6a. The specific gravity of steel is 7.8, yet steel battleships can float. How can this be?
- Only what you see on the outside is made of steel, the interior of the ship is mainly filled with air. This means that overall the average density of the battleship (filled with air) is light when compared to the average density of water. Only a small portion of the battleship must be submerged into the water to displace the weight of the ship.
6b. Water expands when heated. Imagine a bobber floating in a cold pond. Will that bobber float higher or lower in hot water? Assume the density of the bobber doesn’t change. Justify your answer using Archimedes’s Principle.
- When fishing at a pond, you may have noticed that on hot summer days your bobber may sink a little lower, making it harder to see. On cooler days the bobber will float a little higher making it easier to see. This is because the atoms and minerals in the colder water are closer together, causing the bobber to be higher above water. The hot water atoms and molecules are more spread out, making the water denser. In this case, Archimede’s Principle states the bobber will need to weigh as much as the water. The denser the water, the lower the bobber floats.
6c. Web Research Question: Visit this webpage for a thorough discussion of Archimedes and the crown story: http://www.math.nyu.edu/~crorres/Archimedes/Crown/CrownIntro.html This page debunks the notion that Archimedes solved the crown problem by measuring its volume by displacement. First, explain in your own words why it’s not very plausible that Archimedes could have exposed the thief by measuring the volume of the crown through water displacement. Then find at least two webpages that explain the crown story the wrong way and paste quotes from them into your answer, along with their URLs. Explain why you think this scientific myth has persisted over the years.
- The reason that Archimedes couldn’t have exposed the dishonest goldsmith because the container he was using was very large, spreading wide enough to accommodate for the size of the crown. With his calculations, the change he would have to look for would be a 0.41-millimeter rise of the crown in the water. That is difficult enough to monitor in current day, and without proper beakers it seems nearly impossible to solve the case just off of this. Most versions of the story mainly focus on the difference between gold and silver, which in fact is very small. There is one such story where it mentions Archimedes “leaped out of the bath and rushed home naked crying ‘Eureka! Eureka!’”, after realizing gold weighs more than silver and would sink more in a tub. https://www.scientificamerican.com/article/fact-or-fiction-archimede/. There is another article that says he was going to “measure the volume of the water spilled from a container filled with water to the brim when the crown was fully dipped in it” (https://www.longlongtimeago.com/once-upon-a-time/great-discoveries/eureka-the-story-of-archimedes-and-the-golden-crown/). A common problem here is that not all liquid levels are completely accurate.
Articles:
- https://science.howstuffworks.com/science-vs-myth/everyday-myths/question254.htm
- In depth description of how steel boats float
- http://physics.bu.edu/~duffy/py105/Pressure.html
- Scientific article about relationship between pressure and buoyancy
- https://sciencewithkids.com/Experiments/Matter-experiments/Hot-and-cold-water-density.html
- Simple experiment showing the differences of hot and cold water density
- https://www.coolkidfacts.com/sink-and-float-facts-for-kids/
- This article could explain to a curious young one why things float
