Imagine That You Have A Sample Of Metal And You Determine Th

Imagine That You Have A Sample Of Metal And You Determine That Its

Imagine that you have a sample of metal and you determine that its mass is 108.4 grams. When you put it into a graduated cylinder initially filled with water up to the 33 ml mark (without the metal in it), the level of the water rises to the 48 ml mark. What is the density of the metal? Which of the metals listed on page 16 of the manual is it? Also: In your own words, give an example of how checking the density of a particular material or object is important in business, industry, everyday life, or in history. If you wish, you can look up the famous story of the ancient Greek scientist Archimedes and the gold crown and summarize it in your own words.

Paper For Above instruction

Determining the density of a metal sample is a fundamental aspect of material identification and quality control in various fields such as manufacturing, archaeology, and science. For this particular problem, we begin by calculating the density of the metal based on the given data. The mass of the metal sample is 108.4 grams, and the water displacement method is used to find its volume, which is derived from the water level difference in the graduated cylinder. The initial water level is 33 ml, and when the metal is submerged, it reaches 48 ml. This displacement indicates the volume of the metal.

The volume of the metal is calculated as:

Volume = Final water level – Initial water level = 48 ml – 33 ml = 15 ml

Using the formula for density:

Density = Mass / Volume

Density = 108.4 g / 15 ml ≈ 7.23 g/ml

The density of this metal is approximately 7.23 grams per milliliter. To identify which metal it could be from the list on page 16 of the manual, we compare this density value with known densities of common metals. For instance, iron has a density of about 7.87 g/ml, copper approximately 8.96 g/ml, zinc around 7.14 g/ml, and aluminum roughly 2.70 g/ml. Our calculated density is close to zinc's density, suggesting that the sample might be zinc or a similar metal with a slightly lower density.

Beyond the calculations, understanding the significance of measuring density extends into various practical contexts. In industry and commerce, density measurements could determine the purity of materials, such as precious metals like gold or silver, where adulteration or alloying can alter the expected density. For example, in jewelry manufacturing, verifying the gold content through density ensures quality and authenticity. An incorrect density reading could indicate a counterfeit or adulterated product, which could otherwise lead to financial loss or legal issues.

Historically, density checking played a critical role in the story of Archimedes and the gold crown. According to legend, King Hiero II commissioned a new gold crown and suspected that the royal goldsmith might have cheated him by replacing some gold with cheaper metals. Archimedes devised an ingenious method to verify the crown’s purity by measuring its displacement in water to calculate its volume and thus its density. By comparing the obtained density with that of pure gold, Archimedes could determine if the king's suspicion was justified without damaging the crown. This story emphasizes how understanding and measuring density can solve real-world problems, assuring fairness, safety, and authenticity in various domains.

In conclusion, the calculation of density is a vital tool across multiple disciplines. It allows for the identification of materials, detection of adulteration, and verification of authenticity. The story of Archimedes illustrates how the principle of density measurement can lead to innovative solutions and reveal truths hidden beneath surfaces. Whether applied in scientific research, industrial quality control, or historical investigation, the concept of density remains a fundamental and powerful measurement.

References

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