Lesson 12

Card 1.1: Archimedes and Buoyancy

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Before Class Reading: The Two-Thousand-Year-Old Cheat Code

A steel ship floats. A steel bolt sinks. Same steel. If floating were about material or weight, the ship, weighing millions of times more, should plummet. It does not, and the reason was worked out in a bathtub twenty-two centuries ago.

Archimedes’ principle, one sentence: water pushes up on a submerged object with a force equal to the weight of the water that object displaces. Read it carefully, because the principle is about the WATER’s weight, not the object’s. Push a basketball underwater and the upward shove you feel is the weight of a basketball’s worth of water, roughly 7 kilograms of force, trying to reclaim its space. The ocean does not know or care what the object is made of; it only knows how much room the object takes up.

So floating is a contest between two numbers: the object’s weight pulling down, and the displaced water’s weight pushing up. The ship wins because its hull is mostly enclosed air; it displaces an enormous volume of water while weighing less than that volume of water weighs. The bolt loses because solid steel weighs about eight times more than the water it displaces. Shape the same steel into a hollow hull and the contest flips.

Between sinking and floating lies the state this class cares about most: neutral buoyancy, where the two numbers exactly tie and the object hovers, weightless, at whatever depth you put it. Divers chase this state. Submarines engineer it. Every ROV wants it, because a robot that naturally hovers spends its thruster power on the mission instead of on fighting its own weight.

The working tool falls straight out of the numbers. Fresh water weighs one gram per cubic centimeter. Therefore every cubic centimeter of displacement buys exactly one gram of upward force. A 5,000 cm³ robot hovers at 5,000 grams, floats below that, sinks above it. Trimming a robot stops being mystical: measure the volume, do the subtraction, add foam or lead until the ledger balances. You will do this arithmetic for real, first on a film canister, eventually on a 15-kilogram robot where guessing wrong costs a pool day.

Prep prompt (bring in writing): Commit to a prediction before class: a sealed object hovers, neutrally buoyant, at 1 meter deep. We move it to 3 meters and release it. Does it stay, rise, or sink? Write your answer AND your reasoning using the two-number contest above, then a second prediction: does your answer change if the object is a sealed rigid box versus a soft air-filled bag? You will test both in the tub, and defending or revising your written prediction is part of the oral check.

Unit: 1, Water Physics Format: Socratic opener + bench challenge Time: 40 minutes Prerequisites: None. First science card of the year.

Core Question

A steel ship floats. A steel bolt sinks. Same material, opposite fates. What actually decides whether something floats, sinks, or hovers, and how do we make a robot do the third one on purpose?

Resource (~10 minutes)

Archimedes’ principle, one sentence: the water pushes up on an object with a force equal to the WEIGHT OF THE WATER the object displaces. Not the object’s weight; the displaced water’s weight.
So the contest is: object’s weight (down) versus displaced water’s weight (up). Heavier than the water it displaces, it sinks. Lighter, it floats. Exactly equal, it hovers: neutral buoyancy, the state every ROV wants.
Freshwater weighs about 1000 kg per cubic meter, or 1 gram per cubic centimeter. That number is your tool: 1 cm³ of displacement buys you 1 gram of lift in the pool.

Bench Challenge (team, ~20 minutes)

Each team gets a film canister (or small capsule), washers, and a water tub. Make the canister hover: fully submerged, neither rising nor sinking, for 5 seconds.

Then the real exercise: BEFORE adjusting further, measure your canister’s volume (the teacher shows displacement measurement with a graduated cylinder), calculate what it should weigh to be neutral, weigh your ballasted canister, and compare. How close was your trial-and-error to the math? Which was faster? Which would you trust for a 15 kg robot where trial-and-error means draining a pool day?

Prep Notes / Written Artifact

Your measured volume, calculated neutral weight, and actual final weight, with the arithmetic shown.
Two sentences: why does a steel ship float? Use the word “displaces.”
One sentence: our float (Ebirah) changes its buoyancy without adding or removing any weight. Based on today, what MUST it be changing instead?

Clearing This Card

Turn in the written artifact, plus a 90-second oral check: the teacher hands you an object and its weight; estimate what volume it needs to displace to hover, and say what you would add (foam? weight?) if it currently sinks.

If You Miss This Class

The tub, canisters, and scale stay available for two weeks. Run the challenge solo or with any cleared student, then same artifact and oral check.

Why This Matters for Competition

Buoyancy and ballast is a named section of the MATE technical documentation, and neutral trim is the difference between a robot that flies and one that fights you through every mission task. The 1 gram per cm³ tool from today is the same math the team uses to trim Godzillah, and question 3 is the entire operating principle of the float you will tune this season.