Lab 11 Buoyancy

Lab 11. Buoyancy Goals • To experimentally determine the relationship between the buoyant force on an object that displaces a known weight of water. • To compare the buoyant behavior of an object more dense than water with that of an object less dense than water. • To calculate the densities of aluminum and wood cylinders from your data and to compare these densities to handbook values. Introduction Buoyancy is the name given to the force that arises when an object displaces a fluid (either a gas or a liquid) in a force field (usually gravity). The buoyant force is responsible for keeping ships from sinking and for keeping hot air balloons in flight. In the absence of other forces, the net force, FN et , acting on a partially or totally submerged object is the sum of the gravitational force, Fg , and the buoyant force, FBuoyant , which is oppositely directed. This can be written in equation form as FN et = Fg − FBuoyant (11.1) In this lab, you will measure the buoyant forces acting on two cylinders as they are submerged in water, and from these measurements, calculate their average densities. The cylinders are marked at centimeter intervals along their lengths. The cylinders are lowered into a beaker with their long axes perpendicular to the water surface, so the volume submerged, Vs , is Vs = πR2 Ls = ALs (11.2) where Ls is the length of the submerged portion of cylinder, R is the cylinder radius, and A is the cylinderÕs cross-sectional area. The weight of the water displaced by the object is given by Ws = ρw V s g 63 (11.3) 64 CHAPTER 11. BUOYANCY where ρw is the density of water (1.000 × 103 kg/m3 ). Buoyant force on an object more dense than water Refer to the Force Sensor section of the Computer Tools Supplement at the back of the lab manual for specific instructions regarding connecting the force sensors to the computers. The force sensor uses one of the analog input channels (A, B, or C) on the SW 750 interface. Carefully hang the aluminum cylinder on the force sensor. With the lab jack near its maximum height, adjust the position of the force sensor so that the cylinder sits completely inside the tall beaker without bumping the sides. Then add water to the beaker until the aluminum cylinder is completely submersed. This ensures that the beaker has enough water to cover the cylinder, but is not so full that water will spill when the cylinder is immersed. Use water from the sink at the back of your lab. To begin the experiment, lower the lab jack so that the aluminum cylinder is completely out of the water. With the aluminum cylinder hanging in the air, tare the force sensor. This sets the force sensor reading to zero with the entire weight of the cylinder applied. The force sensor reading as the cylinder is immersed will then equal the change in force, that is, the upward buoyant force. Since the force sensor in this orientation reads positive for upward forces, the upward buoyant force will be sensed directly as a positive force. Now vary Ls , the length of the cylinder that is submerged (in 1-cm increments), measuring the buoyant force for each increment, until the cylinder is completely submerged. Try to complete these measurements within about five minutes. This minimizes the effect of sensor drift on the force readings. Make a graph that compares the buoyant force (on the y-axis) with the weight of the water displaced (on the x-axis) for each value of Ls . From the graph, can you deduce a simple mathematical relationship between the two? Discuss/Explain. Look up Archimedes’ Principle in a textbook. Do your results support the validity of Archimedes’ Principle? Buoyant force on an object less dense than water Do not remove the threaded screw in the top of the wood cylinder! Its mass is negligible relative to the mass of the cylinder itself. Do not screw the cylinder more than 5 mm (about 1/4 inch) into the force sensor. The force sensor can be damaged by screwing it in too far. Replace the aluminum cylinder with the wood cylinder, which attaches directly to the force sensor by a screw. Again, measure the buoyant force as the submerged portion of the cylinder is increased in 1-cm increments. Do the buoyant force and the weight of the displaced water obey the same relation in this case? Discuss/explain. 65 Relative density of aluminum and wood Show that the density of any solid unknown material ρU nknown obeys the following relationship: WU nknown ρU nknown = ρw FM axBuoyant (11.4) where WU nknown is the weight of the unknown object, FM axBuoyant is the maximum buoyant force on the object when it is totally submerged in water, and ρw is the density of water. Use Equation 11.4 to calculate the density of the aluminum and the wood. Compare your calculated densities with accepted values from a textbook or handbook. A copy of the Handbook of Chemistry and Physics should be in your lab room. Do they agree within the limits of expected error for this experiment? If your measurement and the handbook value disagree by more than three standard deviations, carefully examine your calculations and procedures for possible sources of error. Some questions for extra credit For extra credit, you may address the following questions in your notes: 1. How can an aircraft carrier (or a concrete canoe) float when the density of the material used to build it is greater than the density of water? 2. Does air create a buoyant force? If so, estimate the magnitudes of the buoyant forces due to the atmosphere on your wood and aluminum cylinders? 3. Is the direction of the buoyant force always opposite the direction of the gravitational force? 4. Does the buoyant force on a totally submerged object change as the object moves farther and farther below the surface of the fluid? Before you leave the lab please: Exit the DataStudio program on the computer. Replace the small hook in the force sensor. Straighten up your lab station. Report any problems or suggest improvements to your TA.