Buoyancy (Ray Oja)

Title: Buoyancy, 8th Grade

Principle Investigated: Archimedes’ Principle - Any object, wholly or partially immersed in a fluid, is buoyed up by a force equal to the weight of the fluid displaced by the object.

California Science Content Standards Grade 8:

8. All objects experience a buoyant force when immersed in a fluid. As a basis for understanding this concept:

c. Students know the buoyant force on an object in a fluid is an upward force equal to the weight of the fluid the object has displaced.

d. Students know how to predict whether an object will float or sink.

Materials:

Demonstration 1-

Glass bowl

Dry pinto beans

Table tennis ball

Steel ball – similar in size to table tennis ball

Magic cloth

Demonstration 2-

1000 mL graduated cylinder

Egg

1 cup table salt

Stirring device

Demonstration 3-

Electronic balance

Erlenmeyer flask

Balloon

Baking soda

Vinegar

Small funnel

Procedure:

Demonstration 1-

a) fill glass bowl with dry pinto beans to a depth of 8 cm

b) bury table tennis ball in beans

c) show class – from a distance – the black steel ball and tell them you will change the ball from black to white

d) place ball on top of beans, cover bowl with the magic cloth

e) shake vigorously

f) remove cloth to reveal a single white ball resting on top of beans

Demonstration 2-

a) fill graduated with water to a level of 800 mL

b) slip egg into cylinder and allow to sink

c) slowly stir in 200 cm³ salt until egg floats to surface

Demonstration 3-

a) add 100 cm³ white vinegar to flask

b) use funnel to pour 100 cm³ baking soda inside balloon

c) without allowing baking soda to pour out of balloon, slip mouth of balloon over mouth of flask

d) place whole assembly on scale, note weight

e) lift body of balloon to pour baking soda into flask

f) after reaction has occurred and balloon has filled, weigh assembly again

g) note change in weight

Prior Knowledge:

Students should know how to measure mass, volume of liquids, and volume of regular and irregular solids.

Students should understand that density is determined by the mass and volume of a substance, and that D=m/V.

Students should understand that solids and fluids with higher density sink in fluids with lower density.

Explanation:

Demonstration 1- Following Archimedes’ principle, if a fluid or solid weighs more than the fluid it displaces, it will sink in that fluid. Although the quantity of pinto beans is not a fluid, the beans can be used to simulate a fluid. The beans are relatively small, and by shaking the container the beans move about, freely sliding past one another. This activity allows the much denser (than the combined density of the pinto beans and air in the bowl) steel ball to sink as if it were in a fluid, and the much less dense table tennis ball to float as if it were in a fluid. (The ratio of the densities of steel ball:beans:table tennis ball is approximately 100:10:1).

Demonstration 2- A typical egg has a density of 1.031 g/cm³, while water has a density of 1.0 g/mL. Therefore the egg sinks in water (since the egg density is greater than water, its weight will be greater than the weight of the water it displaces). When salt is added to the water, once dissolved it does not add significantly to the volume of the water, yet it does add significant mass. If the mass of the combined salt and water increases (compared to the straight tap water) while the volume remains unchanged, the density will also increase. After enough salt is added the density of the salt water surpasses the egg’s 1.031 g/cm³, and at this point the weight of the salt water displaced by the egg is greater than the weight of the egg. The upward buoyant force is then greater than the downward gravitational force, and the egg rises to the surface. At the surface, a small amount of the egg’s volume will rise above the water line until the weight of the still submerged egg volume exactly matches the weight of the water displaced by the still submerged egg volume, and the egg neither sinks nor rises further.

Demonstration 3- The balloon/flask assembly has a specific weight, mass and volume. The mass remains the same throughout the demonstration, but both the volume (and therefore the density) and the weight change due to the chemical reaction. When the baking soda (sodium bicarbonate or NaHCO₃) is mixed with the vinegar (acetic acid or CH₃COOH), CO₂ fills the balloon.

CH₃COOH + NaHCO₃ → CH₃COONa + H₂CO₃

That last product is carbonic acid which quickly decomposes into

carbon dioxide and water:

H₂CO₃ → H₂O + CO₂

Once the balloon is inflated, the total volume of the assembly increases. Increasing the volume also increases the buoyant force applied by the room air, since more room air is displaced. This additional upward buoyant force reduces the apparent weight of the assembly.

Questions and Answers:

Why does a steel ship float when the density of steel is much higher than the density of water?

The shape of a ship’s steel hull cradles a volume of air which greatly reduces the density of the whole unit. As the ship’s hull sinks down into the water, the weight of the fluid displaced by the ship eventually becomes equal to the weight of the ship’s structure and contents plus the weight of the air inside the hull. At this point the ship floats.

When an object is immersed in a fluid, why does the buoyant force only push up when there is fluid all around the object?

Actually, the fluid pushes on every surface of the object. The sideways forces created by the fluid pressure cancel out, and the pressure from above cancels some of the pressure from below. But because the pressure from below occurs at a greater depth where the cumulative pressure is greater, the pressure from above cancels only some of the pressure from below. The buoyant force we speak of is actually the net force on the object, and if the object is submerged in a fluid that is only being acted upon by gravity, the buoyant force is always opposite the gravitational force.

Why is the buoyant force equal to the weight of the fluid displaced?

If you push a block of wood into a bucket of water and fully submerge it, the block of wood will displace a volume of water equal to wood block’s volume. And that equal volume will be displaced upward. The water didn’t just get pushed aside, or pushed down. The water had to be lifted against the pull of gravity. Once the block is submerged, the volume of water will continue to be pulled downward by gravity, effectively trying to fill in the space the block is occupying by pushing it up and out of the way. There is pressure on the sides of the wood block, but these forces act all around the block and cancel each other out. If the block is pushed farther underwater there is pressure from the water above the block, but this is negated by the additional pressure (due to increased depth) from beneath the block, and the net force is again equal to the weight of the displaced water.

Applications to Everyday Life:

A hot air balloon floats because it is buoyed up by a force equal to the weight of the air displaced. The weight of this air, and therefore the upward force, is greater than the gravitational force acting on the hot air balloon because the air inside the balloon has been expanded by adding heat energy. This means there are fewer air molecules inside the balloon than in the same volume outside the balloon, which in turn means the balloon weighs less than the air it displaces. If it weighs less than the air it displaces, the buoyant (or upward) force is greater than the gravitational (or downward) force, and the balloon rises.

A submarine submerges by taking water into its ballast tanks and increasing its total weight. Once this new full-ballast weight of the submarine is greater than the weight of the fluid it displaces, it sinks. To remain at a particular depth the submarine adjusts its ballast tanks to make the total weight of the submarine match the weight of the water it displaces. To rise to the surface the water is pumped out and replaced by air, reducing the total weight of the submarine until it is lower than the weight of the water it displaces.

Due to hydrogen bonding liquid water molecules line up into hexagonal crystals as water solidifies. In water, this solid structure is less compact than when liquid, and therefore water expands as it freezes. This means that the same number of water molecules have a greater volume when solid compared to when liquid. So the weight of solid water (ice) is lower than the weight of the liquid water it displaces, and therefore ice floats.

Video Link:

Sinking/Floating Egg http://www.youtube.com/watch?v=fhiKdvXVIT4

References:

Bean demonstration-

Bean Buoyancy. Harvard University Natural Science Lecture Demonstrations.

http://www.fas.harvard.edu/~scdiroff/lds/NewtonianMechanics/BeanBuoyancy/BeanBuoyancy.html

2010, October 4.

Robert B. Prigo, Liquid Beans, TPT 26, 101, (1988).

Rolf G. Winter, On the Difference between Fluids and Dried Beans, TPT 28, 104 (1990).

Balloon Demonstration-

F2-13: Buoyancy - Expanding Balloon Conundrum. The University of Maryland Physics Lecture-Demonstration Facility. http://www.physics.umd.edu/lecdem/services/demos/demosf2/f2-13.htm

2010, October 6.

Archimedes’ Principle-

Buoyancy. Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Buoyancy

2010, September 28.

Ice-

Ice. Wikipedia, The Free Encyclopedia. http://en.wikipedia.org/wiki/Ice

2010, October 8.

Egg Density-

SpringerLink. Biomedical and Life Sciences.

http://www.springerlink.com/content/k1122vgx60768454/

2010, October 6