Experiment 11: Archimedes' Principle, Study notes of Acting

Download Experiment 11: Archimedes' Principle and more Study notes Acting in PDF only on Docsity! Experiment 11: Archimedes’ Principle Figure 11.1 EQUIPMENT Triple-Beam Balance with string Graduated Cylinder Pipette Cylinders: (2) Metal, (1) Wood (Note: The cylinders have sharp hooks) Overflow Container Spouted Can Digital Balance (2) 123-Blocks Wood Board/Block Rod & Clamp Paper Towels Water 1 2 Experiment 11: Archimedes’ Principle Advance Reading Text: Archimedes’ principle, buoyant force, density Objective The objective of this lab is to investigate the buoyant force acting on a variety of objects, the density of the objects, and the density of our tap water. Theory Archimedes’ principle states that a body wholly or par- tially submerged in a fluid is buoyed up by a force equal in magnitude to the weight of the fluid displaced by the body. It is the buoyant force that keeps ships afloat (ob- ject partially submerged in liquid) and hot air balloons aloft (object wholly submerged in gas). We will inves- tigate the buoyant force using the following methods: • Direct Measurement of Mass • Displacement Method When an object is submerged in water, its weight decreases by an amount equal to the buoyant force. The direct measurement of mass will measure the weight of an object first in air, then while it is sub- merged in water. The buoyant force, FB , is equal to the weight in air (Fg) minus the weight in water, F � g = m�g: FB = Fg − F � g (11.1) The displacement method requires measurement of the volume of fluid displaced by the object. The weight of the fluid displaced is equal to the buoyant force ex- erted on the object. Thus, the buoyant force is given by: FB = ρgV (11.2) where ρ (Greek letter, rho) is the density of the fluid displaced, V is the volume of fluid displaced by the object, and g is the acceleration due to gravity. The following exercises will be informative, as both floating and sinking objects are used in this experi- ment. • Sketch a free-body diagram for an object that is floating in water. How much water does it displace? Does it displace its volume in water? Does it displace its weight in water? • Sketch a free-body diagram for an object that is submerged in water. How much water does it displace? Does it displace its volume in water? Does it displace its weight in water? The accepted value for the density of pure water at 4◦C and 1 atm is ρwater = (1000 ± 1) kg/m3. We will use this value for the density of water for Part 2 through Part 5. That is, we assume a temperature in the lab of 4◦C! We will then experimentally determine the density of the tap water we used (Part 6) and compare it to the density of water at 20◦C. The density of pure water at 20◦C is: ρwater = (998.21± 0.01) kg/m 3 (11.3) When comparing the experimental densities of your objects or tap water, please use Table 1.1 provided at the end of Experiment 1: Measurement & Analysis on Page 8. 5 Part 2: Direct Measurement - Mass 7. Calibrate the triple beam balance. 8. Suspend the object (brass cylinder) from a string attached to the balance. 9. Partially fill the overflow container with water, then submerge the object. Do not allow the object to touch the container. Measure the apparent mass of the object in water, m�. Calculate F � g. m� brass: (2 pts) m� Al: (2 pts) m� wood: (2 pts) F � gbrass : (2 pts) F � gAl : (2 pts) F � gwood : (2 pts) 10. Determine FB for the object. How much less does it weigh in water than in air? FB = Fg − F � g FBbrass : (2 pts) FBAl : (2 pts) FBwood : (2 pts) 11. Calculate ρobj : ρobj = ρWFg FB ρbrass: (3 pts) ρAl: (3 pts) % Error: (3 pts) % Error: (3 pts) 6 Part 3: Displacement Method - Volume 12. Partially fill the graduated cylinder with water; take note of the water level. Use the pipette to fine-tune the meniscus. 13. Carefully submerge the object in water and determine the volume of water displaced by the object. Vbrass: (2 pts) VAl: (2 pts) Vwood: (2 pts) 14. Remove and dry the object, then empty the graduated cylinder and invert it on a paper towel to dry. 15. Determine FB on the object: FB = ρW gV FBbrass : (2 pts) FBAl : (2 pts) FBwood : (2 pts) 16. Calculate ρobj : ρobj = m V Use the volume determined from the displacement method and m, not m�. ρbrass: (3 pts) ρAl: (3 pts) % Error: (3 pts) % Error: (3 pts) Part 4: Aluminum Cylinder 17. Repeat Part 1 through Part 3 for the next object (aluminum cylinder). 18. Draw a free-body diagram for this object submerged in water. (5 pts) 7 Part 5: Buoyant Force - Floating Object 19. Although you need to modify or omit certain steps, repeat Part 1 through Part 3 for the wood cylinder: • Omit Step 6, Step 11, and Step 16. • Modify Step 9 and Step 13 Allow the wood object to float. 20. Draw a free-body-diagram for the wood object floating in water. (5 pts) Part 6: Density of Tap Water 21. For each metal object: Use the following equation and the graduated cylinder volume from Part 3 to determine the density of our tap water. m−m� V = ρW Using brass cylinder ρW : (3 pts) % Error: (3 pts) Using aluminum cylinder ρW : (3 pts) % Error: (3 pts)