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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
- the concept of density and how it influences floating,
- buoyancy and Archimedes’ principles,
- the importance of experimental studies and skills,
- the skills for data analysis and presentation, and
- 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
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:
- matter—anything that has mass and occupies space
- volume—the amount of space something takes up
- density—the amount of mass per one unit of volume of the material
- mass—the amount of matter in a substance
- weight—a measure of the heaviness of an object
- specific gravity—the ratio of the weight of an object to the weight of an equal amount of water
- displacement—the amount of water displaced by a floating or submerged body
- buoyancy—the capacity of an object to remain afloat in a liquid
- 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
- Law of floatation—a floating body displaces its own weight of the liquid in which it floats
- buoyant force—the upward-acting force on a body due to the pressure of the liquid in which it is fully or partially submerged
- center of gravity—the point at which the weight of the body is concentrated
- 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
W < FB Positive buoyancy
W = FB Neutral buoyancy G and B coincide at the geometric center of the body.
W > FB Negative buoyancy G and B coincide at the geometric center of the body.
From this principle, we can see that whether an object floats or sinks is based not only on its weight, but also the amount of water it displaces. That is why a very heavy ocean liner can float. It displaces a large amount of water.
Archimedes’ principle works for any fluid, but in this experiment, we are mostly concerned with water and a solution of salt and water. The salt particles dissolved in the water increase the density of the solution (the same volume has a greater mass). For example, a cubic foot of fresh water weighs approximately 62.4 pounds, while a cubic
W = weight The force of the weight acts downward through the center of gravity. The center of gravity (G) is located at the geometric center of the body (bottom of downward pointing arrow) for uniformly dense bodies
W
FB = buoyant force The buoyant force acts upward through the center of buoyancy. The center of buoyancy (B) is located at the geometric center of submerged part of the body (top of the upward pointing arrow).
FB
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
- How does the density relate to whether the can of soda floats or sinks?
Activity 2 Density of water
Procedure:
- Weigh your 100 mL graduated cylinder. Record the mass in Data Table 2. This will be your starting mass for all trials.
- 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.”
- Subtract the mass of the graduated cylinder from the mass of the graduated cylinder + water. Record this value in Data Table 2.
- Read the volume of water in the graduated cylinder. Record the volume in Data Table 2.
- Calculate the density of water. Record the density in Data Table 2.
- Repeat steps 2-5 using 75 to 80 mL of water.
- 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.
- Answer the questions below Data Table 2.
Data Analysis and Reporting:
Data Table 2 Note: 1 mL = 1 cm 3 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:
- What happens to mass as the volume increases? Explain this observation.
- What happens to density as volume increases? Explain this observation.
- What happens to the density of water as the temperature increases? Explain your reasoning for your answer.
Activity 3 Density and layering of salt solutions
Procedure:
- Use the procedure outlined in Activity 2 (Steps 2 through 6) to obtain the densities of the red and blue salt solutions provided. Record densities and your answers in Data Table 3.
- Add about 2 mL of the red solution to a small test tube. Carefully add about 2 mL of the blue solution using a dropper. Record your observations.
- Repeat step 2, starting with the blue solution on the bottom. Record your observations and answer the questions below Data Table 3.
Data Analysis and Reporting:
Data Table 3 Solution color
Mass of dry cylinder (g)
Mass of cylinder
Mass of solution (g)
Volume (mL)
Density (g/mL) Red
Blue
Questions:
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:
- Compare the 2 volumes for your block of wood. Are they equal? Explain what could cause a significant difference.
- Compare the 2 volumes for your block of foam. Are they equal? Explain what could cause a significant difference.
- Based on density should the block of wood sink or float? Explain your answer.
- Based on density should the block of foam sink or float? Explain your answer.
Activity 5 Make and sink clay boats
Procedure and questions:
- Use provided clay. Make it into a shape that you think will float. You may use any design you want.
- Add pennies until your vessel sinks. How many pennies did it take to sink your _vessel?______________
- 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:
- Seal any tears or openings in the upper end of the bag with a minimum of tape.
- Record room temperature
- Weight the bag
- The bag will be heated by blowing warm/cool air into it.
- Paper clips will be attached so that when released the bag neither rises nor sinks.
- Insert the thermistor from the bottom and record the temperature in the middle of the balloon.
- Weigh paper clips
- 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
- Which bag supported more weight? Why do you think this is so?
Instructor page
NATURE
Sunday Academy
Eugene Lehr (SBC), Heather Marxen (CCCC), and G. Padmanabhan (NDSU)
Activity 1: Answers to Questions
- Regular Coke sinks, Diet Coke floats.
- The one with a density greater than 1 g/mL sinks.
Activity 2: Answers to Questions
- Mass becomes greater. A larger amount of the same material has more mass.
- Density remains the same. This shows that density can be found using any (reasonable) amount of a given material.
- Consider 1 gm of water. It will occupy a larger volume at 70C compared to 40C because water will expand as the temperature increases. The mass remains the same. Therefore density will decrease as temperature rises from 40C to 70C. Water at 40C will be more dense.
Activity 3: Directions for mixing 10% and 20% salt solutions (Double or triple the recipe if your site needs more than 100 mL of each solution):
- Weigh out 10 g NaCl and add to 100 mL water. Stir or shake until all of the crystals dissolve. Color this solution blue using food coloring.
- Weigh out 20 g NaCl and add to 100 mL water. Be sure all of the crystals dissolve. Color this solution red.
- When layering the solutions, do not pour them together, but use eyedroppers or dispopipets. Tilt the test tube and have the mouth of the dropper right against the lower wall of the test tube. Have the students experiment to see if adding the solutions in a different order makes a difference.
Answers to Questions
- There is a separation, and this works both ways.
- The bottom layer is denser. The heavier layer sinks to the bottom. The lighter layer will buoy up due to buoyant force being greater than its weight.
Activity 4:
Small wood blocks will be supplied. Use 100 mL graduated cylinders to determine volume of the blocks experimentally. To determine volume, subtract initial volume measurement from final volume.
Answers to Questions
- The 2 values should roughly be the same. Differences could be due to spillage, errors in reading volumes or lengths, not submerging the block completely, etc.
- The block should float; it is less dense than water. .
Activity 5: Use Plastalina modeling clay, not pottery clay. It takes about 14 pennies to sink the vessel. The addition of pennies makes the weight great enough to overcome the buoyant force.
