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Name: ___________________________ Group Members: ___________________________ ___________________________ ___________________________ Archimedes’ Principle PURPOSE & OBJECTIVES The buoyancy force FB on an object submerged in a fluid is caused by differences in pressure at different heights in the fluid. This difference in pressure can be shown to result in a net upward force at the center of buoyancy and is equal to the weight of the displaced fluid. FB = weight of the displaced fluid (Eq 1) If a solid is lowered into a fluid using a string, one finds that it “weighs” less as measured by the tension force in the string. T Fig. 1 The free-body diagram for the mass in the fluid is shown in Fig 2. T Fg = Weight; FB FB = The Buoyancy Force; Fig. 2 T = Tension in the supporting string. Fg 1 06A- Archimedes’ Principle Since the acceleration of the mass is zero, we expect the vector sum of the three forces to be zero. T FB Fg 0 and obviously T = Fg - FB (Eq 2) Fg is the weight of the block. FB is the buoyancy force which based on Eq 1 will equal the weight of the displaced fluid. In this lab you will use a cubical block of base area A, and submerge it to various heights (h). Equation 2 then becomes. T = mg – 0(Ah)g= mg – 0(V)g (Eq 3) where 0 is the density of the fluid. A graph of T vs (Vg) can then be used for finding the density of the fluid. Plot the apparent weight as measured by the tension T against (Vg). The slope of the resulting straight line will yield 0. Compare your results with known values for the density of water at the temperature of the water. From (3) we can also derive the following relationship for the density () of a solid. mg 0 mg T (Eq 4) In this experiment, we will : Determine the density of a fluid Determine the buoyant force acting on a solid Determine the density of solids using buoyant force and fluid density. MATERIALS Laboratory balance Force Sensor Solid samples Beakers Support Stand Temperature Probe fluid samples PROCEDURE 1. Be sure to use units that are consistent. For instance m, m2, m3, cm, cm2, cm3, etc. 2 06A- Archimedes’ Principle 2. Measure the bottom sides and calculate the area A of the solid’s base. Take the temperature of the water. 3. Make a mark on the solid block every 0.5 cm vertically starting from the bottom. 4. Make a loop of string so that the block can be hung without touching the beaker located below the stand holding the Force Sensor. 5. Make sure the balance is zeroed properly. Determine the mass of the block. Set the empty beaker in position. Hang the block inside the beaker using the string. Now pour water from another beaker slowly from the side. Fill the beaker to a level matching the first of your marks. 6. Record the new force. Repeat for the next mark. 7. Repeat for the next block sample. Do three sample blocks in total. 8. Plot the graph of tension T against (Vg), then determine the 0 of the fluid. You will have three lines on your graph. Determine the average slope. Compare with the accepted value of water at the temperature. 9. Using the density determined from the slope of the line and Equation 4, determine the density of two other solid blocks. 10. Repeat the procedures to determine the density of another unknown fluid. DATA Mass of Block Block 1 Block 2 Block 3 ( ) Height ( ) Block 1 Area ( 2) Tension (N) Height ( ) Block 2 Area ( 2) Tension (N) 3 06A- Archimedes’ Principle Water Temperature (OC) Height ( ) Block 3 Area ( 2) Tension (N) ANALYSIS 1. What was the known value for the density of water at the temperature that your sample was? 2. How did you compare the two values? Show your calculation. 3. If you were to have used water at a higher temperature, how would the tension values been affected? 4. If you were to have used water at a lower temperature, how would the buoyant force have been affected? 4 06A- Archimedes’ Principle