try it!

- He got a stone and a block of lead with equal masses - not exactly 1 kg, that does not matter - and puts them on both sides of the balance. -

S: You see!

T: Take them in your hands, are they equal?

S: Yes.

T: And now put both hands into water - are they equal?

S: No, now the stone weighs less than the lead.

T: You see!

S: Yes in water, there it is different. - Wood has in water no weight, it will even go up, like a balloon!

T: Why?

S: Because it weighs less than water.

T: And the stone??

S: Is heavier than water and lead is still heavier.

T: Remember - both is 1 kilogram.

S: But they are of different size. - The density is different. - The buoyancy makes the stone and the wood weigh less. - The lead too, but only a little bit.

T: And outside?

S: There is no buoyancy.

T: And the balloon?

S: Oh...

T: If I take a balloon - or better an empty plastic bag and blow it up with air - will it become heavier?

S: No.

T: Is in a full plastic bag more inside than in an empty one?

S: (Laughter)

T: Will the full plastic bag have more mass than the empty one?

S: Yes, maybe some grams. - But you cannot weigh that. - However where there is no air. - Water has in water no weight. - The bag will burst! (The plastic bag with air in it in vacuum).

T: What is heavier, a gram of lead or a gram of air?

S: Air weighs nothing.

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

S: In styrofoam ist air? - Yes. - I don't know. - That doesn't matter.

T: Why not matter?

S: Air weighs nothing. - How do you want to get the real weight? - Without air. - How do you want to get the air out? - No, I mean in vacuum. - Will it not burst?

T: Try it!

- A styrofoam ball of about 4 inch in diameter is placed under the glass cover. Then the glass cover is evacuated. The secretly expected catastrophe fails to come. -

S: Can you weigh it?

T: In vacuum?

S: Yes. - But afterwards also in air.

- The experiment is performed with a little balance, small enough to fit under the glass cover, but sufficient to hold the ball. -

T: What now? Did vacuum make it heavier or did the air make it lighter?

S: Vacuum is nothing, can do nothing! - In water it was not correct, then in air it is not correct, too. At least not exactly.

T: Therefore - what is heavier, a kilogram of lead or a kilogram of feathers?

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

T: Are you sure?

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

T: Then ask your parents at home!

S: Oh Yes!

You see, such a situation can only occur when the students have some knowledge. About mass and weight are fundamentals essential, buoyancy, at least in liquids, must be known. To know that air has a mass is necessary as well as to know about the powerlessness of vacuum ("Vacuum is nothing, can do nothing!"). This example is not adequate to introduce the difference between mass and weight, but very useful to understand it better finally. That dependant on the available material (e.g. a sensitive spring balance) and the spontaneous answers of the students another way of discussion will lead to the aim, that is evident. Of course such sequences are possible (and useful!) not only in secondary level I but also short before graduation.
And in a seminar session? - Try it!

Published by the 100th birthday of Martin Wagenschein in:
Physik in der Schule 34 (1996)12 p. 429-430
Paedagogischer Zeitschriftenverlag, Berlin