Principles of Buoyancy: Understanding Density and Archimedes' Principle, Study notes of Law

Download Principles of Buoyancy: Understanding Density and Archimedes' Principle and more Study notes Law in PDF only on Docsity! 1 NATURE Sunday Academy Still Floating Eugene Lehr (SBC), Heather Marxen (CCCC), and G. Padmanabhan (NDSU) Frank Martin (SBC) Description: In this Sunday Academy session, students will learn the principles that cause some objects to float and other objects to sink. The mathematics and science of floating will be explored. Methods of conducting some experiments and data analysis will be introduced. Real-life examples such as ships, boats, and canoes will be related. Concepts of density, buoyancy, and Archimedes’ principle will be the focus. Objectives: Objectives of this session include learning 1. the concept of density and how it influences floating, 2. buoyancy and Archimedes’ principles, 3. the importance of experimental studies and skills, 4. the skills for data analysis and presentation, and 5. the connection between the topic and real-life engineering designs. Standards covered: 9-10.2.2.Use appropriate safety equipment and precautions during investigations 9-10.2.3. Identify questions and concepts that guide scientific investigations 9-10.2.7.Maintain clear and accurate records of scientific investigations 9-10.2.8.Analyze data found in tables, charts, and graphs to formulate conclusions 11-12.3.8.Identify the principles and relationships influencing forces and motion Session Organization: 11:00-11:30 Introduction and Cultural relevance 11:30-12:00 PowerPoint presentation 12:00-12:30 Lunch 12:30-3:30 Hands-on activities and classroom discussion 2 Cultural Connection: North American rivers and streams were an essential mode of transportation for Native Americans. The principal of buoyancy was used in the construction of Canoes and other Native American transport. Vocabulary: 1. matter—anything that has mass and occupies space 2. volume—the amount of space something takes up 3. density—the amount of mass per one unit of volume of the material 4. mass—the amount of matter in a substance 5. weight—a measure of the heaviness of an object 6. specific gravity—the ratio of the weight of an object to the weight of an equal amount of water 7. displacement—the amount of water displaced by a floating or submerged body 8. buoyancy—the capacity of an object to remain afloat in a liquid 9. Archimedes’ principle—any object, wholly or partly immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object 10. Law of floatation—a floating body displaces its own weight of the liquid in which it floats 11. buoyant force—the upward-acting force on a body due to the pressure of the liquid in which it is fully or partially submerged 12. center of gravity—the point at which the weight of the body is concentrated 13. center of buoyancy—the point at which the buoyant force is concentrated Equipment and Supplies Needed: Balance Regular soda Water Diet soda 10% salt solution (blue) Small test tubes 20% salt solution (red) Wood block Ping pong ball Masking tape Golf ball Pennies Ball of clay (Plastalina) Bucket Graduated cylinder (100mL, 10mL) Beaker Meter stick or ruler (cm) Calculator Eye droppers or dispopipets dry cleaning bag Paper clips Thermistor Blow dryer Scotch tape 5 foot of salt water weighs approximately 64 pounds. The extra weight is because of the dissolved minerals in salt water. If an object, one cubic foot in volume and weighing 63 pounds, is placed into fresh water and completely submerged, the object displaces 62.4 pounds of water, but weighs 63 pounds. This object will be negatively buoyant—it will sink. However, it is being pushed up with a force of 62.4 pounds, so if it were weighed in water, it would only weigh 0.6 pounds. If the same object were placed in salt water, it would still weigh 63 pounds, but would be pushed up by a force of 64 pounds, and it would float. It would be positively buoyant in salt water. To make the object neutrally buoyant, one pound of weight would have to be added to the object without changing its size (without changing its water displacement). Then, it would weigh 64 pounds, and be buoyed up with a force of 64 pounds, thus being neutrally buoyant. Density is determined by dividing the volume of an object into its mass; see the circle formula below. (Mass is the amount of matter an object has. Weight, on the other hand, is the mass of an object times the force of gravity; weight measures an object’s heaviness.) Another way to state Archimedes’ principle is to say that a solid object will sink in a fluid if its density is greater than the fluid’s density, and the object will float if its density is smaller than that of the fluid. This explains why wood and styrofoam float on water, but steel and concrete sink. It also explains why it is possible to make boats out of steel or even concrete. As long as there are portions of the boat below the surface of the water that are hollow (contain air), the effective density of the boat can be less that that of water, even though the real density of the material is greater. To use the circle formula, cover the letter representing the quantity you want to calculate (D = density, M = mass, V = volume). The letters that remain are in the correct positions for you to do the calculation. For example, if you want to calculate density, cover the D in the formula. You will be left with M over V, so you will divide mass by volume. If you want to calculate M, cover the M. The remaining letters are D next to V, so you will take density times volume. D M V 6 Archimedes’ principle is helpful for determining the volume of an irregular object. The volume of displaced fluid is exactly equal to the volume of the submerged object. By weighing the irregular object in air and in water and knowing how much one unit volume of the fluid weighs, it is possible to calculate the volume of the irregular object. Think about this to make sure you understand the method and why it works. Activity 1 Coke and Diet Coke Procedure: 1. Each group should have a can of Coke and a can of Diet Coke. Predict what will happen if these cans are placed in a bucket of water (will the can of soda sink or float). Record your prediction in Data Table 1. 2. Weigh both cans of soda separately and record the masses (in grams) in Data Table 1. 3. Place both cans of soda into the bucket of water and record your observations in Data Table 1. 4. Record the volume (in mL) given on the can in Data Table 1. Calculate the density of both cans of soda. Record your results in Data Table 1. 5. Get the density of Coke and Diet Coke from another group and calculate the average for each. Record your results in Data Table 1. 6. Answer the questions below the data table. Data Analysis and Reporting: Data Table 1 Prediction Observation Mass (g) Volume (mL) Density (g/mL) Density from other group Average Coke Diet Coke Note: 1 mL = 1 cm3 Questions: 1. Did your observation agree with your prediction about whether the cans of soda would float or sink? Explain your observation. 7 2. How does the density relate to whether the can of soda floats or sinks? Activity 2 Density of water Procedure: 1. Weigh your 100 mL graduated cylinder. Record the mass in Data Table 2. This will be your starting mass for all trials. 2. Add between 25 and 30 mL of water to your graduated cylinder, then weigh it again. Record this value in Data Table 2, in the column labeled “Mass of cylinder + water.” 3. Subtract the mass of the graduated cylinder from the mass of the graduated cylinder + water. Record this value in Data Table 2. 4. Read the volume of water in the graduated cylinder. Record the volume in Data Table 2. 5. Calculate the density of water. Record the density in Data Table 2. 6. Repeat steps 2-5 using 75 to 80 mL of water. 7. Repeat steps 2-5 twice using 75 to 80 mL of water. Record the temperature of the water. Use “hot” water for trial 3 and “cold” water for trial 4. 8. Answer the questions below Data Table 2. Data Analysis and Reporting: Data Table 2 Note: 1 mL = 1 cm3 Mass of dry cylinder (g) Mass of cylinder + water (g) Mass of water (g) Volume (mL) Density Temp Trial 1 (25-30 mL) X Trial 2 (75-80 mL) X Trial 3 (75-80 mL) Trial 4 (75-80 mL) Questions: 1. What happens to mass as the volume increases? Explain this observation. 10 Wood Block (water disp.) Water + block___________ Water alone_____________ V(block)________________ Foam Block (calculated) Foam Block (water disp.) Water + block___________ Water alone_____________ V(block)________________ Length(l)__________ Width(w)__________ Height(h)_________ V = l  w  h V = _______________ Questions: 1. Compare the 2 volumes for your block of wood. Are they equal? Explain what could cause a significant difference. 2. Compare the 2 volumes for your block of foam. Are they equal? Explain what could cause a significant difference. 3. Based on density should the block of wood sink or float? Explain your answer. 4. Based on density should the block of foam sink or float? Explain your answer. 11 Activity 5 Make and sink clay boats Procedure and questions: 1. Use provided clay. Make it into a shape that you think will float. You may use any design you want. 2. Add pennies until your vessel sinks. How many pennies did it take to sink your vessel?_____________ 3. Use the principles of density and buoyancy to explain why your vessel sank. Activity 6 Hot Air Balloon Supplies: dry cleaning bags, several small paper clips, scotch tape, heat source Procedure: 1. Seal any tears or openings in the upper end of the bag with a minimum of tape. 2. Record room temperature 3. Weight the bag 4. The bag will be heated by blowing warm/cool air into it. 5. Paper clips will be attached so that when released the bag neither rises nor sinks. 6. Insert the thermistor from the bottom and record the temperature in the middle of the balloon. 7. Weigh paper clips 8. Repeat steps 4-7 using “hot setting”. “Warm” bag Mass of Bag (g) Mass of paper clips (g) Combined mass of balloon and clips (g) Room Temperature (C) Bag Temperature (C) Room-Bag temperature difference “Hot” Bag Mass of Bag (g) Mass of paper clips (g) Combined mass of balloon and clips (g) Room Temperature (C) Bag Temperature (C) Room-Bag Temperature difference 1. Which bag supported more weight? Why do you think this is so? 12 2. Do you think a hot air balloon would be more buoyant on a hot day or a cool day? Explain your answer. Activity 7 Buoyancy online (time permitting) 1. Go to website https://www.planetseed.com/node/19120 Find out the following combinations: A. What are the only two materials that sink in Bromine? B. What is the only material to sink in Mercury? C. Only Pine, Oak and Balsa float in __________. D. What materials float in honey but not in Corn Syrup?