Hy Density: Archimedes Revisited Teacher Information Page Activity 3B Part 4 Activity Description: Students will read the background on Archimedes and the Golden Crown. After having done the Buoyancy and Equal Arm Balance activities, they will apply what they learned to design an experiment based on how Archimedes helped Hiero II, king of Syracuse. Activity Background: Archimedes is best known as one of the greatest mathematicians of all time; particularly in the area of geometry. In ancient Greece he would have been known by local farmers not as a mathematician, but as the guy who invented the screw so that they could easily move water from a stream up a hill to their fields! Greek soldiers would have known Archimedes as the inventor who helped them defend Syracuse by using mirrors to burn ships or the Claw used to hook a ship and tip it over! Archimedes exact time of birth and death are not known for certain. It is believed that he lived around 287-212 BC. Archimedes lived in Syracuse of Greek Sicily. The fact that it was considered Greek Sicily gives one an added insight. Sicily was a multicultural island, mainly due to a variety of invaders. In Archimedes time, it happened to be the Greeks. The story of the Golden Crown is well known among mathematicians and scientists. In essence, Hiero II, king of Syracuse, commissioned a goldsmith to make him a golden crown in the shape of a wreath. This was the common shape for crowns during that time. Hiero II wanted to use the crown on a statue of a god or goddess he worshiped. After the goldsmith had shaped the gold into the wreath crown he returned it to Hiero II. As the story goes, this is when the rumors began about the crown. The rumors that reached Hiero II were that the goldsmith had not used all the gold but had replaced some of it with another metal. Hiero II asked Archimedes to help him determine if the crown was indeed made of pure gold or not. The problem was that the crown was considered holy because it belonged to a god or goddess. Archimedes could not do anything to the crown that would change it in anyway. Archimedes was the kind of man that would sink himself in his work; mind and body. One day while he was sinking himself into a bath tub he solved the problem he had with the crown. He had noticed that the farther he sank in the tub the more water would overflow. 2007 The University of Texas Health Science Center at San Antonio 1
When Archimedes realized he had figured out a way to answer King Hiero s question, he literally jumped out of the tub and took off running to find the king. As he ran he was yelling Eureka! Eureka! which means I have found it! I have found it! The end of the story is that while Archimedes had found the answer of how to test the crown, he had forgotten his towel and clothes. Yes, he ran through Syracuse naked! It is believed that Archimedes did not just dunk the crown in water and measure the amount of water that overflowed. You see, Archimedes had already written two laws that helped him find the solution: the Law of Buoyancy and the Law of Levers. Some experts believe that Archimedes would have used a lever with the crown on one end and the same mass of gold as was originally given to the goldsmith. Archimedes would have lowered both objects into water at the same time. If the crown was not pure gold then the gold would make the lever (balance) uneven. Since gold has a greater density, and thus displaces more water, the end of the balance with gold on it would sink more than another common metal of the time: silver. Archimedes determined the mass of the wreath and found that it was the same mass as the original lump of gold. The equal arm balance was level. This was fine but Archimedes knew that if there was anything in the crown other than gold that that metal would not have the same buoyant nature as gold. When Archimedes lowered both the wreath crown and the gold he would have seen the equal arm balance tilt down on one end the end with the gold, see Figure 1. Archimedes proved that the goldsmith had cheated Hiero II. It is believed that Hiero II had the goldsmith killed. Activity Materials 1 Bin of materials provided by your teacher (per group) 1 copy of the Student Information Page (from class set) 1 copy of the Student Data Page (per student) Activity Management Suggestions: Figure 1 Was It Pure Gold? Modifications: Students need to work in groups of 3-4; try to make sure that you have at least 1 person in the group who excels at recording information; a person who is kinesthetic; a person good at helping others stay on task Extensions: Have students write another scenario in which they apply the same equipment and techniques to determine density of other materials. 2007 The University of Texas Health Science Center at San Antonio 2
Hy Density: Archimedes Revisited Student Information Page Activity 3B Part 4 Activity Introduction: The story of Archie, Deuces and Goldie was a fictionalized version of the story of Archimedes and the Golden Crown. In this activity you will read a more accurate version of what is believed to be the story of how Archimedes (aka Archie) helped Hiero II (aka: Deuces), king of Syracuse of Greek Sicily. After reading the Activity Background you will design the experiment Archimedes would have done to find out if the crown was as buoyant as the lump of gold. You will re-test your crown and lump of gold from Part 1 The Golden Crown activity. Activity Background: Archimedes is best known as one of the greatest mathematicians of all time; particularly in the area of geometry. In ancient Greece he would have been known by local farmers not as a mathematician, but as the guy who invented the screw so that they could easily move water from a stream up a hill to their fields! Greek soldiers would have known Archimedes as the inventor who helped them defend Syracuse by using mirrors to burn ships or the Claw used to hook a ship and tip it over! Archimedes exact time of birth and death are not known for certain. It is believed that he lived around 287-212 BC. Archimedes lived in Syracuse of Greek Sicily. The fact that it was considered Greek Sicily gives one an added insight. Sicily was a multicultural island, mainly due to a variety of invaders. In Archimedes time, it happened to be the Greeks. The story of the Golden Crown is well known among mathematicians and scientists. In essence, Hiero II, king of Syracuse, commissioned a goldsmith to make him a golden crown in the shape of a wreath. This was the common shape for crowns during that time. Hiero II wanted to use the crown on a statue of a god or goddess he worshiped. After the goldsmith had shaped the gold into the wreath crown he returned it to Hiero II. As the story goes, this is when the rumors began about the crown. The rumors that reached Hiero II were that the goldsmith had not used all the gold but had replaced some of it with another metal. Hiero II asked Archimedes to help him determine if the crown was indeed made of pure gold or not. The problem was that the crown was considered holy because it belonged to a god or goddess. Archimedes could not do anything to the crown that would change it in anyway. Archimedes was the kind of man that would sink himself in his work; mind and body. One day while he was sinking himself into a bath tub he solved the problem he had with the crown. He had noticed that the farther he sank in the tub the more water would overflow. 2007 The University of Texas Health Science Center at San Antonio 3
When Archimedes realized he had figured out a way to answer King Hiero s question, he literally jumped out of the tub and took off running to find the king. As he ran he was yelling Eureka! Eureka! which means I have found it! I have found it! The end of the story is that while Archimedes had found the answer of how to test the crown, he had forgotten his towel and clothes. Yes, he ran through Syracuse naked! It is believed that Archimedes did not just dunk the crown in water and measure the amount of water that overflowed. You see, Archimedes had already written two laws that helped him find the solution: the Law of Buoyancy and the Law of Levers. Some experts believe that Archimedes would have used a lever with the crown on one end and the same mass of gold as was originally given to the goldsmith. Archimedes would have lowered both objects into water at the same time. If the crown was not pure gold then the gold would make the lever (balance) uneven. Since gold has a greater density, and thus displaces more water, the end of the balance with gold on it would sink more than another common metal of the time: silver. Archimedes determined the mass of the wreath and found that it was the same mass as the original lump of gold. The equal arm balance was level. This was fine but Archimedes knew that if there was anything in the crown other than gold that that metal would not have the same buoyant nature as gold. When Archimedes lowered both the wreath crown and the gold he would have seen the equal arm balance tilt down on one end the end with the gold, see Figure 1. Archimedes proved that the goldsmith had cheated Hiero II. It is believed that Hiero II had the goldsmith killed. Activity Materials: 1 Bin of materials provided by your teacher (per group) 1 copy of the Student Information Page (from class set) 1 copy of the Student Data Page (per student) Activity Instructions: 1. As a group you will devise a procedure to find out if the crown you used in Part 1 is truly gold. 2. Figure 1 Was It Pure Gold? On the Student Data Page you will find a guide and a rubric to help you plan your investigation. 2007 The University of Texas Health Science Center at San Antonio 4
Hy Density: Archimedes Revisited Student Data Page Activity 3B Part 4 Activity Materials (list only the materials that are needed for the activity and describe them fully): Conclusion: (After analyzing your results, describe the final outcome of your investigation): Problem Statement (this should be a sentence that states what this activity is about): Activity Background Title: Procedures (write instructions in numbered steps so that anyone could repeat them; you will need to write how to set-up and equal arm balance as well as how to attach the crown and lump of gold and how to read the results): (information that helps others understand what has been done in the past related to this investigation): Results: (Draw a data table in which to collect your results): 2007 The University of Texas Health Science Center at San Antonio 5
Hy Density: Archimedes Revisited Rubric Exemplary 4 Accomplished 3 Developing 2 Beginning 1 No Attempt Made Score Problem Statement Presents a concise sentence that states the problem. Gives too much information more like a summary. Gives very little information. Does not give any information about what to expect in the lab. a problem statement. Presents a concise background for Activity Background the activity with relevant information. Gives too much information rambles. Background lacking in relevant information. Gives only one or two relevant facts. a background. Materials List format, includes all the materials needed and exact quantities needed to complete lab. List format and includes all the materials needed to complete lab. List format, but does not include all the materials needed to complete lab or materials not well described. List format, but incomplete and poorly described. Did not list materials. Procedure Presents easy-to-follow steps which are logical and adequately detailed. Most of the steps are understandable; some lack detail or are confusing. Some of the steps are understandable; most are confusing and lack detail. Not sequential, most steps are missing or are confusing. a procedure. Conclusion Presents logical conclusion based upon analysis of results. Conclusion based upon analysis of results, but is not complete. Conclusion is incomplete and does not clearly explain the results. Conclusion written, but not based upon analysis of results. a conclusion. Grammar and Spelling All grammar and spelling are correct. Only one or two errors. More than two errors. Very frequent grammar and/or spelling errors. No attempt made to write the assignment. Total 2007 The University of Texas Health Science Center at San Antonio 6