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4CArchimedes 05/31/2007 03:27 PM Density, the Buoyant Force, and Archimedes' Principle Goal: To verify Archimedes' principle by comparing the density of a metal cylinder obtained by two methods. Equipment List: graduated cylinder beaker vernier calipers metal cylinder string pan balance with rods for raising paper towels for cleaning up Pre-lab Exercise: none Background: Archimedes' principle states that an object wholly or partially submerged is buoyed up by a force equal to the weight of the displaced fluid. The pressure at any point in a volume of fluid is due to the weight of the column of fluid above it. In an incompressible liquid, the pressure is a linear function of depth: P = Dgh where D is the density and h is the depth. This pressure is independent of the horizontal cross-sectional area of the liquid or of the object submerged in it. Since the pressure, P, increases with depth, there is a higher pressure on the bottom of the object than the top. Thus there is a greater force up on the object than down. The net force, called the buoyant force, is equal to the weight of the fluid displaced by the object. If the object is less dense than the fluid, it sinks until the buoyant force is equal to its own weight and it then floats at equilibrium. If the object is more dense than the fluid, the buoyant force is less than the weight of the object, but the apparent weight of the object is less by the amount of the buoyant force which is still equal to the weight of the fluid displaced. Note the following relationships: spec. gravity = weight of object in air = Do weight of an equal vol of water Dw = weight of the object in air apparant weight loss Where Do is the density of the object and Dw is the density of water . Procedure: Part 1: Direct calculation of the density of water: Measure and record the mass of the small beaker (or the graduated cylinder if you have one), with an uncertainty. Partially fill the graduated cylinder with tap water. Record the volume and estimate the uncertainty in the volume. Pour the water into the small beaker and determine the mass of the water alone, with an uncertainty. http://nebula.deanza.fhda.edu/physics/Dickson/4C/Archimedes.html Page 1 of 3 4CArchimedes 05/31/2007 03:27 PM Determine the density of water with an uncertainty. Is your value within the uncertainty of the accepted value? (Note: the density of water is 1.0 g/cm3 .) Why or why not? Part 2: Direct calculation of the density of the metal block: Measure and record the mass of the metal block, with uncertainty. Partially fill the graduated cylinder with water. Record the volume of water (with uncertainty). Completely immerse the metal block in the water, determine the volume of the block with uncertainty. Compare the volume of the block measured by immersion to a measurement of the volume using the vernier calipers. Determine the density of the block with uncertainty. Part 3: Using Archimedes' Principle to determine the density of a metal block: Using the small metal rod, raise the pan balance off the surface of the table. Tie a string to the small metal block and measure its mass by attaching the string to the underside of the balance. This is called a Jolly balance after German physicist Philip Van Jolly. Verify that your reading for the mass of the block is the same as it was on the pan itself. Remember there is additional mass due to the string. Fill the small beaker with water. Completely submerge the metal block attached to the underside of the pan balance in the beaker filled with water. Record the new apparent mass. Using Archimedes' Principle, determine the specific gravity of the metal block and use that to determine the density of the block with uncertainty. Use your value for the density of water calculated in part a. Then, try it again using the accepted value for the density of water. http://nebula.deanza.fhda.edu/physics/Dickson/4C/Archimedes.html Page 2 of 3 4CArchimedes 05/31/2007 03:27 PM Do your values for the density of the block from part 2 and 3 agree within uncertainty? Why or why not? Conclusion: Review your results. http://nebula.deanza.fhda.edu/physics/Dickson/4C/Archimedes.html Page 3 of 3