Download Experiment 8: Archimedes’ Principle | PHYS 0004A and more Lab Reports Physics in PDF only on Docsity! Physics 4A Experiment 8: Archimedes’ Principle Introduction: There is a story that is told about Archimedes (287-212b.c.) that occurred when he was commissioned by King Hiero II to determine whether the royal crown was made of pure gold. The king did not trust the goldsmith, and he worried that some silver (alloyed with gold) may have been used rather than the pure gold the King paid for. This request of Archimedes was difficult at the time because the only known way to take a piece of the crown material and chemically test it. This was strictly forbidden, so the problem Archimedes faced was how to determine the crown’s composition without altering it in any way. As the story goes (according to Syracuse), one day Archimedes was seen running naked down a street in central Athens screaming “Eureka! Eureka!” (L: “I’ve found it!). What he had found was a way to solve the crown problem, and this was not just coincidence. What followed was Archimedes’ famous principle and the death of the dishonest goldsmith. In this experiment, you will find out how to measure the density of irregularly shaped objects and more using this principle. Theory: 1. In the space below, state Archimedes’ Principle and define density, then show mathematically how one can measure the density of an object using this principle. Be sure to diagram the apparatus you will use to clarify your derivation. You may want to see your lecture notes for Chapter 14, slide # 28. 1 Theory, continued: 2. In a similar manner, derive an equation for determining the density of a wooden object using Archimedes’ Principle. F = T1 + FsB – mwg – msg = 0 FsB = mwg + msg – T1 F = T2 + FwB + FsB – mwg – msg = 0 FwB = mwg + msg – T2 – FsB Substitute FsB from top equation into bottom equation: FwB = mwg + msg – T2 – (mwg + msg – T1) FwB = mwg + msg – T2 – mwg – msg + T1 FwB = T1 – T2 = mb1g – mb2g = mg m is the difference in balance readings between water levels 1 and 2 shown. Can you finish this derivation resulting in the following formula? water mwood m 3. Finally, derive an equation using Archimedes’ Principle showing how the density of a liquid can be measured. Apparatus: 2 T 1 m s g m w g Fs B T2 msg mwg FsB FwB Water Level 1 Water Level 2 2. In a similar manner, calculate the density of the wood object (Theory #2). 3. Finally, show the calculation of the density of the liquid used (Theory #3). 5 Results: Table 2: Measured Densities Substance Measured Density * Reference Density % Error Aluminum Brass Bolt Rock Wood NaCl (aq.) *Using the handbook (or other similar references), look up and record the densities of as many of these materials as you can find. Conclusions: Can you identify the chemical composition of the unknowns? If you are successful, report their identities in the space below and list your source(s). 6
