School Science Lessons
Density of solids and liquids, r.d., buoyancy
2009-10-11
Please send comments to: J.Elfick@uq.edu.au
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Table of contents
11.0.0 Density
11.1.0 Density of a solid
11.2.0 Density of a liquid
11.3.0 Relative density, r.d.
11.4.0 Buoyancy, flotation, Archimedes' principle
11.1.0 Density of a solid
3.27 Separate solids using density differences
4.12 Density of a solid
11.1.1 Density of liquid with U-tube and liquid of known density
11.1.2 Density of irregular solid, using mass and volume
11.1.3 Density of irregular solid, not using volume
11.1.4 Density of beans
11.1.5 Density of a boy
11.2.0 Density of a liquid
3.26 Separate immiscible liquids of different density
4.13 Density of a liquid, relative density
4.31 Temperature of water at maximum density, 4oC
11.2.1 Density of liquid using mass and volume
11.2.2 Maximum density of water, negative expansion coefficient of water
11.2.3 Density of ice
11.3.0 Relative density, r.d.
5.11 Relative density, r.d. (formerly specific gravity) (Geology)
11.3.0.1 Relative density, r.d. and specific gravity
11.3.1 Relative density of a liquid, using a relative density bottle
11.3.2 Hydrometers
11.3.3 Triple scale wine hydrometer
11.4.0 Buoyancy, flotation, Archimedes' principle
4.200 Buoyancy of water
4.201 Cartesian diver
4.202 Density of irregular solid, overflow can
4.203 Weight of a floating body
4.204 Float a lighted candle
4.205 Float different kinds of wood
4.206 Float an egg in tap water and salt water
4.207 Float grapes at different levels in water
4.208 Drinking straw hydrometer
4.209 Floating in different density liquids
4.210 Model diving bell
4.211 Float a metal boat, Plimsoll line
4.118 Cold air is heavier than warm air
6.12 Floating and sinking (Primary)
11.4.1 Buoyancy of water
11.4.2 Buoyancy of air
11.4.3 Floating, sinking and rising under liquid
11.4.6 Floating in different liquids
11.4.6.1 Liquids float on liquids
11.4.7 Model diving bell, model submarine, diving bottle
11.4.8 Archimedes' principle
11.4.9 Archimedes' principle, bucket and cylinder experiment
11.4.10 Measuring buoyancy using method of weighing in water
11.4.11 Estimate the load of a boat
11.4.12 Plimsoll line, load lines
11.4.13 Board and weights float
11.4.14 Density of liquid comparison
11.4.15 Density ball
11.4.16 Equidensity drops
11.4.17 Finger in beaker
11.4.18 Floating square bar
11.4.19 Float a battleship in a cup of water
11.4.20 Reaction balance
11.4.21 Measure specific gravity of fluids
11.4.22 Spherical oil drop
11.4.23 Rice grains rising and falling in aerated water
12.3.3 Air has mass, air has weight
12.3.3.1 Carbon dioxide has mass
11.1.0 Density of a solid
Density of a regular solid, irregular solid, liquid, gas
Density, rho or d, definition and units. Density is the ratio of mass to volume of a substance. The symbol is the Greek letter rho. However, this document uses "d". Some authorities use "d" for relative density. This document used "r.d." for relative density, and s.g. for specific gravity, Density = Mass / Volume, d = m / V kg / m3. The density of air at sea level is about 1 / 800 the density of water. The density of a solid is the ratio of mass to volume. Use a balance to measure the mass. If the solid is insoluble in water, measure the volume from how much water it displaces, whatever the shape of the solid. Half fill a graduated cylinder with water. Note the reading. Immerse the solid in the water and note the reading again. The difference in the two readings is the volume of the solid. Examples of substances and their densities in g cm-3 which can be of interest to the chemist are as follows: sulfur: 2.0, quartz: 2.6, calcite: 2.7, copper: 8.9, lead: 11.4. Ores such as malachite, cassiterite and cerussite are not uniform in density as they contain variable quantities of quartz, feldspar and other minerals.
Material Water Air Aluminium, Iron Mercury Gold
Density kg / m3 1.00 × 103 kg / m3 1.29 kg / m3 2.7 × 103 kg / m3 7.9 × 103 kg / m3 13.6 × 103 kg / m3 19.3 × 103 kg / m3
11.1.1 Density of liquid with U-tube and liquid of known density
See diagram 11.1.1: U-tube
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 h1 and 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 Po is 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. Repeat the experiment for different values of h1 and h2 by using a less dense liquid and then calculate the density.
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. Read the scale and record the weight, w1. Immerse the irregular solid in a breaker of water and weigh again using the spring balance. Record weight, w2. To calculate the density of the irregular solid:
The buoyant force on the solid = mass of water displaced x gravitation acceleration, i.e. (Fb = mwater g = rwater x Vwater x g)
However, buoyant force also equals the difference between the two weights measured, i.e. (Fb = w1 - w2)
Therefore w1 - w2 = (rwater x Vwater x g)
Vwater = Vsolid.
Vsolid = msolid / rsolid
So (w1 - w2) = (rwater x msolid / solid x g)
msolid x g = w1,
So (w1 - w2) = (rwater x 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. To 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) Relative density 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 a 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. The volume of the boy = (level 2 - level 1). The density of the boy = weight of the boy / (level 2 - level 1).
11.2.1 Density of liquid using mass and volume
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, negative expansion coefficient of water
See diagram 11.2.2: Density of ice and water depends on temperature
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, however, when water is cooled from 4oC to 0oC, it is expanding in volume. 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. The lower density of ice is caused by the formation of a hydrogen bonded tetrahedral network of water molecules. The temperature of water decreases with salinity. A freezing mixture of ice and sodium chloride drops 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. In 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. 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.
1. 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.
2. 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.
3. 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.
4. 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.
5. To study the expansion of freezing water, use identical drinking cups. Put a tray into the freezing compartment of a refrigerator. Fill a cup with tap water at room temperature so that the water heaps up to form a meniscus. Put the cup in the tray in the freezing compartment of the refrigerator. Add some extra water to the cup to get the highest possible meniscus. When the water in the cup is frozen, fill an identical cup with water at room temperature. Compare the meniscus of the frozen water with the meniscus at room temperature. The frozen water heaped up because it had expanded. Some people claim that the heaping up is in a north south direction due to Coriolis effect!
11.2.3 Density of ice
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.
11.3.01 Relative density, r.d. and specific gravity
1. Relative density, r.d., relative density bottle, hydrometer, r.d. water and ice, specific gravity
Relative density, r.d., is the ratio of the mass of a volume of a substance with the mass of an equal volume of water at a temperature of 4oC. It is a physics quantity of no dimension. For convenience, use this ratio instead of quoting the density, e.g. the density of mercury = (13.6 ×103 kg/m3), so r.d. mercury = 13.6.
2. Specific gravity
Relative density was formerly called specific gravity, so SG. water = 1. Specific gravity is still used to measure the concentration of the sulfuric acid electrolyte in a motor car battery, the brewing industry and laws applying to that industry and the processed foods industry.
11.3.1 Relative density of a liquid, using a relative density bottle
Use a beam balance to measure the mass of a relative density bottle, specific gravity bottles, which accurately contain a known volume. Record the mass m1. Fill the bottle with a liquid whose density is unknown and insert the stopper. Wipe dry the surface of the bottle. Weigh the bottle, m2. Density of liquid = (m2 - m1) / V, where V = volume of the bottle. Pour the liquid out of the bottle then clean the bottle. Fill the bottle with water and insert the stopper. Wipe dry the surface of the bottle. Record the mass, m3. Calculate the relative density of a liquid. Density of liquid = (m2 - m1) / V, density of water = (m3 - m1) / V, where V = volume of the bottle. Density of a liquid relative to water = ([m2- m1] / V) / ([m3 - m1] /V). So the relative density of a liquid, RD = (m2 - m1) / (m3- m1) Repeat the above steps then calculate the relative density.
11.3.2 Hydrometers
Hydrometers include test-tube hydrometer, battery acid hydrometer, food testing hydrometers, constant weight hydrometer, constant volume hydrometer, and the Nicholson hydrometer and Mohr-Estphal balance are used with liquids of various density.
See diagram 11.3.2: Simple hydrometer
A hydrometer is a device for measuring the specific gravity of a liquid relative water, specific gravity of 1.0 measuring the density of the liquid in grams per cubic centimetre. Put a hydrometer in water then in alcohol. Show the buoyancy of hot and cold water with a hydrometer that sinks in warm water and floats in cold water. The Nicholson balance is a float that allows determination of loss of weight in water very accurately. Totally submerge the Nicholson hydrometer except for a small platform. Put it in water and load small weights on the platform until the water level reaches a mark on the wire stem. Then put the hydrometer in the unknown liquid, and add weights to the platform until the same mark on the wire stem is reached. Calculate the relative density of the unknown liquid knowing the mass of the hydrometer and the value of the two sets of masses used to bring the hydrometer to the reference line.
11.3.3 Triple scale wine hydrometer
See diagram 11.3.2: Wine hydrometer
By using this hydrometer you can follow the process of fermentation. As yeast converts sucrose sugar into ethanol the specific gravity of the juice of the crushed grapes, a called the "must or wort", decreases and the hydrometer sinks until fermentation is complete. If you put wine s.g. > 1.006 into bottles, the fermentation is incomplete and the bottles may burst from the extra carbon dioxide produced in the bottle. To test the specific gravity of the "must", use a plastic tube to siphon off a sample of the liquid. Put in the hydrometer so that it floats freely. Use your thumb and first finger to spin the hydrometer to spin off any bubbles clinging to the surface of the hydrometer. When the hydrometer stops spinning and does not touch the sides of the container, read the upper meniscus. The hydrometer will be calibrated to give correct readings at a certain temperature, e.g. 20oC. For other temperatures, you must apply a correction to the final specific gravity reading, e.g. 10oC (- 0.002), 15oC (- 0.001), 25oC (+ 0.001), 30oC (+ 0.003), 35oC (+ 0.004). You can estimate the percentage alcohol content if you measure the specific gravity before and after fermentation. based on the fact that 2,7 grammes of sugar gives 1 hydrometer degree in 1 litre of liquid and 17 grammes of sugar gives 1% of alcohol in one litre of wine. The wine hydrometer has its own container of known volume so besides a specific gravity scale it can also have a scale to estimate the percentage alcohol content if all the sugar is converted into alcohol. If initial specific gravity before fermentation = 1.090, then potential percentage alcohol by volume = 11.8%. If final specific gravity = 1.010 after fermentation, then potential percentage alcohol by volume = 1.3%, the fermentation has stopped. So alcohol contents = (11.8 - 1.3) = 10.5%. Also the hydrometer has a scale to estimate how much sugar to add to give a required alcohol content.
So the triple scales are as follows:
1. Specific gravity scale
2. Potential alcohol content scale
3. Amount of sugar to add scale
11.4.0 Buoyancy, flotation, Archimedes' principle
(Archimedes of Syracuse, about 287 - 212 BC) Statics of fluids, density and buoyancy, pressure and density P = F / A, d = m / V and application to fluids, P = dgh and Pascal's Principle, Archimedes' Principle and its application to buoyancy, fluid dynamics, streamline and turbulent flow
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 X 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 X 103 kg / m3), so relative density of mercury = 13.6. 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 X area X density), so pressure = height X area X density X g /A = density X g X 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 X g X 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 X g X (h2 - h1) newton / metre2, which provides the buoyancy due to the upthrust of the fluid.
Archimedes' principle states: The upthrust, or buoyancy force, on an object immersed in a fluid, is equal and opposite to the weight of the fluid displaced. 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.
11.4.1 Buoyancy of water
1. Use a metal can that has a tightly fitting cover. With the cover on, push the can into a bucket of water, cover end down, and quickly let go of it. Observe the upthrust on the can. Put some water in the can and repeat the experiment. Keep adding water a little at a time and repeating until the can no longer floats. Fill the can with water and put the cover on. Put a double loop of string around the side of the can and then attach a large rubber band to the other end of the cord. Lift the can by holding the rubber band and observe how much the band stretches. Now lower the can in a bucket of water and observe the stretch in the rubber band. How do you account for the difference? The buoyant force a fluid exerts on a submerged object is equal to weight, mg, of the volume of fluid displaced.
2. 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.
3. Repeat the experiment with a string attached to a spring balance instead of the elastic.
4. Measure buoyant force. Lower a weight suspended from a spring scale into a beaker of water suspended from a spring.
5. 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.
11.4.2 Buoyancy of air
1. 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.
2. 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.
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.
11.4.6 Floating in different liquids
See diagram 4.209: Floating in different liquids
1. Use a measuring cylinder or tall glass jar, water and kerosene. You will also need a piece of wood that at sinks in water paraffin wax or candle wax and a piece of cork. Pour water into the 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 at 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. 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. You should pure 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
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.
11.4.7 Model diving bell, model submarine, diving bottle
See diagram 4.210: 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 wrecking a sank boat [viz. saving a wrecking 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
See diagram 4.200.1: Archimedes' principle
1. Fill an overflow can. 2. Put a wooden block in the overflow can. 3. Collect the water displaced in a balance pan. 4. Remove the wooden 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. 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 x gh1A - density x gh2A) = density x 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.
11.4.9 Archimedes' principle, bucket and cylinder experiment
See diagram 11.4.9: Archimedes' principle
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.
11.4.10 Measuring buoyancy using method of weighing in water
See diagram 11.4.10: Buoyancy
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 up 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 other piece of string and tie it to a heavy object (for example, a stone) then hand 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 sand 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 it. 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, and 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 which floats on water, measure the depth which 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.
11.4.12 Plimsoll line, load lines
See diagram 11.4.12: 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.
11.4.13 Board and weights float
A board sinks equal amounts as you add equal weights.
11.4.14 Density of liquid comparison
Material Relative density
Honey 1.36
Light maple syrup 1.33
Dish washing liquid 1.03
Water with food colouring 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. 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.
11.4.15 Density ball
metal sphere barely floats in cold water and sinks in hot water.
11.4.16 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.
11.4.17 Finger in beaker
With beaker on a balance, put finger in beaker of water.
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 a battleship in a cup of water
Float a 2500 g juice can in 500 g water. A small amount of water floats a wood block shaped to just fit in a graduated cylinder. Float a cup three quarters full in a cup one quarter full. A small amount of water floats a wood block shaped to just fit in a graduated cylinder. Will a cup three quarters full float in a cup one quarter full?
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 Rice grains rising and falling in aerated water
See 24.1.01: Nucleation
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 relationaship between number of nucleation sites and frequency of movements up to the surface of the aerated water.
4.118 Cold air is heavier than warm air
Use two identical paper bags that are the same size. Inflate each bag by blowing into them as if they are balloons. Tie the openings closed tightly with string. Tie the end of the string into a loop and suspend the bags from the end of a balanced rod. Move the loops along the rod until the inflated bags are exactly balanced. Gently heat the air beneath one of the bags with a small candle. The bag containing the heated air moves up and the bag containing the cooler air moves down. Move the candle to under the other bag to see the same result. [Comment: The bags are sealed and so the mass of gas is unchanged when heating or cooling takes place. This experiment shows Archimedes Principle in action, not mass change]