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Volume Displacement Introduction: Archimedes was a Greek mathematician, inventor and physicist who lived from 287 - 212 B.C. A king once gave him a difficult task. The king had a crown. He had paid for pure gold. He was afraid that the crown-maker had mixed silver with the gold. He wanted Archimedes to find out if the crown was pure gold, or gold mixed with silver. Archimedes knew that all he had to do was to figure out the density of the metal. Silver's specific gravity is 10.5 and the specific gravity of gold is 19.3. It should be easy to detect the difference. There was a serious problem, though. Archimedes needed the mass of the crown and the volume of the crown. The mass was easy to measure. The problem was to determine the volume of the crown. The king did not want Archimedes to harm the crown in any way. How could Archimedes calculate the volume of a crown? Archimedes went home to think about the problem. He filled his bathtub with water and stepped in. He watched the water rise and overflow onto the floor when he sat. Suddenly, his problem was solved! The story tells that he ran out into the street, naked and dripping, shouting "Eureka!", which means "I have found it!" What did he find? When an object is submerged in water, the level of the water rises. This is because the object has moved some of the water out of the way, to make room for itself. (This is called displacement. The object displaces water. When Archimedes sat down in his bathtub, his body took up so much room that the water overflowed onto the floor. He realized that the water that he pushed out of the tub was the same volume as his body. If he submerged the crown in water, he could measure the volume of the crown. It was easy to measure the mass of the crown. He could compare the volume of the crown to the volume of an equal mass of pure gold. If the volume of the crown was greater than the volume of the pure gold, then the crown was a fake. We will test to see if Archimedes' idea was correct. Purpose: This experiment will test 1. to see if an object displaces its own volume when submerged. 2. to determine the volume of a small number of marble chips and find the density of marble. We will compare the density that we calculate with the known density. Equipment: two graduated cylinders (one 100 ml and one 10 ml), water, vernier calipers, three regularly-shaped objects, a small quantity of marble chips, a scale. Method: Part I. 1. Calculate the volumes of the three regularly-shaped objects. o You will have to measure the objects with the vernier calipers. Write the measurements in a table 2. Choose a graduated cylinder. o Remember that a graduated cylinder shows you the volume of the liquid in it. o Make sure that the objects will fit into it. o Partially fill it with water. o Write down the level of the water in the cylinder. (Measure at the bottom of the meniscus. The meniscus is the bottom of the curved surface of the water.) 3. Lower the object into the water slowly. 4. Write down the new level of the water in the cylinder. 5. Subtract the first level of water (from step 2) from the second level (from step 4) 6. Write down the difference in the water levels. o This difference is called the change of volume of the water. 3 o Remember that a ml is a cm . The markings on the graduated cylinder tell you the volume of the water. 7. Compare the change in volume of the water to the volume of the object. 8. Record your results in a table: Object Volume Of Object Volume Of Water In Graduated Cylinder New Volume Of Water In Graduated Cylinder Amount Of Change In Volume Of Water Answer these questions: Question 1: Compare the change in the volume of the water to the volume of the object. Are they the same? Question 2: Suppose you drop an irregular object (an object with no simple shape, like a rock) into the graduated cylinder. The water rises 25.3 ml. What is the volume of the irregular object? Part II. 1. 2. 3. 4. 5. 6. Measure the mass of your marble chips. Partially fill the smallest graduated cylinder. Write down the volume of water in the cylinder. Drop the chips into the cylinder. Write down the new volume of the water in the cylinder. Subtract the beginning volume from the second volume. o This is the change of the water's volume. o in Part I, you learned that the change of the water's volume is equal to the volume of the object. 7. Write down the volume of the marble chips. 8. Calculate the density of marble. 9. Calculate the specific gravity of marble. 10. The accepted specific gravity of marble is 2.6. Compare the specific gravity of your marble chips to the accepted specific gravity of marble. Is it the same or different? Volume Of Water In Cylinder Volume Difference Volume Of In Of Water Volume Marble + Chips Marble Chips Mass Of Marble Chips Density Of Marble Chips Specific Gravity Of Marble Chips Answer these questions: Question 3: The marble chips displaced water. We assumed that the amount of displaced water was equal to the volume of the chips. If this assumption had been incorrect, would you have gotten the correct specific gravity for marble? Why or why not? Question 4: What can you conclude about the displacement method for determining the volume of an irregular object?