School Science Lessons
UNPh11
2018-11-10
Please send comments to: J.Elfick@uq.edu.au

11. Density
Density, buoyancy, Archimedes' principle, floating, fluid density, fluid pressure, hydrometers
Table of contents

11.4.0 Buoyancy, Archimedes' principle, floating

11.5.0 Density of air

Density of gases (Table)

11.2.0 Density of liquids

11.1.0 Density of solids

See: Density (Commercial)

10.2.0 Hydrometers, relative density, RD

11.4.0 Buoyancy, Archimedes' principle, floating

See: Buckets, (Commercial)

11.4.0 Archimedes' principle

10.5.1 Archimedes and the gold crown of King Hiero
Experiments
11.4.8 Archimedes' principle experiment
11.4.01 Buoyancy
11.4.9 Archimedes' bucket and cylinder experiment
11.4.2.0 Buoyancy of air with a balloon
11.4.1.0 Buoyancy of water
4.201 Cartesian diver
11.4.1.1 Centre of buoyancy and centre of gravity of a boat
4.243 Cold air is heavier than warm air, inverted paper bag balance
11.4.23 Dancing rice grains
11.4.24 Dancing sultanas
11.4.6.2 Density of different liquids
4.202 Density of irregular solid, overflow can
4.210 Diving bell
4.208 Drinking straw hydrometer
11.4.6.4 Equidensity drops
11.4.11 Estimate the load of a boat
11.4.17 Finger in glass of water
11.4.6.0 Float cork, wax and wood in different density liquids
11.4.4 Float corks in a glass jar
4.205 Float different kinds of wood
4.206 Float eggs in water
4.207 Float grapes at different levels in water
11.4.1.1 Float ice cubes
4.212 Float iron ball in mercury
4.204 Float lighted candles
4.211 Float metal boats, Plimsoll line
4.213 Float needles on water, float metals
11.4.5 Float oil spheres
4.214 Float razor blades on water
11.4.19 Float oranges
11.4.02 Flotation
9.0 Floating (Primary)
11.4.3 Floating, sinking and rising under liquid
11.4.18 Floating square bar
11.4.03 Fluid density
11.4.04 Fluid pressure
11.4.2.1 Lifting power of hydrogen compared to helium
11.4.6.1 Liquids float on liquids, miscible and immiscible liquids
11.4.21 Measure specific gravity of fluids
11.4.7 Model diving bell, model submarine, diving bottle
11.4.12 Plimsoll line, load lines
11.4.20 Reaction balance
11.4.22 Spherical oil drop
11.4.11.1 Stone in a boat
11.4.05 Water-resistant, waterproof
11.4.10 Weigh block in air and in water
4.203 Weight of a floating body
11.4.14 Weight overboard

11.2.0 Density of liquids
See: Density (Commercial)
11.2.0 Density of liquids, relative density, RD, density bottle
11.4.6.3 Density ball
11.2.5 Density of cola and diet cola
11.4.6.2 Density of different liquids
11.2.1 Density of liquids using mass and volume
11.1.1 Density of liquids with U-tube, balancing columns
11.2.3 Density of ice
11.2.4.0 Float an ice cube
11.2.4.1 Float an ice cube in oil over water
11.4.6.4 Equidensity drops
11.2.2 Maximum density of water
3.26 Separate two immiscible liquids of different density
4.31 Temperature of water at maximum density, 4oC

11.1.0 Density of solids
See: Density, blocks, cubes, equal mass, (Commercial)
11.1.0 Density of solids
4.12 Density of solids
11.1.4 Density of beans
11.1.5 Density of boy
11.1.3 Density of irregular solid, not using volume
11.1.2 Density of irregular solid, using mass and volume
4.202 Density of irregular solids, overflow can
3.27 Separate solids using density differences

11.5.0 Density of air
See: Balloons, balloons helium chart, (Commercial)
11.3.20 Density of air with a balloon
11.3.22 Density of Freon and air, with a balloon
11.3.19 Density of hot air and cold air
11.3.21 Equidensity bubbles
4.229.1 Mountain sickness and hyperventilation

11.1.0 Density of solids
Density is a measure of the compactness of a substance, expressed as its mass per unit volume.
Density is measured in kilograms per cubic metre, symbol ρ (rho).
However, this document may use "d", but some authorities use "d" for relative density.
So this document used "RD" for relative density, and "SG" for specific gravity.
In SI units, measure density in kg m-3, e.g. density of dry air at sea level = 1.29 kg / m3.
For example, Iron 7.9 × 103kg / m3, Gold 19.3 × 103kg / m3.
Density of metals
Examples of the densities of elements, in g cm-3, are as follows: aluminium: 4.70, copper: 8.92, gold: 19.30, iron: 7.86. lead: 11.30,
magnesium: 1.74, mercury: 13.60, nickel: 8.90, platinum: 21.40,
silver: 10.50, zinc 7.14.
The five metals with the greatest density are as follows: Osmium 22.6 g/cc, Iridium 22.4 g/cc, Platinum 21.45 g/cc, Rhenium 21.2 g/cc, Uranium 20.1 g/cc Experiment 1. Measure the density of examples of different metallic substances, then decide whether they are pure substances.

2. To find the density of a regular solid, use a balance to measure the mass, measure its linear dimensions and calculate its volume.

3. To find the density of a regular floating solid, e.g. block of wood, calculate the density as above or float the block and compare
the depth of immersion, h1 with the complete dimension, h2.
The relative density = h1 / h2.

11.1.1 Density of liquids with U-tube, balancing columns
See diagram 11.1.1: U-tube
1. U-tubes can be 50-70 cm in height and are mounted on wood with a length of metre rule fixed to the wood.
The relative density of a liquid, e.g. methylated spirits, is shown by pouring water into one arm and noting the depth on the metre rule,
then pouring the methylated spirits into the other arm so that it has exactly the same depth as the water.

2. Clamp an U-tube in an upright position.
Pour in some liquid of greater density to about the depth shown in the diagram.
With the aid of the glass rod, introduce a quantity of the less dense liquid.
Using a 50 cm ruler and a set square, measure the heights h1and h2 of the free surfaces of the liquids above the surface of separation.
Calculate the density of the unknown liquid.
The pressures at any two points in the same horizontal line in a liquid at rest are the same.
Pressure depends on depth.
Po+ d1gh1 = Po + d2gh2, where Pois atmospheric pressure, d1 is the density of one liquid, d2 is the density of the other of the liquid.
Then d1h1= d2h2.
So the density of the unknown liquid, d2= d1h1 / h2.

3. Mercury is not permitted in schools except in some school systems where it is allowed only in barometers and thermometers.
Repeat the experiment for different values of h1and h2 by using a less dense liquid and then calculate the density.
An U-tube contains mercury.
Water, relative density 1, is poured into one arm of the U-tube and oil, relative density 0.8, is poured into the other arm until the
mercury columns in the arms of the U-tube are level.
If the height of the water is 15 cm, the height of the oil is 18.8 cm.

4. Find the relative density of mineral turpentine, a liquid immiscible with water.
Pour water into one arm of the U tube and the turpentine into the other arm until their levels are equal.
Then relative density of the mineral turpentine is given by the appropriate ratio of the column heights about the level XY.

5. Find the relative density of methylated spirits, a liquid miscible with water.
Pour mercury into the U-tube so that is has the same few centimetres height in both tubes.
Pour water into one arm of the U tube and the turpentine into the other arm so that the mercury levels are the same.
The relative density of the methylated spirits is obtained from the ratio of column heights.
[This experiment is no longer done in schools because free surface mercury is not permitted in schools except in some school systems
where it is allowed in barometers and thermometers.]

11.1.2 Density of irregular solid, using mass and volume
Use a beam balance to weigh mass of an irregular solid.
Record the mass, m.
Pour water to about half depth of a measuring cylinder.
Record the volume, V1.
Put the solid into water in the cylinder.
Read the scale and record the volume, V2.
Calculate the density of the irregular solid.
Volume of the solid = (V2- V1).
The irregular solid's density = mass / volume.
So the density of the irregular solid, d = m / (V2 - V1)
Repeat the above steps then calculate the average density.

11.1.3 Density of irregular solid, not using volume
See diagram 11.1.3: Density of irregular solid
Tie around an irregular solid a thin and strong string and tie a loop at the other end of the string.
Use the loop to weigh the irregular solid with a spring balance in air.
Read the scale and record the weight, w1.
Use the loop to weigh the irregular solid with a spring balance with the solid immersed in
water.
Read the scale and record the weight, w2.
To calculate the density of the irregular solid, the buoyant force on the solid = mass of water displaced × gravitation acceleration,
i.e. (Fb = mwater, g = rwater × Vwater × g)
However, buoyant force also equals the difference between the two weights measured, so buoyant force = w1 - w2.
So w1 - w2 = (rwater × Vwater × g), Vwater= Vsolid., Vsolid= msolid /rsolid.
So (w1 - w2)= (rwater × msolid / solid × g).
msolid × g = w1.
So (w1 - w2)= (rwater × w1 /rsolid)
Density water = 1 kgm-3, then rsolid= w1 / (w1 - w2)

11.1.4 Density of beans
Use beam balance to weigh a dry, empty bottle with a stopper.
Record the mass of the empty bottle, m1.
Pour in the beans to about one third depth of the bottle and weigh again.
Record the mass of the bottle with beans, m2.
Fill the remaining space in the bottle with water.
o prevent the beans from absorbing water and expanding, use cold water and work as quickly as possible.
Shake gently to remove air bubbles.
Plug the stopper.
Wipe away excess water and then weigh again.
Record the mass of the bottle with beans and water, m3.
Empty the bottle and then clean it with water.
Fill the bottle with water, plug the stopper, wipe dry and then weigh again.
Record the mass of the bottle with water, m4.
Calculate the relative density of beans.
Mass of beans = m2- m1,
Mass of water filling bottle = (m4- m1),
Mass of water filling the space left by the beans = (m3- m2),
Mass of water equal volume to the beans = (m4- m1) - (m3- m2)
RD of beans = (m2 - m1) / ([m4 - m1] - [m3- m2]), i.e. the mass of the beans divided by the mass of an equal volume of water.

11.1.5 Density of boy
Weigh a boy.
Half fill a tub with a known volume of water.
Mark the level of water in the tab, level 1.
Put the boy in the tub and press him under the water with a thin stick.
When the boy stops moving under water, mark the level of the water in the tub, level 2
Let the boy leave the tub slowly to catch any drips.
Note whether the level has water in the tub has returned to level, if not fill the tub to level 1.
Add a measured volume of water to the tub until it reaches level 2.
Volume of the boy = (level 2 - level 1).
Density of the boy = weight of the boy / (level 2 - level 1)

11.2.0 Density of liquid, relative density, RD, density bottle
See: Density (Commercial)
See diagram 11.2.0: Density bottle
Relative density, RD (formerly specific gravity, SG), is the ratio of mass of a volume of a substance to the mass of an equal volume
of water, at 4oC.
Relative density has no units because it is a ratio:
Petrol (r.d. 0.70), Ethanol (r.d. 0.79), Ice (r.d. 0.90), Olive oil (r.d. 0.92),
Water (r.d. 1.00),
Sea water (r.d. 1.03), Glass (r.d. 4.50), Mercury (r.d. 13.60), Gold (r.d. 19.30).
Carbonated water used in "fizzy drinks, aerated water, has a higher density if the gas is dissolved in the water, but a lower density
if the dissolved gas forms bubbles.
However, the difference can only be detected in distilled water.
Similarly, sea water has a density of about 1.025 kg / litre.
The density of water is close to 1 g per cc (1g cm-3), so you can compare the density of substance with the density of water as
relative density, RD.
Relative density (formerly specific gravity, G), is the ratio of mass of a volume of a substance to the mass of an equal volume of water,
at 4oC.

1. A special bottle called a density bottle, gives an accurate measure of relative density.
Let mass of empty density bottle = A,
Mass of bottle + liquid = B,
Mass of liquid = (B - A),
Mass of bottle + water = C,
Mass of water = (C - A).
Relative density = (B - A) / (C - A).

2. If weight of an empty 50 mL density bottle is tared out to zero and weighings are made when the bottle is full of the liquid, w1, and
water w2, relative density = w1 / w2.
Experiment
Weigh a density bottle with the liquid inside.
Pour the liquid into a graduated cylinder to find the volume of the liquid.
Use a balance to find the mass of the container and the mass of liquid transferred to the measuring cylinder.
Obtain the density by dividing the mass of the liquid by the volume.
The density of water is close to 1 g per cc, cm3, so you can compare the density of substance with the density of water as relative
density.

3. Weigh a small container with the liquid inside.
Pour the liquid into a graduated cylinder to find the volume of the liquid.
Use a balance to find the mass of the container and the mass of liquid transferred to the measuring cylinder.
Obtain the density by dividing the mass of the liquid by the volume.
The density of water is close to 1 g per cc, cm3, so you can compare the density of substance with the density of water as relative density.
Relative density (formerly specific gravity) is the ratio of mass of a volume of a substance to the mass of an equal volume of water, at 4oC.
Relative density has no units because it is a ratio: petrol (r.d. 0.70), ethanol (r.d. 0.79), ice (r.d. 0.90), olive oil (r.d. 0.92), water r.d. (1.00),
sea water (r.d. 1.03), glass (r.d. 2.50), mercury (r.d. 13.60), gold (r.d. 19.30).

4. Use a special bottle, called a density bottle, to find an accurate measure of relative density.
Let mass of empty density bottle = A,
mass of bottle + liquid = B,
mass of liquid = (B - A),
mass of bottle + water = C,
and mass of water = (C - A).
So relative density = (B - A) / (C - A).
Use a small bottle to measure the density of different liquids.
A more convenient way to measure the density of a liquid is to use a hydrometer.

5. Find the density of a cola drink in an aluminium drink-can.
Weigh the full aluminium can.
Open the aluminium can and drink the cola.
The weight of the aluminium can is approximately 13 g.
The volume of the cola is written on the side of the aluminium can, e.g. 375 mL or 355 mL (12 oz).
Calculate the density of the cola.
Density = weight of unopened can of cola - 13 g / volume of cola mL.
Repeat the experiment with "diet" cola where sugar is substituted by a chemical sweetener, e.g. phenylalanine, aspartame.

11.2.1 Density of liquid using mass and volume
See: Density (Commercial)
Weigh a small container with the liquid inside.
Pour the liquid into a graduated cylinder to find the volume of the liquid.
It will not matter if any of the liquid sticks to the side of the container.
Use a balance to find the mass of the container and find the mass of liquid transferred to the measuring cylinder.
Obtain the density by dividing the mass of the liquid by the volume.

11.2.2 Maximum density of water
See: Density (Commercial)
See: Salinity, (Commercial)
Maximum density of water, negative expansion coefficient of water, "anomalous" properties of water
11.2.2a Experiments
See diagram 11.2.2: Density of ice and water depends on temperature
1. Ice has a larger volume than the original volume of water before it freezes.
Water has a maximum density at 4oC.
When water cools from room temperature to 4oC, it is contracting in volume.
Most solids are denser than their liquids, but when water is cooled from 4oC to 0oC, its volume expands.
At 4oC, the density of water is 1000 kg m-3.
At 0oC the density of water is 999.87 kg m-3 and the density of ice is 918 kg m-3.

2. The lower density of ice is caused by the formation of a hydrogen-bonded tetrahedral network of water molecules.
The temperature at which water remains liquid decreases with salinity.
Some people refer to the "anomalous" properties of water when its volume increases by about 9% on freezing.
The "anomalous" properties can be explained by how the size of the oxygen atom and its nuclear charge affects the electronic
charge cloud of the hydrogen atoms bonded to it to form larger hydrogen bond aggregates.
Above 4oC, the vibration of the O-H bonds is enough to move the water molecules apart.
Another "anomalous" property of water is its high boiling point.
Most molecules show an increase in boiling point with molecular weight, although this relationship is complicated by the shape of the
molecule.
In water, hydrogen bonding keeps the molecules in a liquid state until 100oC.
However, if water behaved as a normal polar molecule, at its molecular weight it would boil at about -100oC.
In that case, the water around us would exist only as a vapour, not a liquid.
It takes a lot more kinetic energy at increased temperature to break the hydrogen bonds to free the water molecules as the gas.
This high boiling point effect is also seen with fluorine and nitrogen.

3. A freezing mixture of ice and common salt (sodium chloride), may drop to -20oC.
In freshwater lakes, during the summer the upper levels are heated by the sun to form a less dense layer, called the epilimnion, above
the cooler more dense layer, the hypolimnion, where anaerobic conditions may occur.
During autumn, the epilimnion cools and mixes with the hypolimnion causing overturn and churning up of nutrients towards the surface.
Algae may use these nutrients to cause algal blooms.

4. If you bore a hole through the surface ice of a frozen river and catch a fish through the hole, the fish will freeze to death when you
pull it up became it has been living at a temperature between 0oC and 4oC.

5. During freeze thaw, erosion of rocks, water enters cracks in the surface of rocks, freezes in cold weather, then expands in warmer
weather and splits off a piece of the rock, a form of weathering.

6. In countries where milk is delivered to front door steps overnight, on very cold nights the metal foil top of the milk bottle may lift up
and the bottle may even shatter because of the expansion of the milk as it freezes.
In very cold weather, freezing water can expand in water pipes and burst them.

11.2.2a Experiments
Maximum density of water
This is a dangerous experiment!
However, it gives a lesson to children to never put a sealed glass container in the refrigerator freezer!
1. Fill a screw-capped glass bottle with water and put the cap on securely.
Wrap the bottle securely in a plastic bag, to prevent the shattered glass from falling.
Put the bottle into the freezing compartment of a refrigerator.
After 24 hours, remove the bottle and examine it.
The bottle may be cracked or shattered, because of pressure from the expanding ice.

2. Put a large piece of ice into a glass of water.
Arrange two thermometers so that they measure the temperatures near the top and the bottom of the water.
The water cooled by the ice falls to the bottom.
This fall continues until the water at the bottom of the glass reaches a temperature of 4oC.
The water stays at this temperature for a long time, the colder water remaining higher up near the ice.
So water at 4oC is denser than the water at 0oC.
So a pond freezes from the surface downwards while the bottom seldom falls below 4oC.

3. Use two identical plastic drinking cups or a plastic ice cubes tray.
Fill the first cup with tap water at room temperature so that the water heaps up to form a meniscus.
Put the second cup in the freezing compartment of the refrigerator then add extra water to the cup to get the highest possible meniscus.
When the water in the cup is frozen, compare the meniscus of the frozen water with the meniscus at room temperature.
The frozen water heaped up because it had expanded.
Water has a maximum density at 4oC.
When water cools from room temperature to 4oC, it contracts in volume.
When water cools from 4oC to 0oC, it expands in volume.
At 4oC the density of water is 1000 kg m-3 (1 g per cc).
At 0oC the density of water is 999.87 kg m-3 and the density of ice is 918 kg m-3, so ice floats on water.
Repeat the experiment with a flat plastic tray full of water.
When the water heaps up to form ice it forms a rough ridge in a general north-south direction.
Some people claim that the heaping up is in a north south direction is due to the Coriolis effect!

4. Use a flask with a narrow stem to show volume changes and a thermocouple to show temperature changes when water is allowed
to warm from 0oC.
Immerse a water thermometer in an ice bath.
Water at the bottom of a cylinder remains at 4oC when surrounded by ice at the middle.

5. Find the temperature at which water attains its maximum density.
Fix two thermometers so that they measure the temperatures near the top and the bottom of a large beaker of water.
Put a large block of ice into the beaker.
The ice floats on the water as the density of ice is 0.91 kg / m3, i.e. less than the density of water.
Note any changes in temperature of water until the temperature of water at the bottom remains constant.
At first, the water near the floating ice is cooled by it and sinks towards the bottom of the beaker until the temperature of water at the
bottom reaches 4oC.
The water at the bottom will stay at this temperature for a long time with water colder 4oC remaining higher up near the ice because
water at 4oC than the temperature of melting ice at 0oC.
This unique behaviour of water explains why a pond or river freezes from the surface downwards while the water at the bottom
seldom falls below 4oC.

6. Put a large piece of ice into a glass of water.
Arrange two thermometers so that they measure the temperatures near the top and the bottom of the water.
The water cooled by the ice falls to the bottom.
This fall continues until the water at the bottom of the glass reaches a temperature of 4oC.
The water stays at this temperature for a long time, the colder water remaining higher up near the ice.
So water at 4oC is denser than the water at 0oC.
This curious behaviour of water is of great practical significance in nature, and explains why a pond freezes from the surface
downwards while the bottom seldom falls below 4oC.
So the floating ice insulates the water below from very cold atmospheric temperatures.

7. Add tap water to a cylindrical cup until the water surface is above the rim of the cup and the water will almost flow out.
Measure the vertical height from the bottom of the cup to the surface of the water in the cup and measure the temperature of the water.
Put the cylindrical cup in the freezer compartment of a refrigerator and leave it there for a few days.
Take the cup out of the freezer compartment and measure the vertical height from the bottom of the cup to the surface of the water
in the cup.
Also, you may note the temperature in the freezer, if you have a refrigerator thermometer.
The ice surface is higher than the original water surface at the rim of the bottle.
Water at 4oC has its highest density, 1g / cm3.
When the water cools to the temperature of 4oC, the density of the water increases, so that the volume of the water decreases.
When water cools from 4oC to 0oC, the intermolecular distance elongates so the volume of the water expands.
The density of water at 0oC is 0.99987 g / cm3.
In winter, water pipes may burst when the temperature of water in a full pipe lowers from 4oC to 0oC.

9. Examine the water in deep ponds may remain unfrozen throughout winter when the air temperature is below 0oC.
Water has a maximum density at 4oC.
When water is cooled, the temperature being above 4oC the density increases as the temperature is lowered.
However, but at 4oC water has its maximum density, and when cooled further the water expands instead of contracting, and so the
density decreases.
At 0oC water freezes to ice and expands on solidifying, so that ice is less dense than water, and floats on water.
The pond is cooled from above, so as the temperature falls the water at the top becomes denser than the water below, and so falls,
so that the warmer water rises to the top, is cooled, and falls in its turn, thus convection currents are set up, and the temperature of
the pond is kept sensibly uniform.
However, at 4oC water has its maximum density and so on further cooling a decrease in density occurs and the water at the top
becoming less dense than that below, convection currents cease.
As the temperature of the air falls, the temperature of the surface falls also, until at 0oC. ice forms.
Ice and water are bad conductors of
heat, and so the temperature of the water deep down in the pond is higher than that of the surface layer, and even when the surface
has been cooled well below 0oC, the bulk of the water in the pond will be at a temperature above 0oC.

11.2.3 Density of ice
See: Ice Model (Commercial)
Prepare ice cubes, some with food colouring, e.g. cochineal.
The ice cubes must be completely frozen and not have unfrozen water trapped inside.
Put equal volumes of water and vegetable oil in a measuring cylinder, the water in first.
Check that the two layers of water and oil are completely separated.
Carefully lower an ice cube into the oil and watch it float in the oil.
As the ice cube melts, the melt water trickles down the side of the ice cube, sinks through the oil and joins the water layer below.
Repeat the experiment with an ice cube stained with food colouring.
Watch the movement of the coloured water droplets and note whether the coloured water merges with the water below or makes a
separate coloured water layer below the water.
The density of ice is slightly below 0.92 g per cm2 and the density of a vegetable oils is slightly above this value.
The density of water is about 1 g per cm2.

11.2.4.0 Float an ice cube
See: Ice Model (Commercial)
1. Observe an ice cube floating in a jar of water.
Fill the jar completely with water and place the jar on absorbent paper.
Measure the proportion of the ice cube above the surface of the water.
Observer the melting ice cube and note any overflow onto the absorbent paper.
Again measure the proportion of the ice cube above the surface of the water.
The water level in the jar does not change as the ice melts.

2. Repeat the experiment with an ice cube floating in salty water.
The ice cube floats higher in the salty water.
Observe any overflow of salty water + ice cube water.
The icebergs that float in the antarctic ocean come from ice formed on the land, so they are composed mainly of fresh water.
So while the amount of salty sea water displaced by the iceberg is equal to the weight of the iceberg, the volume of melted fresh water
will be slightly higher than the displaced sea water, so the sea water level will rise when all the icebergs melt.

11.2.4.1 Float an ice cube in oil over water
See: Ice Model (Commercial)
Use a gas beaker half full of water and vegetable oil.
Add an ice cube.
Note the level at which the ice floats.
The ice cube should float with the top above the upper level of the vegetable oil, so use a vegetable oil that is dense enough.
Most vegetable oils have density 0.91 - 0.93 g / mL.
The temperature of a melting ice cube is 0oC and the temperature of the oil and water in the beaker is the room temperature, the
standard being 25oC.
Also, for this experiment the lower level of the ice cube should be well above the lower level of the vegetable oil, so use sufficient
volume of vegetable oil.
Examine the surface of the ice cube as it melts.
Some teachers ice cubes containing a dye.
The density of the ice is less than the density of the vegetable oil, so when the ice melts the melt water runs down the sides of the ice
cube and collects below it as a downwards pointing drop.
As the drop gets bigger, it may weigh down the ice cube.
This water drop remains suspended below the ice cube because it is covered below by a layer of vegetable oil and sits at the
interface between the oil and water.
Eventually, the oil drop becomes so heavy that the water bursts through the layer of oil and, being colder and more dense than the oil
and water below, plunges down to the bottom of the beaker.
If a dyed ice cube is used, the water will develop an even colour after some time.

11.2.5 Density of cola and diet cola
See: Density (Commercial)
1. Put an unopened can of cola and an unopened can of the same brand of diet cola in a large container of water.
The cans have the same volume.
The can of diet cola floats, but the can of cola sinks.
Cola contains sucrose, but diet cola contains a sucrose substitute, an artificial sweetener.
So the cola is more dense than the diet cola.
To verify the difference between the colas dry the full beverage cans and weigh them.

2. Use a small bottle to measure the density of different liquids.
A more convenient way to measure the density of a liquid is to use a hydrometer
Find the density of a cola drink in an aluminium beverage can.
Weigh the full aluminium beverage can.
Open the aluminium can and drink the cola.
Weight of full aluminium can = w1.
Weight of empty aluminium can = w2.
Volume of cola = v
(The volume is usually written on the side of the aluminium can, e.g. 375 mL or 355 mL (12 oz).
Density of the cola w1 - w2 / v.
Repeat the experiment with "diet" cola, where sugar is substituted by a chemical sweetener, e.g. phenylalanine, aspartame.

11.3.19 Density of hot air and cold air
Heat one of two cans hanging from a balance.

11.3.20 Density of air with a balloon
Temperature and mass of dry air, kg / m3, at STP | 0oC 1 292 kg / m3 | 25oC 1 184 kg / m3
(Maximum water content = 0.023 kg / m3)
Use carbonated water to fill a balloon for use in measuring the density of air.

11.3.21 Equidensity bubbles
Blow a soap bubble with air and then gas to give a bubble of the same density as the surrounding air.

11.3.22 Density of Freon and air, with a balloon
Fill a pan with Freon and float a balloon on it to show the difference in density with air.

11.4.0 Archimedes' principle
Archimedes of Syracuse, about 287-212 BC
See diagram 11.4.0: Archimedes' principle
Archimedes' principle: A body immersed in a fluid is subject to an upward force equal in magnitude to the weight of fluid it displaces.
The apparent loss in weight of a body immersed in a liquid will equal the weight of the displaced liquid.
Buoyancy force = (force on top surface of object - force on bottom surface of object) = (F2 - F1)
= (P1A - P2A)
= (density × gh1A - density × gh2A)
= density × gA (h2 - h1)
= weight of displaced fluid.
The upthrust or buoyancy force on an object, wholly or partially immersed in a fluid, is equal in magnitude and opposite to the weight
of the fluid it has displaced.
A body wholly or partly immersed in a fluid is subject to a buoyancy force of magnitude equal to that of the weight of the displaced
fluid.

11.4.01 Buoyancy
Buoyancy is the vertical upward force of a fluid on a floating body or immersed body.
The force is equal to the weight of the fluid displaced by the body
The apparent loss in weight of a body immersed in a liquid equals the weight of the liquid displaced by the body.
The upthrust, or buoyancy force, on an object immersed in a fluid, is equal and opposite to the weight of the fluid displaced.
An object with more buoyancy than another object has a greater tendency to float.
Buoyancy force = weight of displaced fluid.
An object displaces its own weight of fluid.
If the upthrust force balances the weight, it will float.
If the upthrust force is less than the weight, it will sink.
When you immerse an object in a fluid, it feels an upward force equal to the weight of the fluid displaced by the object.
This is called buoyancy.
If the fluid is incompressible, then the buoyancy is given by F = rVg, where r is the fluid density, g is the acceleration of gravity, V is
the volume of fluid displaced by the object.

11.4.02 Flotation
An object floats in a liquid when the weight of the body is equal to the weight of liquid displaced.
When an object is placed in a liquid with greater relative density than the object it will sink until the weight of the liquid displaced is
equal to the weight of the body.

11.4.03 Fluid density
Liquids and gases both have the capacity to flow so are called fluids.
The mass of a substance divided by its volume is called its density, density air = 1.29 kg / m2, water = (1.00 × 103 kg / m2).
Specific gravity or relative density is the ratio of the density of the substance to the density of water,
e.g. density of mercury = (13.6 × 103kg / m3), so relative density of mercury = 13.6.

11.4.04 Fluid pressure
1. Fluids in an open condition, e.g. atmosphere, large swimming pool, river.
The pressure at equal depths in a uniform liquid is the same, it acts in all directions, and always acts perpendicular to any surface with
which it is in contact.
The pressure on area due to force = force / area, newton / metre2, pascal, Pa.
For a fluid, the force is due to the weight of the fluid above the area, A, so pressure = weight / area pascal = mg / A pascal.
(m = height × area × density), so pressure = height × area × density × g / A = density × g × height).
The atmospheric pressure at the earth's surface is the pressure due to mass of air above the earth.
At the earth's surface, it can push mercury up an evacuated tube to a height of 0.76 metre.
Pressure of air = pressure of mercury = density mercury × g × height pascal.
If the top of an object is at depth h1 below surface of a fluid, and the bottom at depth, h2, the difference in pressure =
density × g × (h2 - h1) newton / metre2, which provides the buoyancy due to the upthrust of the fluid.

2. Fluid in a closed condition, 2.1 The fluid may be dynamic, e.g. when moving through a pipe, hydrodynamics, or in a constrained
flow, e.g. air moving around a wing, aerodynamics.
2.2 The fluid may be static, e.g. compressed in a syringe.

11.4.05 Water-resistant, waterproof
Water-resistant.
For electronics, the IP (Ingress Protection) scale, 1 to 8, only IPX8 means that you can safely take the item under water.
IPX7, means they can be dropped in water and retrieved.
Watches have an entirely different grading than most other electronics.
The International Organization for Standardization issued a standard for water resistant watches which also prohibits the term
waterproof to be used with watches.
The international standard ISO 2281 Horology Water-resistant watches defines the water resistance of watches intended for
ordinary daily use and are resistant to water during exercises such as swimming for a short period.
The standard specifies a detailed testing procedure for each mark that defines not only pressures but also test duration, water
temperature, and other parameters.
For tents or clothes, waterproofing is measured on Hydrostatic Head scale, HH.
If a tube containing water is placed on top of their material the HH rating is how much water in the tube before the pressure and
weight of the water pushes through the material.
The "waterproof" level" is 1 000 mm of water, but tents have an HH rating of over 2000 mm, and waterproof jacket 3000 mm+.

11.4.1.0 Buoyancy of water
See diagram 4.200.1
: Archimedes' principle
See diagram 4.200.2
: Buoyancy of water
According to Archimedes' principle (Archimedes of Syracuse 287 - 212 B.C.), an object wholly or partly immersed in a fluid will be
subjected to an upward force, upthrust, equal to the weight of the fluid it has displaced.
If the density of the object is greater than the density of the fluid, its weight will be greater than the upthrust and it will sink.
If the density of the object is less than the density of the fluid, the upthrust will be the greater than its weight and the object will be
pushed upwards towards the surface.
As the object rises above the surface, how much fluid it displaces decreases.
Also, the upthrust decreases until the upthrust acting on the submerged part of the object equals the weight of the object and the
object floats.
Let v = submerged volume of floating regular solid, and V = volume of whole solid.
Let d = density of floating solid, and D = density of liquid
Weight of floating solid = upthrust (weight of liquid displaced)
d = m / v, so m = v X d
V X d = v X D, so v / V = d / D
The ratio d / D is the relative density of the solid compared with the liquid and v / V is the fraction submerged.
So the fraction submerged = density ratio.
If the floating solid has uniform cross-section area, v/V = submerged length / total length
So relative density of liquid = submerged length of floating solid / total length of floating solid.
So buoyancy does not increase with depth.

Experiments
See diagram 4.200.1: Archimedes' principle
1. Fill an overflow can, A.
Put a wooden block in the overflow can.
Collect the water displaced in a balance pan, B.
Remove the wooden block, dry it, put it in the other balance pan, C.
The weight of the wooden block is equal to the weight of the water displaced.

2. Buoyancy does not increase with depth.
Use a metal container with a tightly fitting cover, e.g. a treacle tin.
With the cover on, push the container into a bucket of water, with the cover end down, and quickly let go of it.
Note the upthrust on the container.
Put some water in the container and repeat the experiment.
Keep adding water until the container can no longer float.
Fill the container can with water and put the cover on.
Put a double loop of string around the side of the container and then attach a large rubber band to the other end of the string.
Lift the container by holding the rubber band and note how much the band stretches.
Lower the container into a bucket of water and note the stretch in the rubber band.
The buoyant force a fluid exerts on a submerged object is equal to the weight of the volume of fluid displaced.

3. Float a small wooden boat carrying a heavy piece of lead in a bucket of water.
Note the level of the water at the side of the bucket.
Remove the piece of lead and drop it into the water.
Again note the level of the water at the side of the bucket.
The water level has fallen because when in the boat the piece of lead displaces its weight of water.
However, when at the bottom of the bucket of water the piece of lead displaces its volume.

4. Use an empty tin with a tight cover, e.g. a coffee tin.
Close the coffee tin and hold it at the bottom of a bucket of water.
The coffee tin will float upwards as soon as release the it.
When putting the coffee tin into the water, your hand feels an upward force.
Fill the coffee tin with water and hold it at the bottom of the bucket of water again.
The coffee tin does not float and you may feel a smaller upward force.
Take the coffee tin out of the water.
Tie a cross tie around the coffee tin then attach an elastic strap.
Suspend the coffee tin by the elastic strap and note the elongation of the elastic.
Lower the coffee tin into the bucket of water but not touching the bottom.
Observe the elongation of the elastic when the coffee tin is at rest.
The elongation of the elastic has reduced compare to the
elongation in the air.
It shows that there is still buoyancy acting on the coffee tin and its direction is still upward.
Repeat the experiment with a string attached to a spring balance instead of the elastic.

5. Measure buoyant force.
Lower a weight suspended from a spring scale into a beaker of water suspended from a spring scale.
Weigh a submerged block.
Lower a 3 Kg block of aluminium suspended from a spring scale into water and note the new weight.
An aluminium block on a spring scale is lowered into a beaker of water taped on a platform balance.
Immerse a lead block suspended from a counter weighted balance in a beaker of water on a counter weighted platform balance and
then transfer a weight to bring the system back into equilibrium.

See diagram 11.279: Buoyancy of water
6. Use a metal container with a tightly fitting cover, e.g. a treacle tin.
With the cover on, push the container into a bucket of water, with the cover end down, and quickly let go of it.
Note the upthrust on the container.
Put some water in the container and repeat the experiment.
Keep adding water until the container can no longer float.
Fill the container can with water and put the cover on.
Put a double loop of string around the side of the container and then attach a large rubber band to the other end of the string.
Lift the container by holding the rubber band and note how much the band stretches.
Lower the container into a bucket of water and note the stretch in the rubber band.
The buoyant force a fluid exerts on a submerged object is equal to the weight of the volume of fluid displaced.

7. Float a small wooden boat carrying a heavy piece of lead in a bucket of water.
Note the level of the water at the side of the bucket.
Remove the piece of lead and drop it into the water.
Again note the level of the water at the side of the bucket.
The water level has fallen because when in the boat the piece of lead displaces its weight of water.
However, when at the bottom of the bucket of water the piece of lead displaces its own volume.

11.4.1.1 Centre of buoyancy and centre of gravity of a boat
See diagram 11.4.24: Centre of buoyancy and centre of gravity of a boat
Centre of Gravity is the point in a body where the gravitational force may be taken to act.
Centre of buoyancy is the centre of the gravity of the volume of water that a hull displaces.
For a floating body to be in equilibrium, the centre of gravity must be in the same vertical line as the centre of buoyancy.
When the hull of a boat is upright the centre of gravity and centre of buoyancy is on the same
vertical line, the hull is stable.
For most hulls, the centre of buoyancy is below the centre of gravity and the hull is said to be metastable.
When the hull tilts, the centre of gravity remains in the same position related to the hull.
The centre of buoyancy moves to fit the new centre of gravity of the volume of water replaced by the hull.
At first the gravity force and the buoyancy force creates a righting torque that tries to move the hull back to the upright position.
However, if the hull is tilted to much, the centre of buoyancy moves to a position where the buoyancy and gravitation force starts to
create a moment that will capsize the hull.

11.4.2.0 Buoyancy of air with a balloon
Balloons, balloons helium chart, (Commercial)
1. Make a buoyancy balloon.
Fill a balloon with dry ice, seal it then place it on a scale and watch the weight decrease as the balloon inflates.
2. Put a brass weight counterbalanced by am aluminium sphere filled with air in a bell jar and evacuate it.
Balance a toilet tank float against brass weights in air and in a vacuum.
Balance a glass ball with a brass weight in a bell jar and then pump the air out.

11.4.2.1 Lifting power of hydrogen compared to helium
Two identical 10-litre balloons containing 1. hydrogen and 2. helium are floating in air and are tethered by a string to a rail.
The balloons displace the same weight of air, so they experience the same upthrust.
The weight of air displaced = mg = density X volume X g = (1.28 g/L) X (10 L) X (9.8 m/sec2) = 125.44 N
The weight of the gases in the balloons will depend on the density of the gas
Hydrogen, weight = mg = density X volume X g = (0.089 g/L) X (10 L) X (9.8 m/sec2) = 8.722 N
Helium, weight = mg = density X volume X g = (0.179 g/L) X (10 L) X (9.8 m/sec2) = 17.542 N
Lifting power of hydrogen in the balloon= 8.722-125.44 = -116.7 N
Lifting power helium in the balloon = 17.542 125.44 = -107.898 N
So hydrogen has (116.7-107.898) / (125.44 X 100) = 7 X the lifting power over helium.

11.4.3 Floating, sinking and rising under liquid
Floating is state of equilibrium in which an object rests on or suspended in the surface of a fluid (liquid or gas).
According to Archimedes' principle, an object wholly or partly immersed in a fluid will be subjected to an upward force, or upthrust
an instantaneous upward force, equal in magnitude to the weight of the fluid it has displaced.
If the density of the object is greater than that of the fluid, then its weight will be greater than the upthrust and it will sink.
However, if the object's density is less than that of the fluid, the upthrust will be the greater and the object will be pushed upwards
towards the surface.
As the object raises above the surface the amount of fluid that it displaces (and therefore the magnitude of the upthrust) decreases.
Eventually the upthrust acting on the submerged part of the object will equal the object's weight, equilibrium will be reached, and the
object will float.

11.4.4 Float corks in a glass jar
A molecule of water is composed of three atoms: two hydrogen atoms and one oxygen atom.
Because the oxygen atom tends to have the electrons orbit it more than the hydrogen atoms, the oxygen atom has a slight negative
charge, and the hydrogen atoms have a slight positive charge.
Because of this property, oxygen is called a polar molecule.
This property also allows the water molecules to form hydrogen bonds with each other, between the positive hydrogen atoms and
negative oxygen atoms.
Because the individual water molecules form these hydrogen bonds, water has a very high surface tension.
This high surface tension actually allows the water level to rise up over the mouth of the cup before the water overflows down the
sides.

1. Half fill a glass jar with water and float a flat cork on the water.
Note where the cork floats.
It floats near or touching the wall of the glass jar.
Add more water to the glass jar until a meniscus forms.
Note where the cork floats.
It floats in the centre of the water surface.
If you push the cork towards the edge of the water surface it returns to the centre.
When the glass jar is half filled with water, the highest level of the water is the circumference of the meniscus due to the adhesive
forces between the water and the glass molecules.
A cork floats at the highest place, so it floats at the circumference.
When the glass container is filled with water, the forces of cohesion
between the water molecules allow a meniscus to form across the whole surface of the water, like a skin.
As the highest level of the meniscus is now in the centre of the water surface, the cork floats at this highest place.

2. Cut 1 cm diameter circles of polystyrene.
Fill a polystyrene cylinder with water 1 cm from the top.
The polystyrene circles tend to float clumped together but using a pencils for weak agitation of the water surface, the polystyrene
circles move outwards towards the surface of the container and stay there.
Take out all but one circle of polystyrene and add water to the cylinder or add stones until a meniscus forms.
The circle of polystyrene moves to the centre of the meniscus.
Use a pencil to push the circle of polystyrene away from the centre.
Remove the pencil and it returns to the centre of the meniscus.
The meniscus in the partially-filled container curves up to meet the sides of the container because water molecules are more attracted
to the polystyrene than to each other.
In the over filled container the water forms a convex bulge because surface tension constricts the are of the water surface to a
minimum.
The water molecules pull evenly on the circle of polystyrene so it remains in the middle of the meniscus.

11.4.5 Float oil spheres
Pour 50 mL water in a beaker.
Hold the beaker in a slant and slowly pour 50 mL ethanol on top.
Leave the beaker to stand.
Fill a dropper with light oil, e.g. olive oil.
Insert the opening of the dropper to where the two liquids meet in the beaker and squeeze out drops of oil.
Withdraw the dropper out of the liquid.
The oil takes the shape of a sphere and stays between the two layers of liquid.
Ethanol has density 0.794 so it can float on water and form a layer.
It is not totally immiscible with water, but when poured slowly it
can form a layer and stay above the water.
Where the two liquids meet, the water and the oil mix and form a liquid with a density very close to the density of oil so the oil forms
a sphere between the two liquid layers.
A sphere is formed because it has the smallest surface area as compared to other three dimensional shapes.
When the beaker is left standing, the alcohol evaporates slowly, and the oil sphere moves up slowly until it reaches the surface and
then the sphere slowly becomes a flat circle when all the alcohol has evaporated.

11.4.6.0 Float cork, wax and wood in different density liquids
See diagram 11.287: Floating in different density liquids: A, B, C, D are liquids with increasing density
1. Use a piece of wood that at sinks in water paraffin wax or candle wax and a piece of cork.
Pour water into a measuring cylinder or tall glass jar.
Then carefully pour the kerosene into the jar on top of the water.
Drop in the solid substances.
The wood sinks in two liquids.
The paraffin sinks in the kerosene but floats on the water.
The cork floats on the kerosene.
Floating condition: if the density of a solid is greater than that of the fluid, then it will sink, if the solid's density is equal to that of the
fluid, the solid will float anywhere in the liquid.
If the solid's density is less than that of the fluid, the solid will float above the surface of the liquid.

2. To understand the condition of a solid floating in a liquid, use a thin and tall glass bottle (or a glass test-tube, a glass cup) and
liquids with different density, e.g. water, kerosene, honey or molasses.
Solids: a steel ball (for example, ball bearing), iron bolt or screw, a small block of ebony or other sinkable into water wood block, a
piece of solid paraffin, a small cork.
Pour liquids into the glass bottle according to the order of density.
Pour the liquids slowly along the rim of the bottle under a glass stick.
Do not make the surfaces between liquids mixed.
Gently put the four solids into the liquid.
Observe the floating in the different layers of liquids with different densities.

3. Float a test-tube in water, kerosene, and a combination kerosene and water.
4. Fill a test-tube with several immiscible liquids of different densities.
Then add solid objects that will float at the various interfaces.

11.4.6.1 Liquids float on liquids, miscible and immiscible liquids
1. Pour water into a bottle.
Carefully pour the same amount of oil on top of the water.
Close the bottle and shake it thoroughly.
The oil and water at first seem to mix together but after some time they separate into different layers.
Oil and water do not mix, i.e. they are not miscible.
They are immiscible.
Also the density of oil is less than the density of water so oil floats on water.

2. Put corn syrup in a tall beaker and add red colouring, e.g. cochineal.
Pour vegetable oil on the corn syrup.
It floats on the corn syrup.

11.4.6.2 Density of different liquids
Liquid relative densities: Honey 1.36, Light maple syrup 1.33, Dish washing liquid 1.03, Water 1.00, Vegetable oil 0.91,
Rubbing alcohol (isopropyl alcohol) 0.87, Baby oil 0.82, Lamp oil 0.80
1. Add different food colouring to 20 mL of the liquids used in the experiment, e.g. water, cooking oil, honey or treacle or golden
syrup.
Pour the liquids into the centre of a measuring cylinder in order of density.

2. Use two exactly same size containers.
Pour the lamp oil into one container and the water into the other container until they are overflowing.
Put a sheet of hard plastic on top of the container with the water.
Invert the water container and place it over the oil
container, keeping the sheet of plastic in place.
Pull the sheet of plastic 2 mm to one side to allow the liquids to mix.

3. Note how the liquids remain separate because of their different densities.
4. Put one branch of a Y-tube in brine (concentrated salt water) and the other in coloured water, then suck the stem of the Y-tube.
5. Prepare sugar solutions with different densities and add a different dye to each solution.
Carefully pour all the solutions into one container and observe the mixing of colours.

11.4.6.3 Density ball
Metal sphere barely floats in cold water and sinks in hot water.

11.4.6.4 Equidensity drops
A beaker of water has a layer of salt solution on the bottom.
Place a drop of mineral oil on top and pipette in some coloured salt solution The drop in an oil sac sinks to the interface.
A globule of oil floats at the interface in a bottle half full of water with alcohol on top.
Aniline forms equidense and immiscible drops when placed in 25oC water.
Pour 80 mL in cool water and heat.
Orthotoluidine has the same density as water at 24oC and is immiscible.

11.4.7 Model diving bell, model submarine, diving bottle
See diagram 11.288: Model diving bell
1. Use a small wide mouth bottle with a two holes stopper.
Put some stones or metal washers in the bottle so it floats in an upright position.
Insert one arm of an U-tube through the stopper so that it extends to the bottom of the bottle.
Insert a short length of glass tubing through the other hole and attach a long rubber tube.
Put the bottle in water.
Sucking on the rubber tube.
Water enters the bottle through the U-tube until the bottle sinks.
You can make the bottle rise by blowing through the rubber tube.
This model illustrates the principle of the tanks or pontoons used to lift sunken ships.
Fasten a weight to the bottle, sink both in water and lift the weight by blowing air into the bottle.

2. Use a tall wide mouthed bottle and a tall, large, glass flume.
Put some small stones into the bottle to spread uniformly on the bottom of the bottle.
Pure some run paraffin on the small stones to fix them to the bottom of the bottle.
It can make the bottle stand upright in water.
Choose a fit cover for the bottle.
Drill two holes on the cover.
Pure water into the bottle.
Cover the bottle with the cover.
Choose a U-tube and a short glass to fit the holes.
Insert one end of the U-tube into the bottle from a hole on the cover of the
bottle and let the end reach nearly the bottom of the bottle.
Insert one end of the glass into the bottle from the other hole on the cover of the bottle but do not insert the end into the bottle too
deeply.
Cover the other end of the glass with a long latex tube.
Wet the end of the latex tube beforehand so that it is easier to insert.
Place the wide mouthed bottle into the flume full of water.
Inspire or blow the latex tube, then the water at the bottle flows in or out, the bottle will sink down or float up in the water.
This simulates the principle of a submarine.
The equipment may simulate retrieving a sank boat
Use a weight on the bottom of the flume.
Let the bottle dive into the bottom of the flume.
Fasten the weight to the neck of the bottle.
Blow the latex tube to make the weight and bottle float together up.

11.4.8 Archimedes' principle experiment
See diagram 11.4.8: Archimedes' principle experiment
Fill an overflow can.
Put a wood block in the overflow can.
Collect the water displaced in a balance pan.
Remove the wood block, dry it, put it in the other balance pan.
The weight of the wooden block is equal to the weight of the water displaced.

11.4.9 Archimedes' bucket and cylinder experiment
See: Buckets, bucket and rod, bucket and cylinder, (Commercial)
See diagram 11.4.9: Bucket and cylinder experiment
The all-metal bucket and cylinder demonstrates the principles of buoyancy and displacement.
The cylinder fits into the cup exactly.
The whole unit can be hung from a spring scale and weighed.
This unit can then be lowered into a container of water and the reduction weight noted.
The weight loss equals the weight of the water displaced.

Experiments
1. A solid metal cylinder C just fits into a cylindrical bucket B.
They are suspended from a balance arm, with the cylinder attached to a hook on the base of the bucket.
Add weights to the other balance pan until the balance arm is horizontal.
Immerse the solid cylinder in water by raising beaker A.
The buoyancy force on the immersed cylinder disturbs the equilibrium of the balance.
Upon filling the bucket with water balance is restored by the balance arm.

2. A mass and bucket of the same volume hang from a spring scale.
Lower the mass into water catch the overflow and pour the overflow into the bucket.
Hang a cylinder and bucket of the same volume
from a scale.
Immerse the cylinder in water, catch the overflow and pour it into the bucket.
Hang a cylinder turned to fit closely inside a bucket from the bottom of the bucket while suspended from the bottom of a balance.
Immerse the cylinder in water and then pour water into the bucket.
Archimedes did not experience buoyancy, only how to measure volume.

3. A cylindrical mass and bucket are suspended from a spring scale above a beaker with an overflow spout.
Note the scale reading.
Submerge the mass by raising the beaker with the lab jack.
Pour the water from the catch bucket into the hanging bucket to return to the original scale reading.
You may also show that the mass exactly fits inside the hanging bucket.
Note the reading of the spring scale suspending a cylindrical mass and hanging bucket above an overflow beaker.
The cylindrical mass fits exactly into the catch bucket.
Raise the overflow beaker to submerge the mass and bucket and let the displaced water flow into a catch beaker.
Lower the overflow beaker and remove the cylindrical mass from the bucket.
Dry the hanging bucket then pour the water from the catch beaker into the catch bucket.
The reading on the spring scale is the same as at the start of the experiment.

11.4.10 Weigh block in air and in water
|See diagram 11.1.3: Weighing block in water
|See diagram 11.4.10a: Weigh submerged block
1. Weigh the block in air, then submerged in water.
The difference is the buoyant force.
2. Weigh a block in air.
Submerge the block in water and weigh it again.
The difference in weights is the buoyant force.
Note that the air provides a small upthrust on the block depending on the density of air at the time of weighing.

See diagram 11.4.10: Buoyancy
3. Measure buoyancy with cylinder and straw.
Differently place an object and a cylinder full of water on the two sides of a beam balance.
Suppose the beam balance balances.
When you immerse the object in another fluid, the balance will be destroyed by the buoyancy.
Reducing the water at the cylinder will be helpful to resume the balance.
When the weight of the water reduced equals the magnitude of the buoyancy, the new balance is set up.
Use a ruler of 30 cm length.
Burn a small hole at the 15 cm mark on the ruler.
Differently groove a shallow groove at 0 cm and 30 cm mark.
Hang the ruler through the middle hole and make the grooves upward.
Use a plastic dish of diameter 8~10 cm.
Burn 3 holes at the rim of the dish and make the distance between any two holes is equal.
Tie a piece of string to each hole on the dish then hang the dish flatly to the ruler with 30 cm mark.
Paste a gasket of M3 with adhesive plaster to each tie at the holes on the dish.
The gaskets can also prevent the string from slipping away.
Use a short piece of string and tie a nut of M10 to either end of the string then hang it at the other side of the ruler.
The string with two nuts corresponds to the weight of a steelyard.
Displace the "weight" to make the ruler balance then fix the weight with adhesive plaster at the position.
You may put some pins or sand to counterbalance the little affection from the adhesive plaster.
Use another piece of string and tie it to a heavy object, then hang the string on the ruler with 0 cm mark.
Place the cylinder of water in the dish to make the ruler balance again.
Firstly let the side of the ruler with the cylinder lighter a bit,
then make a little adjustment with pins or so that the ruler balances.
Record the volume of the water at the cylinder V1 now.
Pure water into a beaker and place it under the object.
When the object immerses in the water, the ruler inclines towards the cylinder.
Suck the water out of the cylinder with a medical sucker to make the ruler balance again.
Record the volume of the water at the cylinder V2 now.
The buoyancy is equal to dg (V1 - V2), where d is the density of water, g is the acceleration of the gravity.
If you do the experiment with a refitted physical balance and microsucker, you can measure the buoyancy accurately.

11.4.11 Estimate the load of a boat
See diagram 11.4.11: Buoyancy of a boat
The magnitude of buoyancy acted on an object in water is equal to the weight of water displaced by the object.
The more the weight of the boat, the more the water displaced, and the greater the buoyancy acted on the boat.
Use a piece of graph paper in 10 cm long and 2 cm wide.
Draw a mark ruler on it.
The scale on mark ruler begin at upper mark 1, then from upward to downward, 2, 3 ..
Tape the ruler you have just made on the paper box with transparent adhesive tape.
Regard it as a "boat".
Tape the mark ruler vertically, i.e. stand up, on the outside of the boat, cut off the surplus part of the ruler at the bottom of the boat.
Put the boat into a water tank.
Note the boundary between water and ruler, called the water level, also called the depth of water by boat.
Record the value of the water level.
Put a 10 g weight in the centre of the boat to ensure the boat remains upright.
Read the value of the water level and record it.
Add weights 10 g every time.
To note the place of the weight on the boat that should ensure the boat being in water vertically all the time.
Record the value of water level every time.
After adding weights on boat, decrease weights.
Decrease 10 g weight every time, record the value of water level until the boat has been empty.
Compare two water levels refer to each weight, and calculate the average of them.
Analyse the value of water level and data refer to weights in the boat.
There is a definite relation between the depth under water of boat and weight of boat.
When you estimate the loads of a boat, you can use the conclusion from the experiment above.
For example, let a person stand on a boat that floats on water, measure the depth that the boat drops, then according to the relation
between the depth under water of boat and weight of boat use ed from the experiment above to estimate the loads of the boat.
Thus, by this simple method you can finish an estimating on maximum loads of a boat.

11.4.11.1 Stone in a boat
1. Put water in a bath and note the original level of the water.
2. Float a toy boat in the bath.
The level of the water rises because the boat displaces its weight of water.
3. Place a stone on the boat.
The level of the water rises further because the boat + stone displace their combined weight of water.
4. Remove the stone and drop it into the water.
The level of water drops to level 2. + the volume of the stone.
In the boat, the stone displaces its weight of water.
In the water the stone replaces its volume of water.
5. A boat sinks lower in the water by equal amounts as add equal weights are added to the boat.
6. A boat starts to sink below the water level, then down to the bottom of the sea, when the weight of the boat + added weights =
the weight of water displaced by the boat.

11.4.12 Plimsoll line, load lines
See diagram 11.211: Plimsoll Line
Lines painted on both sides of a ship to indicate the minimum freeboard allowed in different parts of the world and at different seasons
to prevent dangerous overloading of the ship.
Samuel Plimsoll, English politician, 1824-1898, campaigned against unsafe conditions at sea in his book "Our seaman", 1872. and
promoted the Merchant Shipping Act, 1876, to provide a legal limit on the volume of cargo a vessel could hold, with a mark on the
side of the vessel to show the correct level of greatest submersion, the load line, later called the Plimsoll line.

11.4.14 Weight overboard
Use a boat that can float in a small tank with a heavy weight in it, e.g. a brick.
Measure the level of water in the tank with nothing floating in it.
Float the boat in the tank and note the level of the water in the tank.
Take the boat out of the tank, check the level of water, then drop a brick into the tank and note the level of the water.
Take the brick out of the tank, dry it then put the brick in the boat, float the boat in the tank and note the level of water.
Take the brick out of the floating boat and drop it into the water.
Note the level of the water with the boat still floating and brick still at the bottom of the tank.
Note whether the water level in the tank increased, stayed the same or decreased when the brick was dropped into the water from
the floating boat.
The brick in the boat displaced a volume of water equal to its weight.
The brick at the bottom of the tank displaced a volume of water equal to its own volume.
So the brick displaced a greater volume of water when it was in the boat because its density is greater than the density of water.
So when the brick dropped into the water from the boat, the level of water in the tank decreased.

11.4.17 Finger in glass of water
See diagram 11.4.17: Balanced beakers of water |See diagram 11.4.17a: Finger in glass of water
When you push your finger into a glass of water you feel an upthrust force pushing up on it, equal to the weight of water displaced by
the finger.
If you apply a force to something, you will feel an equal and opposite force, every action has an equal and opposite reaction.
If the water is applying an upthrust force to your finger, your finger must be applying a downward force to the water.
When you put your finger in the water, it will increase the level of water in the glass, so there is more water pressure at the bottom of
the glass, acting on the same area, so the force is greater.
The force on the bottom of the glass = pressure X the area of the bottom of the glass.
When you put your finger in the liquid your finger actually weighs less by the same amount that the scales measuring the weight of the
beaker increase.
The extra weight shown on the scale is the weight of the water displaced by the part of the finger that is under water.

1. Put a glass of water on a top pan balance and note the weight.
Put a finger down into the glass of water.
The weight shown on the balance increases equal to the weight of water displaced by the finger.

2. Balance two identical beakers containing the same original volume of water.
Note the same original level of water in each beaker.
Lower a square cross-section rod into the water in the right hand beaker and fix it in position.
The level of water rises and the beaker moves down.
Note the final level of water in the right hand beaker.
Calculate the volume of (final level - original level) or calculate the volume of water displaced by observing the volume of the rod
under water.
Used a beaker to add water to the left hand beaker until the two beakers are level again.
The volume of water added to the left hand beaker is equal to the volume of water displaced in the right hand beaker.

3. Place a ruler over a pencil to act as a crude fulcrum.
Place identical glasses of water on each end of the ruler so that they balance.
Turn the pencil back by a very small angle to leave one glass raised and the other glass lowered.
Very carefully lower the end of the pointing finger into the water in the raised glass, but do not touch the glass.
The raised glass becomes heavier by the weight of water displaced by the finger and the two glasses can be made to balance again.

4. Repeat the experiment using a live goldfish instead of the finger.
Do not hurt the goldfish.
The weight of the raised glass is increased by the weight of the water displaced by the goldfish.

11.4.18 Floating square bar
A long bar floats in one orientation in alcohol and switches to another orientation when water is added.

11.4.19 Float oranges
The orange with its peel on floats because its ratio of mass to volume is less than that of the water.
Removing the peel reduces the volume of the orange and reduces its mass to increase the density of the peeled orange to be greater
than water, so it sinks.
Cut the orange in half, to halve the orange's mass and halve its volume, but not change its density so it float.
Remove the peel and the half orange sinks.
Weigh the orange and measure its volume.
Use a beam balance to compare the mass of the peel and the peeled orange.
Use a spring balance to find the weight of the peel and the peeled orange.
Use an overflow can and a measuring cylinder to compare the volume of the peel and the peeled orange.
Calculate the density of the orange, the peeled orange and the peel.

11.4.20 Reaction balance
Immerse an empty test-tube in a beaker of water taped on a platform balance to displace the beaker of water.
Then immerse your finger in the beaker of water.

11.4.21 Measure specific gravity of fluids
Raise water and an unknown liquid to different heights in vertical tubes by a common low pressure.

11.4.22 Spherical oil drop
Olive oil forms a large spherical drop in a stratified mixture of alcohol and water.

11.4.23 Dancing rice grains
1. Drop some grains of rice, raw or cooked, into a glass of soda water or lemonade or any clear beverage made with aerated water.
The rice grains first sink to the bottom of the glass.
After a few minutes small bubbles form on the rice grains at nucleation sites.
Later some of the rice grains with bigger bubbles attached rise to the surface of the aerated water.
At the surface the bubbles burst and the rice grains sink again.

2. Repeat the experiment with cooked rice grains and other foods, e.g. salted peanuts.
Note the relationship between number of nucleation sites and frequency of movements up to the surface of the aerated water.

11.4.24 Dancing sultanas
Drop dry sultanas into a container of soda water.
The sultanas sink to the bottom of the container.
Later, bubbles of carbon dioxide form on the sides of the sultanas.
The collective density of the sultana with the bubbles decreases, and with enough bubbles the density of the sultana drops below the
density of the soda, and the sultana rises.
At the surface, the bubbles burst, so the sultanas sink to the bottom of the container again.