ARCHIMEDES PRINCIPLE Investigation A: Measuring Buoyant Forces Purpose: to measure the buoyant force pushing up on an object submerged in a container of water and to verify Archimedes' principle. Introduction: When an object is immersed in a liquid, it experiences an upward buoyant force that may cause it to float. In a liquid, the pressure increases with depth. Therefore, the pressure on the lower surface of an object is always greater than that on the upper surface. This pressure difference produces an upward force on the object, which is called the buoyant force. This buoyant force is described by Archimedes' Principle: when an object is immersed into a liquid it is pushed up by a force equal to the weight (of the volume) of liquid it displaces. Materials: stand, clamp, force probe, aluminum cylinder, beaker, graduated cylinder Procedure: 1. Check the calibration of the force probe. Hang the force probe on the stand so the hook is facing downwards. Click on Zero, Zero Force. Click on Collect. Wait about 1-2 seconds and then put 400g on the hook (use the 50G weight holder plus a slotted mass of 50G and three slotted 100G masses). The graph should show zero force for the first 1-2 seconds and a horizontal line at slightly less than 4N at the end. If it did not, then call the instructor to check your setup. 2. Measure the weight of the aluminum cylinder. Zero the force probe again, and then hang the aluminum cylinder from the force probe using the string wrapped around the cylinder. The force probe is now reading out the weight of the cylinder. Record the force below. Four = 1./8/ N 3. Fill up the beaker about half way with water. Hold the aluminum cylinder so the string goes slack, and then zero the force probe. Place the beaker under the force probe and place the aluminum cylinder in the water. It should be completely submerged. The probe should now be reading out a force less than the weight measured in step 2. Record the force below. 0.737 NIn the space below, draw a free body diagram of the aluminum cylinder when it is submerged in the water. A complete free body diagram shows all forces acting on an object with arrows denoting the direction. There are three different forces to consider: the downward weight of the cylinder (Four), the upward tension in the string (Fin), and the buoyant force (B). 5. The cylinder is at rest (not moving) when immersed in the water. The acceleration of the cylinder is therefore equal to a = m/'s 6. Newton's 2" law tells us that the net force acting on an object is equal to its mass times its acceleration. Use Newton's 2" law to find the buoyant force. Show your calculation below and have me check your work before you move to the next step. B= N7. Archimedes principle says that the buoyant force acting on an object is equal to the weight of the fluid it displaces. Let's measure the volume of water the cylinder displaces. Fill up your graduated cylinder about half way with water. Measure the volume of water and record your value below. Note that I mL = 1 cm'. V, = 53 _cm3 8. Place the cylinder in the graduated cylinder so that it is completely submerged in the water. Measure the new volume and record your value below. V8 = 98 cm' 9. The volume of water displaced by the cylinder is equal to Vs - V7. Calculate this value and record your result below. V dis cm 10. The density of water is 1.0 g/em'. Find the mass of the displaced water using the fact that density is mass over volume (p = mais/Vdis). D= "/V S m= DV mdis kg 11. Calculate the weight of the displaced water using Wais = mang. Record your result below. W dis = N 12. The weight of the displaced fluid should equal the buoyant force you measured in step 6. Calculate the % difference between your answer to step 6 and your answer to step 11. Show your calculation below. % diff =Investigation B: Archimedes Squeeze Purpose: to investigate how changing the density of a floating object changes the percentage of the object that is submerged. Introduction: One consequence of Archimedes principle is that an object will float if placed in a fluid that is denser than itself and it will sink if placed in a fluid that is less dense than itself. We will gradually squeeze a foil ball down, increasing its density, until it sinks when placed in water. Materials: aluminum foil, beaker, hammer Procedure: 1. Using the ruler and a pen, measure out a square of aluminum foil that is 25 cm on each side. Use the scissors to cut this square out. . Mark the four corners of each sheet with permanent marker so you can spot the corners later. 3. With your hands, pull the corners of the aluminum sheet together and crumple the sheet of aluminum into a loose ball that is approximately 6 cm in diameter. Use the colored corners as guides as you crumple the ball-this will be important later. 4. Measure the mass of the 5. Measure the diameter of the aluminum ball with the ruler and record the exact measurement in your data table below. Mass = _ 2.7 grams Target diameter (cm) Actual diameter (cm) % submerged 6 5:9 2% 5./ 4 %% 4 3.8 10% 3 2.7 25 % 2.5 2.4 2 1.8 90%% 1.5 1:6 100% 6. Set the ball gently in the beaker of water. To avoid the ball filling up with water, since it does have some air pockets inside when it is loose, put the ball in the water so that the colored corners that you marked and brought together during crumpling are at the top of the ball. 7. Get down low so that you are at eye level with the aluminum foil, and try to determine (by eye) approximately what percentage of the ball is submerged in the water. Record this value in the table. 8. Remove the ball from the bowl of water, shake out any water, and dry it on the towel.9. Now crumple the same aluminum ball a little more tightly, into a smaller ball that is approximately 5 cm in diameter. If you crumple it too much, just carefully pull apart some of the aluminum foil to get the desired size. Repeat steps 6-8. 10. Continue to squeeze the ball down to complete the table. Try to get close to each target diameter shown in the table, and try to maintain a spherical shape. Be sure not to let any water seep into the ball. At some point, you may need to use the hammer to make the foil ball smaller. 11. Estimate the diameter of the ball when it becomes 100% submerged after being placed in water. Record your value below. d = cm 12. The radius of is equal to half of the diameter. Record the radius below. cm 13. What is the volume of the ball when it becomes 100% submerged after being placed in water? Use the formula for the volume of a sphere. Show your calculation and record your result below. V= cm' 14. What is the density of the ball when it becomes 100% submerged after being placed in water? Use the fact that density is mass over volume (p = m/V). Show your calculation and record your result below. Density = g/cm 15. The ball should become completely submerged when its density equals the density of water, which is 1.0 g/em'. Calculate the % difference between the density of water and the density you calculated in step 14. % diff = 5