Archimedes and the Crown “It’s your density” – George McFly Back to the Future

Archimedes – lever Archimedes: “Give me a long enough lever, and a place to stand and I will move the earth.”

Archimedes – Ancient Physicist Born about 287 BC in Syracuse, Sicily.Syracuse Archimedes was an ancient Greek physicist. He is credited with the following inventions: Lever (Explained principle behind it) Death ray. Block & tackle system Archimedes’ screw – for removing water from ships. Improved the catapult design: (A “machine-gun” catapult, which could continuously fire without reloading) An odometer (a cart with a gear mechanism that dropped a ball into a container after each mile traveled) A planetarium (A complex gear mechanism) Designed the largest transport ship of the time.

Archimedes – Claw Archimedes also developed a “claw” for lifting up invading Roman navy vessels. Ships too far away had their sails set fire by his “death ray.”

Archimedes – Ancient Physicist I know… don’t believe the death ray idea. Mythbusters “busted” it, you say.

The king’s crown In 265 BC King Liero II, king of Syracuse, had commissioned a goldsmith to make a gold crown. Later he heard that the goldsmith may have mixed in some silver, keeping back some of the gold for himself. Archimedes was commissioned to test the crown to determine if it was made of pure gold. (He was only 22.)

Archimedes’ Commission That night Archimedes thought that he would weigh out some gold of the same weight as the crown. If the volumes were different, then he would have uncovered a fraud. But, how to determine the volume of the irregular- shaped crown?

Archimedes’ Commission One day while taking a bath, and thinking about the king’s problem… The water overflowed, which got Archimedes to thinking about possibilities. “Eureka!”

Archimedes’ Discovery Archimedes realized that his body caused an equal volume of water to overflow when he got into the tub. He had his method for measuring the volume of the crown!

Archimedes’ Commission Archimedes uncovered fraud. The goldsmith was thrown into the dungeon.

Archimedes’ Principle The buoyant force is equal to the weight of the fluid (typically water) displaced.

How can we use Archimedes’ principle?

Density Density is the ratio of mass to volume   density.  = m/vol in Kg/m 3  (water) = 1 gm/cm 3 = 10 3 Kg/m 3  (gold) = 19.3 gm/cm 3 = Kg/m 3

Density For some of you, when we start talking about the density of metals, , buoyant forces… you feel uncomfortable. But actually we just need a little common sense. Density of various metals:  of Al = 2.7  of Ag = 10.5  of Au = 19.3

Density Density of various metals:  of Al = 2.7 – Aluminum  of Zn = Zinc  of Sn = Tin  of Fe = Iron  of Bronze = Copper and usually Sn (tin) or Al alloy  of Brass = 8.4 – Cu (copper) and Zn (zinc) alloy  of Ni = Nickel  of Cu = Copper  of Ag = Silver  of Pb = Lead  of Hg = Mercury  of Au = 19.3 – Gold

What Archimedes actually did  o /  l = F g / F B Say the crown weighed 10N (almost 2 lb.) 19.3 x 10 3 / 1 x 10 3 = 10N / Buoyant Force If crown weighs 9.3N in water, then F B = 0.7N Is this crown pure gold? (White boards!)

Demo time How can I determine the density of an object? Use Archimedes’ principle!

Test Your Understanding: Archimedes Principle How did Archimedes determine if the King’s crown was made of pure gold? For this experiment, assume that Archimedes weighed the King’s crown and found its weight to be 7.84 N. He then weighed it while it was completely immersed in water of density 1000 kg/m 3 and found its weight to be 7.26 N. What is the density of the crown? Is it pure gold? A 2 nd crown (7.84N), weighs 7.43N in water. Is it pure gold?

How do Submarines Dive & Surface? Does the buoyant force change? ____ A sub has “ballast tanks” that can be filled with _______ or _____. To dive, a sub must become heavier, so the tanks allow _______ in while venting ____ out. To surface, a sub must become lighter. A supply of compressed air on the sub is used to force ______ back out of the ballast tanks. NO waterair waterair water

Hot Air Balloons If balloon is floating (not accelerating up or down): (includes the weight of the balloon, the basket, the riders, and the ___ _______ balloon!) W total air inside the

How does a balloon accelerate up? Heaters heat the air … As temperature ↑, pressure __. Some of the air escapes out the bottom of the balloon, since air will move from _____ to ____ pressure. Thus, the weight of the balloon ____. The upward buoyant force is now greater than the downward weight. ↑ highlow ↓

How does a balloon accelerate down? Heaters are turned off, causing the air to cool … As temperature ↓, pressure __. Air from the outside enters this lower pressure area, ___________ the total weight of the balloon. The upward buoyant force is now less than the downward weight. ↓ increasing

Water Bridge in Germany

500 million euros later, and 918 meters long..... This is a channel-bridge over the River Elbe and joins the former East and West Germany, as part of the unification project. It is located in the city of Magdeburg, near Berlin. The photo was taken on the day of inauguration. Did this bridge have to be designed to withstand the additional weight of ship and barge traffic, or just the weight of the water? Six years to build

Answer: It only needs to be designed to withstand the weight of the water! Why? A ship always displaces an amount of water that weighs the same as the ship, regardless of how heavily a ship may be loaded. The water level will rise, but the weight will be the same.