Buoyant Force and Archimedes' Principle, Exercises of Physics

Download Buoyant Force and Archimedes' Principle and more Exercises Physics in PDF only on Docsity! Buoyant Force and Archimedes' Principle Introduction: Buoyant forces keep Supertankers from sinking and party balloons floating. An object that is more dense than a liquid will sink in that liquid. If it is less dense, it will float. Archimedes' Principle states: A body wholly or partially immersed in a fluid will be buoyed up by a force equal to the weight of the fluid that the body displaces. As an equation: FB=W liquid=mliquid g . Given mliquid= liquidV object , the buoyant force acting on a submerged object is FBuoyant=liquid gV object . FB can be found by measuring the difference between the weight of the object measured in air and the apparent weight of the submerged object. Study I: Buoyant Force on fully submerged objects. You will measure FB=W inAir−W inWater using an equal arm balance for several objects and plot FB vs Volume to calculate water . As you take your measurements consider the following question: Why does FB depend on water rather than object ? Procedure: 1. Measure and record the diameter and thickness (neglect uncertainties) of the cylinders using the Vernier caliper. Measure the masses. cylinder ID d, diameter (cm) t, thickness (cm) M , mass (g) Aluminum Iron Copper 2. Check that your equal arm balance is high enough to easily suspend the masses, but low enough to immerse the hanging masses in the container provided. See the diagram on the following page. 3. Test whether your equal arm balance is well balanced: with no additional weights, its center of mass should be close to the middle of the meter stick. Your equal arm balance needs to be perfectly balanced, otherwise you will have systematic errors. The accuracy of the measurements may not be as good as the precision. If you are careful, the systematic errors should be fairly small and they will tend to cancel when you take the difference between masses. 4. Check for systematic errors: Determine how much mass is required to balance a cylinder (DON'T forget the 50g mass hanger). If the cylinder/balancing mass values are very different, adjust the balance. 1 How to read a Vernier Caliper 5. Using your balance, hang the cylinder from one hanger clamp, and the mass hanger with standard masses from the other hanger clamp as shown. Measure the mass required to balance the hanging cylinder in air and water. Data Table 2: The three cylinders can be used alone or combined. • Make sure that the cylinders do not rest on the bottom or rub against the side of the container when making the measurements. Your water level will affect your results if you are not careful. Make sure it is high enough. • The sensitivity of this balance should, with some care, be better than 1 gram. Since the smallest standard mass provided is 1 gram you may be able to determine mass to a precision of perhaps half of a gram by estimation. cylinder used Balancing mass in air (g) Balancing mass in water (g) m±m Aluminum (A) Iron (I) Copper (C) A + I A + C I + C A + C + I 6. By hand or with Graphical Analysis, calculate the values of m (in grams) for each combination of cylinders in Table 2. Given an error in each mass measurement of .5 g, what is the error in m=minAir−minWater ? 2 Conditions for static equilibrium: if the equal arm balance is symmetric about the knife edge, the meter stick should remain balanced when equal weights are suspended from the two hanger clamps. Stand