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PASCO scientific Science Workshop 1 Physics Experiment Library: 06020 P18 Buoyant Force LAB 1 Archimedes Principle PURPOSE The purpose of this laboratory activity is to show that the buoyant force of an object depends on the volume of the part of the object that is submerged and to calculate the density of the fluid by plotting the buoyant force versus the depth of the submerged part of the object. THEORY According to Archimedes’ Principle, the buoyant force on an object wholly or partially submerged in a fluid is equal to the weight of the fluid displaced by the object. m g V g F where f is the density of the fluid, V is the volume of the object that is submerged, and g is the acceleration due to gravity. Since the volume is equal to the cross-sectional area, A, multiplied by the submerged height, h, the buoyant force is given by F ( A h ) g If the object is lowered into the fluid while the buoyant force is measured, the slope of the graph of Fb versus h is proportional to the density of the fluid. PROCEDURE For this activity, the force sensor will measure the buoyant force on a metal cylcinder as it is lowered into water. You will enter values for the depth to which the object is submerged. Equipment Setup 1. Measure the diameter of the metal cylinder. Calculate the radius (R) and the cross-section area (A). Record the cross-section area in the Data Table. A R 2. Hang the metal cylinder from the force sensor hook with a string. 3. Put about 800 ml of water into the beaker. The bottom of the cylinder should be touching the water. ds ©1996, PASCO scientific P18 - 1 PASCO scientific Science Workshop 2 Physics Experiment Library: 06020 P18 Buoyant Force 4. Position the metric ruler next to the edge of the lab jack. Note the initial height of the top of the lab jack. Force Sensor Aluminum cylinder Ruler, metric Beaker Lab jack ANALYZING THE DATA 1. Make a graph of Fb versus h 2. Find the slope of tge graph 3. Calculate the density of water by setting the slope equal to Ag and solving for . 4. Compare the calculated value to the accepted value. 1. DATA TABLE: Water Item Area (cross-section A R Value ) m2 Slope (from graph) ds ©1996, PASCO scientific P18 - 2 PASCO scientific Science Workshop 3 ., Density of water (calculated) ., Density of water (accepted) Percentage difference Physics Experiment Library: 06020 P18 Buoyant Force kg/m3 1000 kg/m3 % QUESTION 1. ds How does your experimental value compare to the accepted value for the density of water? ©1996, PASCO scientific P18 - 3