School Science Lessons
Materials, alloys, heat treatment, environmental pollution, mechanical properties of materials
2009-10-11
Please send comments to: J.Elfick@uq.edu.au
See: Interesting websites
Table of contents
3.61.0 Construction materials
34.1.0 Alloys
34.2.0 Heating metals, heat treatment
34.3.0 Materials from the Earth
34.4.0 Environmental pollution
34.5.0 Mechanical properties of materials, elastic, ductile, malleable
36.51.0 Space science
34.1.0, Alloys
3.61 Tin-lead alloys
3.62 Tin-lead alloys and pure metals, hardness
3.63 Melting point of metals and alloys
3.64 Heat treatment of steel needles
5.5.0.0 Eutectic mixture
5.5.01 Low melting point alloys
5.5.02 Higher melting point alloys and parts by weight
5.5.03 Copper-zinc alloys, brass
5.5.04 Copper-tin alloys, bronze
5.5.05 Copper-aluminium alloys, bronze
5.5.06 Copper-nickel alloys
5.5.07 Tin-lead alloys
5.5.08 Alloys of "noble metals", Au, Ag, Pt, Pd
5.5.09 Cast iron alloy, steel
5.5.09.1 Paper clips and rusting
5.5.1 Alloy collection
5.5.2 Copper in brass
15.3.14, Corrosion of alloys, restore bronze coin
34.2.0 Heating metals, heat treatment
34.2.1 Heat treatment of needles
34.2.2 Annealing
34.2.3 Quenching
34.2.4 Tempering
34.3.0 Materials from the Earth
34.3.01 Portland cement
3.65 Strengths of mud, clay and sand bricks
3.66 Make bricks with cement
3.66.1 Strength of cement with changing water content
3.66.2 Alkalinity of concrete
3.67 Strength of plaster of Paris
2.16.1.1: Pass carbon dioxide through calcium hydroxide solution
4.5 Physical properties of a mineral
4.21 Major groups of rocks
4.36 Soils
4.45 Soil and water
34.3.1 Strength of paper
34.4.0 Environmental pollution
34.4.1 Pollution from noise, noise effects thinking and learning, white noise
34.4.2 Noise sources, Test A
34.4.3 Noise control, Test B
34.4.4 Pollution from light of buildings
34.4.5 Electrostatic Precipitation
34.5.0 Mechanical properties of materials
3.44 Potato masher squeeze (Primary)
34.5.1 Hooke's law, elastic limit, deforming force, stress and strain
34.5.1.1 Stretch a wire
34.5.1.2 Spring in series and parallel, stretching a spring
34.5.1.3 Strain gauge
34.5.1.4 Ductility and elongation of metals
34.5.1.5 Breaking strains, brittleness
1.3 Weighing devices (Primary)
34.5.2 Tensile and compressive stress
34.5.2.1 Breaking threads
34.5.2.2 Elastic limits
34.5.2.3 Young's modulus
34.5.2.4 Poisson's ratio
34.5.2.5 Bending beams, bending the metre stick, rectangular bar under stress, different woods
34.5.2.6 Sagging board, aluminium / steel elasticity paradox
34.5.2.7 Stretch a hole, deformation under stress, stress on a brass ring
34.5.2.8 Bologna bottle, squeeze the bottle
34.5.2.9 Prince Rupert's drops
34.5.3 Shear stress
34.5.3.1 Shear book, foam block
34.5.3.2 Spring cube
34.5.3.3 Plywood sheets
34.5.3.4 Torsion rod, modulus of rigidity, bending and twisting
34.5.4 Coefficient of restitution (coefficient of elasticity)
34.5.4.1 Bouncing balls
34.5.4.2 Dead and live balls
34.5.5 Crystal structure
34.5.5.1 Crystal models, solid models, sphere packing
34.5.5.2 Ice model
34.5.5.3 Poisson contraction model
34.5.5.4 Ice nuclei
34.5.5.5 Crystal growth in a film
34.5.5.6 Crystal faults, crushing salt
4.5 Lustre
36.51.0 Space science
4.129 Magnifying power of a lens
4.142.1 Measure solar ultraviolet radiation
36.16 Diurnal aberration of a star
36.51 Discover action-reaction on roller skates
36.52 Build action reaction engines
36.53 Discover thrust
36.54 Discover weightlessness, reference systems
36.55 Angle, degree, arc minute, arc second, radian
36.68 Demonstration sundials (Southern hemisphere)
36.69 Sundial for your home
36.70 Universal globe sundial
36.70B Parallel rays of the sun
36.70.5 Building sundials
36.70.6 Make a pocket sundial
36.76 Make a constellarium
36.76B Umbrella constellarium
36.77 Seasonal shift of the sky
36.78 Tell the time and the date by the stars
36.78A Star calendar
36.78B Star clock
36.91 Star trails in colour
36.92 Photograph constellations
36.93 Photograph satellites
36.101 Make a spectroscope for materials analysis
36.106 Satellite launcher
36.107 Kepler's laws of planetary motion (Johann Kepler 1571-1630)
36.108 Newton's universal law of gravitation, gravitational constant, G
36.109 Gravitational potential energy
37.44 Navigation data used by a ship at sea
36.14.1 List of constellations
36.14.2 Light-year
35.3.0 Abundance of elements in the Earth's crust
35.3.01 Abundance of elements in the Sun
34.1.0 Alloys
Lower melting alloys. These may be produced by using a Bunsen burner. Where both bismuth and lead occur together in an alloy, the bismuth and lead are melted together, and then the other ingredients added. The temperature should not be higher than necessary to prevent excess oxidation. The parts shown are by weight. The higher melting alloys. e.g. bronze and brass, are produced in a furnace with the copper melted first and the other metals added.
Alloy Bismuth Cadmium Copper Lead Tin Zinc
Wood's metal 7 1 - 4 2 -
Solder - - - 1 1 -
Electric fuse alloy 1.3 - - 8.5 2.5 -
Bronze - - 80 - 5 15
Brass. malleable - - 58 - - 42
Brass, casting - - 72 - 4 24
34.2.1 Heat treating needles
Heating steel material to "red heat" then cooling it slowly is called annealing. Putting steel material heated to red heat into cold liquid to cool it quickly is called quenching. Reheating steel material quenched to the temperature slightly lower than "red heat" temperature then cooling it slowly is called temper. Anneal, quenching and temper are heat treating material to change its rigidity, brittleness and toughness by changing the range of iron atoms. Annealing: This is a form of heat treatment to soften a metal and make it easier to work Annealing is often used to soften steel to relax its inner stress to change its shape by forging, pressing and machining. Obtain some sewing needles about four to 5 cm long. These needles are alloys of iron and carbon, but the proportion of carbon is very small. Try bending a needle. It is tough and springy. These properties of this carbon steel are dependent on the arrangement of the carbon atoms among the iron atoms. The effect of annealing, quenching and tempering is to alter this arrangement in a specific way. Some types of razor blades can be used in place of the needles.
34.2.2 Annealing
1. Heat a needle to bright red heat. Hold it vertically in the flame and then very slowly raise it out of the flame taking about one minute. When it is cool, try bending it. It should be soft and easily bent round a pencil.
2. Use pliers to clamp a needle's tail and forcibly insert a needle into the hard block then try to bend the needle. You may find it is very difficult because the needle has strong rigidity and toughness. Now use the pliers to clamp its tail and place it on an alcohol burner to heat. About one minute later, its most part changes dark red. Lay it aside to cool slowly. When its temperature lowers to the room temperature, insert it into the block. You may find that it is easy to bend it.
34.2.3 Quenching
1. Neither the soft needle nor the brittle needle is very useful. However, the tough springy form can be restored. Heat and quench a needle as before to obtain the hard, brittle form. Carefully clean and shine the surface with emery cloth. The needle must now be heated very gently until a deep blue oxide film appears on the surface. This colour is an indication of the temperature at which the needle is tempered. When the needle is cool, try bending it. Is it tough and springy like the original needles?
2. Heat a needle to bright red heat and, while it is still hot, plunge it completely into cold water. Try to bend it now. It should be brittle and easily broken into small pieces.
3. Use the pliers to clamp the tail of another needle and heat it on an alcohol to dark red. Place it into cold water at a beaker to cool it quickly. Insert it into the block then bend it. You may find that it becomes very hard but brittle and easy to break.
34.2.4 Tempering
Polish the needle quenched at Test B with the sand paper then reheat it on the alcohol burner. When it becomes blue black, take it from the burner and lay it aside to cool slowly. When its temperature lowers to the room temperature, insert it into the block to bead it. You may find that it becomes tough.
34.3.0 Materials from the Earth
minerals
building materials
materials used in commercial products Renewable / non-renewable resources of the Earth
Natural and Processed Materials
The properties and structure of materials are interrelated.
1. Types of materials
solid, liquid, gas, plasma
crystals, fibres, fabrics, plastics, wood
metals, non-metals
polymers, acids/bases
building materials 2. Properties of materials
taste, odour, colour
lustre, texture, acoustic
characteristics
absorbent, porous
transparent, translucent, opaque
magnetic, non-magnetic
density light / heavy, floats / sinks
solubility
strength, hardness, flexibility
viscosity, See 13.3.0
conduction / insulation
heat/electricity reactivity with other substances
1. Natural materials
Organic
plants: wood, fibres
animals: wool, leather, glue
Inorganic rocks, ores, minerals
2. Processed materials
metals
alloys
plastics
salts
synthetic fibres
paper
glass
brick
cement
3. Uses
building
tools
clothing
food
cleaning
medicine
recreation
4. Changes made to properties of materials to meet required uses
34.3.01 Portland cement
Cement is any material that binds loose sediment into a rock and may be ferruginous (containing iron), calcareous (containing calcium) and siliceous (containing silica). Builders' cement contains calcium and aluminium silicates. Portland cement hardens as it reacts with water. It was thought to have the same colour as stone on Isle of Portland, U.K. Concrete contains aggregate (gravel and sand), cement, and water. Concrete can be cast into shape to become load bearing. Mortar contains sand, cement and water and is used for plasters. Grouts contain cement and water and are used to fill gaps. Portland cement is a fine powder produced by grinding Portland cement clinker and some gypsum. The raw mixture is mainly chalk or limestone containing clay or silicon dioxide and other materials, including clay, shale, sand, iron ore, bauxite, flies ash and slag, i.e., minerals containing calcium oxide, silicon oxide, calcium aluminate, aluminium oxide, ferric oxide, and magnesium oxide. Calcium and silicon form the calcium silicates that give strength to the concrete. Aluminium and iron compounds produce the liquid solvent flux in the kiln that helps in the formation of silicates at a conveniently low temperature. The raw mixture is heated in a cement kiln at 1400-1450 oC so that the ingredients become sintered, i.e. about one third melted, but not fused into a molten mass. It cools to become grey-coloured clinker containing at least two thirds by weight of calcium silicates. Calcium sulfate as gypsum is added to the clinker. The gypsum hydrates very rapidly during the concrete setting reaction and helps to control the initial setting rate. The mixture is ground to form fine cement powder that can be stored dry and later mixed with water to form an alkaline cement workable slurry for casting.
Portland cement powder may contain 50% tricalcium silicate, 3(CaO).SiO2, 25% dicalcium silicate, 2(CaO).SiO2, 10% tricalcium aluminate, 3(CaO).Al2O3, 10% tetracalcium aluminoferrite, 4(CaO)4.Al2O3.Fe2O3, and 5% gypsum, CaSO4.2H2O. So Portland cement contains approximately 65%, calcium oxide, CaO 25%, silicon oxide, SiO2, 5% aluminium oxide, Al2O3 , 1% ferric oxide, Fe2O3 and 4 % calcium sulfate, CaSO4. Different types of cement contain the same four major compounds that make up at least 90% of the total weight, but in different proportions.
Tricalcium silicate + Water (yields) Calcium silicate hydrate + Calcium hydroxide + heat
When water is added to concrete powder, hydration occurs and during this chemical reaction the concrete gradually hardens as calcium silicate hydrate gel that forms in the first few days at the surface and later deeper in the pour. The strength of hard concrete comes from the solid part of the paste, the calcium silicate hydrate and other crystalline phases. The pores remaining in hard concrete are filled with water and air and have no strength.
dicalcium silicate and dicalcium silicate + water --> calcium silicate hydrate + calcium hydroxide + heat
The volume of setting concrete should not change because the added water should be used up in the hydration process. So the weight of cement powder + water + aggregate = weight of the set concrete block (conservation of mass). The water-cement ratio (by weight) of completely hydrated cement is 0.22 to 0.25, excluding evaporable water. So the warning "Do not touch wet concrete until it dries" is inaccurate because nearly all the water is lost of the hydration reaction, not by evaporation. The rate of reaction of the cement with water is proportional to the surface area of the particles. Cement production requires high energy input and produces large quantities of carbon dioxide, so it contributes to global warming. However, EMC, Energetically Modified Cement, uses very finely ground ingredients that have increased surface area for the chemical reaction and uses less energy to produce it.
34.3.1 Strength of paper, relationship between the shape of material and its mechanical strength
See diagram 34.3.1: Folded paper, crossbeams
A flat piece of paper placed over two rods can support only light weight. However, if the piece of paper is folded into many alternate ditches and edges it can support heavier weight. Draw parallel lines on A4 paper 1 cm apart. Fold the paper alternately each way along the parallel lines. Cut out a 4 cm square of cardboard and put it on folded paper. Add weights to the cardboard or put an empty glass on it and add water until the paper begin to change its shape. Repeat the experiment with paper folds 0.5 cm apart and 2.0 cm apart. Compare the results of the two experiments. Crossbeams made of reinforced concrete are used in building construction. Why place them as in diagram 34.3.1.(b), not as in 34.3.1(c)?
34.4.1 Pollution from noise, noise effects thinking and learning, white noise
Often people use the word "sound" for something they want to hear, and "noise" for what they do not want to hear. In general, musical sounds are made up of a certain limited number of frequencies. They are regarded as sounds even though some people may not want to hear them. Motor traffic, aircraft and trains all produce a complex range of sounds of many unrelated frequencies at the same time. This is described as noise. It is a random mixture of sounds of different frequencies and amplitudes. Study the reasons causing noise and the ways lowering noise.
34.4.2 Noise sources, test A
Use a knock-down [be able to be dismantled] transformer. Install its primary coil and secondary coil well and let its iron core in not closed state (viz. do not install the upper iron frame). Turn on the AC electrical source for the primary coil and observe the vibration and sound of the iron core. Make the iron core closed but do not screw the screws tightly and note the change in sound. Screw the screws tightly. You may find noise lowers observably. Many noises are caused by disordered vibration of some components without being fixed well. Be careful not to touch the metal parts of the transformer because it carries AC of more than 36V. Place a plastic ruler on a tabletop flat and let it spread 1/3 long out of the table and vertical to the table rim. Press the end at the table with your left hand and take a press on another one with your right to make the ruler vibrate. Note the vibration on the tabletop and the noise it emits. Place a large, thin, sponge pad under the ruler to separate the ruler and the table. Repeat the above experiment. You may hear only the sound the ruler vibrates. Adding some elasticity materials under vibrating objects may lower vibration noise effectively because elasticity materials may absorb vibration energy.
34.4.3 Noise control, test B
Use a small radio and a box Turn on the radio to the most volume. Place the radio into the box then cover its cap. Listen to the sound. You may find the sound decreases a bit. Separately put some cotton, sponge and broken stones in the space between the radio and box wall. Listen to the sound again. You may find cotton and sponge make the sound decrease more observably. Actually many spongy materials are sound absorption materials. If place them at the places transferring noise, they can lower noise effectively.
34.4.4 Pollution from light of buildings
Many modern buildings' outside walls are decorated with glass mirrors. Thus there is much sunlight being reflected to fixed direction. The inhabitants living at the places opposite to the buildings are under the strong light pollution. For example, their rooms are hotter in summer, their children's eyesight lowers due to the strong light's stimulation. To study how reflected sunlight makes the temperature at a small space increase in summer obtain two same large boxes. For paper boxes, wrap a layer of thin heat insulation materials such as foam sponge and cotton pad to imitate the walls of a room. Cut a window at a side of each box, making sure the two windows with the same size. Shade the windows with transparent glass paper or plastic film. Place the boxes in the sunlight in summer but without sunlight shining in the boxes directly. Insert a thermometer into each box. Place a large mirror and adjust its position to make reflected sunlight into a box through its "window". You may find the temperature at the box shined by reflected sunlight increases quickly. Carefully note the difference in temperature of the two "rooms" until the temperature at this box increases no longer. Record the readings of the temperatures and calculate the difference in temperature between two boxes. Remove the transparent glass paper shading each window to imitate "opening windows to air". After a while, you may find the temperature at the box shined by reflected sunlight decreases more slowly than another box. Carefully note the difference in temperature of the two "rooms" until the temperature at each box decreases no longer. Record the readings of the temperatures and calculate the difference in temperature between two boxes.
34.4.5 Electrostatic precipitation
See diagram: 34.4.3
To build a model to show the action of an electrostatic precipitator you need concentrated hydrochloric acid, concentrated ammonia solution, gas jar or measuring cylinder, test-tubes, thin metal rod, glass and plastic tubing, stoppers, induction coil and leads, aquarium pump and aluminium foil. The aluminium foil making up the outer electrode should be in the form of a cylinder inside the walls of the jar, but if you want to see what is happening inside, you may leave a space. Turn on the pump. Hydrogen chloride from the acid reacts with ammonia from the next test-tube to form a smoke of ammonium chloride. Notice the amount of smoke emerging from the chimney. Gradually increase the flow of air from the pump then turn on the induction coil to supply the high voltage. Note any change in the smoke from the chimney.
34.5.0 Mechanical properties of materials, elastic, ductile, malleable
See 3.64: Heat treatment of steel needles, annealing, quenching, tempering
If forces are applied to a body remaining in equilibrium, the length volume or shape alters temporarily or permanently, i.e. it becomes deformed. If the forces applied to the body stop and the body regains its original length, volume and shape then the deformation occurred within the elastic limit of the body. The magnitude of the elasticity of the body or the material comprising the body is expressed as a modulus of elasticity.
Ductility is the ability of metals or alloys to keep their strength and not crack when their shape is altered. Some ductile metals, e.g. copper, can be drawn through a die to reduce the cross-section by plastic flow and form wire, but other metals lose their strength and crack.
A malleable metal can be hammered, pressed or extruded out of the original shape and not tend to return to the original shape or to fracture or break.
Both ductile and malleable metals or alloys have large crystals.
34.5.1 Hooke's law, elastic limit, deforming force, stress and strain
See diagram 34.5.1: Young's modulus
Materials that recover their original shape after an applied force is removed show elastic deformation. Materials that do not recover their original shape after an applied force is removed show plastic deformation because the applied force was greater than the elastic limit.
Stress is the applied force per unit area of a material. Stress may cause a strain, the change in dimensions of a material / original dimensions of the material. Hooke's law states that, within the elastic limit, the stress is proportional to the strain. The constant of proportionality, elastic constant, for a material is called Young's modulus, E. Y With wires made of iron or annealed steels, at the elastic limit, yield point, a sudden plastic deformation occurs. The wire "gives" and despite decrease of stress the wire does not return to its previous shorter length. Hooke's law does not apply to polymers or rubber. When a small stress results in a big strain, the material is soft. When a big stress results in a small strain, the material is hard. When a small stress results in permanent deformation, the material is plastic.
Let force = F, A = area, P = pressure
1. Bulk modulus, modulus of incompressibility, K
Compressive stress / Volumetric strain = Deformed force per unit area / Change in volume per unit volume = K. so K = (F/A) / (change in volume v / original volume V) = PV /v = K
[Compressibility = 1/K]
2. Young's modulus, linear modulus, elastic modulus, E
Linear stress / Linear strain = Deforming force per unit area / Change in length per unit area = (F/A) / (increase in length e / original length L) = FL/eA = E
(c) Shear modulus, modulus of rigidity, G
Shearing stress /Shear strain = (F/A) / change in an angle of pi/2 radians (90oC)
If forces are applied tangentially to the upper and lower surfaces of a cube causing the shape to change without change in volume, section of the cube at right angles to those two faces will have their angles changed from pi/2 to (pi/2 + theta) or (pi/2 - theta).
Young's modulus is related to shear modulus, G, Poisson's ratio v, and bulk modulus, K, by the formula: E = 2G(1+ v) = 3K(1-2v) = 9KG / (3K + G). Solids have modulus K, modulus E and modulus G. Liquids have modulus E and modulus K only. Gases have modulus K only.
(d) Poisson's ratio, v
A longitudinal pull in one direction produces an extension in that direction and a contraction at right angles to that direction. the stretched body becomes thinner. The ratio of the lateral contraction per unit breadth to the longitudinal extension per unit length in the line of the applied force is the poisson's ratio for the material., v.
34.5.1.1 Stretch a wire
1. Pull on a horizontal spring with a spring scale. Use 2 metres of copper wire, e.g. 32 SWG, stretched by weights attached to the end the wire through a pulley. Plot a graph of load against extension of the wire. The graph is a straight line to show that Hooke's law applies, extension is proportional to stretching force. Take off weights and observe that the wire returns to its previous lengths at the same tensions.
2. Repeat the experiment by adding weights until the wire suddenly "gives" or "runs". This is called the yield point. The wire has stretch proportionally much more than previously for the load added. The wire can support heavier loads. However, when the weights are removed, the wire can no longer return to its original lengths. At the yield point the wire had reached its elastic limit and Hooke's law no longer applies. In engineering, metal components should carry loads only within their elastic limits.
34.5.1.2 Stretching a spring
Add masses to a pan balance and measure the deflection with a vernier or cathetometer (travelling microscope). Examine the force / displacement curve at small extensions. Add 10, 20 and 30 newtons to a large spring.
34.5.1.3 Strain gauge
Pull to various lengths a spring attached to a dynamic force transducer and show the resulting force on a voltmeter.
34.5.1.4 Ductility and elongation of metal
Use pieces or iron wire and copper wire. Beat the wire flat with a hammer to make them thinner. Note the thickness at which they break. Repeat the experiment with folded zinc and lead sheet.
34.5.1.5 Breaking strains, brittleness
A material distorted by forces acting on it is in a state of strain, is strained. So strain is the ratio: change in dimension / original dimension., and has no units. Direct tensile or compressive strain = elongation or contraction / original length. Shear strain causes a rectangle to become a parallelogram. Volumetric strain, bulk strain = change in volume / original volume.
Approximate breaking strain in kg of some metals and wires hard-drawn through the same gauge (No. 23)
Copper, breaking strain 12 kg
Tin, breaking strain < 3 kg
Lead, breaking strain < 3 kg
Tin-lead (20% lead) 3 kg
Tin-copper (12% copper) 3 kg
Copper-tin (12% tin) 40 kg
Gold (12% tin) 9 kg
Gold-copper (8.4% copper) 32 kg
Silver (8.4% copper) 20 kg
Platinum (8.4% copper)20 kg
Silver-platinum (30% platinum)34 kg
However, the malleability, ductility, and power of resisting oxygen of alloys is generally diminished. The alloy formed of two brittle metals is always brittle. The alloys formed of metals having different fusing points are usually malleable while cold and brittle while hot. The action of the air on alloys is generally less than on their simple metals, unless the former are heated. A mixture of 1 part of tin and 3 parts of lead is scarcely acted on at common temperatures, but at a red heat it readily takes fire, and continues to burn for some time. Similarly, a mixture of tin and zinc, when strongly heated, rapidly decomposes both moist air and steam.
Brittleness is the tendency for metals or alloys to have a brittle fracture when under tension, without plastic deformation, i.e. still keeping its shape. Brittleness mean a low value of fracture toughness, toughness. A brittle fracture is causes bu cracks leading to more cracks usually along certain crystal planes.
34.5.2.1 Breaking threads
1. Place a broom handle across two stools. Attach a thread to be tested to the centre of the broom handle. Attach the lower end of the thread to a large plastic bottle. Add water to the jar until the thread breaks. Note the volume of water needed to break the thread
2. Add heavy masses to different threads until they break, e.g. cotton thread, copper wire (fuse wire), fishing line, dental floss, wool yarn, catgut, piano wire. Compare the breaking strain of the fishing line with this information on the packet.
34.5.2.2 Elastic limits
Stretch springs of copper and brass. The copper spring remains extended.
34.5.2.3 Test the shear strength of thin sheets
See diagram 34.5.2.3: Clothes-pag tester
Cut sheets of material to be tested so that they just fit around a spring clothes-peg, e.g. newspaper, paper towel, potato chip packet, thin plastic, cling film. All the sheets should have the same shape and area. Wrap each sheet around the spring clothes-peg and squeeze the ends of the clothes-peg handles with the thumb and first finger. Note which materials stretch or break.
34.5.2.4 Poisson's ratio
Stretch a rubber hose to show lateral contraction with increasing length.
34.5.2.5 Bending the metre stick, rectangular bar under stress, bending beams, different woods
Hang 2 kg from the centre of a meter stick supported at the ends. Place the meter stick on edge and then on the flat bending beam. Load a rectangular cross-section bar in the middle while resting on narrow and broad faces. Hang weights at the ends of extended beams. Use beams of different lengths and cross-sections. Use different woods
34.5.2.6 Sagging board, aluminium / steel elasticity paradox
Place the ends of a thin board on blocks then add mass to the centre. Show that copper and brass rods sag by different amounts under their own weight but steel and aluminium do not.
34.5.2.7 Stretch a hole, deformation under stress, stress on a brass ring
See: 3.8.0 Conic sections, ellipse
Stretch holes arranged a circle in a rubber sheet to deform into an ellipse. Paint a pattern on a sheet of rubber and deform by pulling on opposite sides. Use a strain gauge bridge to measure the forces required to deform a brass ring.
34.5.2.8 Squeeze the bottle
Fit a bottle with a stopper and a small bore tube. Squeeze the bottle and watch the coloured water rise in the tube.
34.5.2.9 Prince Rupert's Drops
Bubbles made by dropping molten glass into water. The shape is like that of a tadpole. If the smallest portion of the end of the tail is nipped off, the whole bubble explodes into fine dust. This novelty was introduced into England by Prince Rupert (1619 - 1682), grandson of James I. He also introduced Prince Rupert's metal, an alloy of brass.
Cool a drop of molten glass very quickly. Hit the round bulb of the glass with a hammer. It does not break. Break off the sharp tip of the drop. The glass shatters.
34.5.3 Shear stress
Shear is a kind of deformation of materials where parallel plates of the material are displaced in a direction parallel to themselves, but the parallel plates remain parallel. So the adjacent planes of parallel plates slide over each other. If a shearing force is applied parallel to one side of a rectangle it becomes a parallelogram. Shear stress is the applied force divided by the area of the material parallel to the applied force, i.e. F / 1.
34.5.3.1 Shear book, foam block
Use a very thick book or stacks of cards to show shear. Push on the top of a large book or a large foam block to show shear.
34.5.3.2 Spring cube
A cube of cork balls fastened together with springs.
34.5.3.3 Plywood sheets
Use a stack of plywood sheets with springs at the corners to show shear torsion bending.
34.5.3.4 Torsion rod, modulus of rigidity, bending and twisting
Twist a rod by a mass hanging off the edge of a wheel. Wind a copper strip around a rod and then remove the rod and pull the strip straight to show twisting bending and twisting. Twist rods of various materials and diameters in a torsion lathe.
34.5.4 Coefficient of restitution (coefficient of elasticity)
1. Newton found experimentally that if two smooth spheres collide with velocities u1 and u2 and rebound with velocities v1 and v2 then - (v2 -v1) / (u2-u1) is a positive constant, e,  independent of the initial velocities, called the coefficient of elasticity or coefficient off restitution. The value of the constant e depends on the substances, e.g. 0.9 for glass and 0.2 for lead.
2. The coefficient of restitution can be used to measure of the elasticity of the collision between ball and racquet. Elasticity is a measure of bounce, i.e. how much of the kinetic energy of the colliding objects remains after the collision. With an inelastic collision, some kinetic energy is transformed into deformation of the material, heat, sound, and not available for movement. For a perfectly elastic collision, coefficient of restitution = 1, e.g. two diamonds colliding. For a perfectly plastic, i.e. inelastic, collision, coefficient of restitution = 1, e.g. two lumps of Plasticine (modelling clay) that do not bounce but but stick together. The coefficient of restitution = difference in velocities of two colliding objects after the collision / difference in velocities of two colliding objects after the collision. For a racquet and ball, v1 = velocity racquet centre before impact, s1 = velocity ball before impact, v2 = velocity racquet centre after impact, s2 = velocity ball after impact
Coefficient of Restitution = (s2 - v2) / (v1 - s1)
For a falling object bouncing off the floor, coefficient of restitution = sqrt (bounce height / drop height), e.g. for a particular bouncing ball, coefficient of restitution = 0.85
34.5.4.1 Bouncing balls
See 7.2.6: Silly putty
Drop balls of different material on plates of various materials. Observe loss of mechanical energy in the coefficient of restitution. Drop balls on a glass plate Drop glass, steel, rubber, brass, and lead balls onto a steel plate. Drop rubber balls of differing elasticity and silly putty on a steel plate. Observe variation in coefficient of restitution n baseballs.
34.5.4.2 Dead and live balls
See 9.4.04: Super ball
Drop a black super ball and a ball rolled from a piece of wax. Make a non-bounce ball by filling a hollow sphere with iron filings or tungsten powder.
34.5.5 Crystal Structure
34.5.5.1 Solid models, sphere packing
Use tetrahedral and octahedral building blocks construct crystal shapes. Use Styrofoam balls and steel ball bearings to make crystal models. Stack balls on vertical rods mounted on a board to build crystal models. Build crystal models with a combination of compression and tension springs. Use old tennis balls glued together to show close-packed crystals. Examine lattice models of sodium chloride, calcium carbonate, graphite and diamond.
34.5.5.2 Ice model
Make ball and stick water molecules that you can stick together to make ice.
34.5.5.3 Poisson contraction model
Use a two-dimensional spring model to show Poisson contraction in crystals.
34.5.5.4 Ice nuclei
Let large ice crystals form on the surface of a supercooled saturated sugar solution.
34.5.5.5 Crystal growth in a film
Observe crystal growth on a freezing soap film through crossed Polaroids.
34.5.5.6 Crystal faults, crushing salt
Arrange one layer of small ball bearings between two Lucite sides. Examine natural faults in a calcite crystal then the single layer of small spheres model faults. Crush a large salt crystal in a big clamp
4.5 Lustre
Lustre is the appearance of the surface of a mineral in reflected light. Minerals are divided into two great groups on the basis of their lustre. One group is opaque and has a metallic lustre like that of a metal. The other group may be opaque or transparent but does not have a metallic lustre.
36.51 Discover action-reaction on roller skates
Put on a pair of roller skates and throw a large ball over the head to another student. Note the direction in which the other student moves. Repeat the experiment with both students on roller skates.
36.52 Build action reaction engines
See diagram 36.52: Balloon boat and rocket
1. Make a balloon-powered boat. Cut away one side of a cardboard box and make a hole in the bottom near the edge. Insert a tube into the hole and attach the balloon to it. Inflate the balloon and place the boat in water. Note the direction the boat moves as air leaves the balloon. Repeat the experiment with the open end of the tube under surface water.
2. Make a balloon-powered rocket. Attach a drinking straw to the side of a long balloon with adhesive tape. Pass a wire through the drinking straw, attach each end of the wire to fence posts and tighten the wire. Inflate the balloon then release it. The balloon travels along the wire.
36.53 Discover thrust
See diagram 36.53: Balloon on scale
1. Turn on the tap and feel the thrust produced when water passes through a garden hose. Turn the tap on more. As the amount of water passing through the hose increases, the hose begins moving in the opposite direction to the moving water. Attach a rotary lawn sprinkler to the hose. Gradually turn on more water and note how the speed of the lawn sprinkler increases as the amount of water increases.
2. Measure thrust with a balance. Put 50 g masses on one pan. Firmly hold an inflated balloon over the other pan. Allow the air to escape against the pan. Note how many gm weight of thrust the escaping air exerts on the pan.
3. Large rockets may produce 300 000 to 1 000 000 kg weight of thrust. If a rocket weighs 5 000 kg, the Earth's gravity is pulling down on this rocket with a force of 5 000 kg weight. Before the rocket can rise, it must overcome that pull towards the centre of the Earth so the rocket's thrust must exceed 5 000 kg weight.
36.54 Discover weightlessness, reference systems
See diagram 36.54: Weightless toy soldier
1. Use string to attach a toy soldier to two arms of a framework. Take the apparatus to a high building and drop it out of the window. While falling, the toy soldier remains in the same position relative to the framework. The toy soldier is not supported by either the string or the frame, but is in a weightless condition with regard to the surroundings, e.g. the reference system being used. To study the motion of an object we need a reference system, e.g. something relative to which it is possible to describe the location of the object at any time. For many experiments we choose a reference system fixed to the Earth, e.g. study a falling object. In such a reference system the Earth is at rest.
2. The weight of an object also depends on its location. Measured in a reference system fixed to the Earth, the weight of an object is the same as the Earth's gravitational force acting on it. This force decreases as the object moves away from the Earth and will eventually become negligible. The weight of the object is changing under the above circumstances. The content of matter of the object does not change, unless approaching that of light. An astronaut whose mass on the surface of the Earth is 90 kg still has the same mass of 90 kg on the surface of the Moon but 90 kg weight on the Earth's surface is only about 15 kg weight on the Moon's surface. Using SI units, the mass is m kg but the weight is mg Newton. Since g at the Moon is about one sixth of g at the Earth, the weight of an astronaut on the Moon will be one sixth of the weight on the Earth.
3. A spaceship in orbit is still within the Earth's gravitational field. Its weight is exactly the force required to keep the spaceship in orbit. However, in a reference system attached to the spaceship, everything inside is weightless.
36.68 Demonstration sundials (drawn for the Southern hemisphere)
See diagram 36.68
Place an upright metre stick in the ground so that it is not likely to be shaded from the sun. Mark the position of the top of the metre stick on the ground at hourly intervals.
36.69 Sundial for your home
See diagram 36.8
Make the base with a flat rectangular piece of wood, metal or polystyrene. The gnomon ABC consists of a thin triangular piece of metal or plastic and such that angle ABC = latitude of the place at which the dial is being set up and angle ACB = 90o. Use a spirit level to test that the base is horizontal. The central line must lie along the north south line, i.e. the meridian. Erect the gnomon vertically so that the hypotenuse points towards the Pole Star in the Northern hemisphere and the celestial south pole in the Southern hemisphere. For approximate results, make the hour markings by noting the position of the shadow of the gnomon at hourly intervals, using a watch set to local mean time. You can obtain more accurate results if the markings are made on 15 April, 15 June, 1 September or 24 December, when there is no difference between watch time and dial time. Errors of up to 16 minutes are possible if you make markings on other dates. For accurate hour markings, find the angles the markings make with BC using the following formulae: tan IOC = tan 15osin lat., tan IIBC = tan 30osin lat, tan IIIBC = tan 45osin lat., tan IVBC = tan 60o sin lat, tan VBC = tan 75osin lat., tan VIBC = tan 90o sin lat. Since the markings are symmetrical about the central line XY you do not need to calculate other angles. If the base of the dial is erected vertically then the angle between the gnomon and the base must equal 90o minus latitude of that
place.
36.70 Universal globe sundial
See diagram 36.70A
With a globe of the Earth you can make a sundial that shows the season of the year, the regions of dawn and dusk, and the hour of the day wherever the sun is shining. The globe is rigidly oriented as an exact model of the Earth in space, with its polar axis parallel to the Earth's axis, and with your own town "on top of the world". First turn the globe until its axis lies in your local meridian, in the true north and south plane. Find this by observing the shadow of a vertical object at local noon, or by observing the Pole Star on a clear night, or by consulting a magnetic compass, if you know the local variation of the compass, the magnetic deviation. Turn the globe on its axis until the circle of longitude through your home lies in the meridian. Tilt the axis around an east west horizontal line until your home town stands at the very top of the world. Now your meridian circle connecting the poles of your globe lies vertically in the north south plane. A line drawn from the centre of the globe to your local zenith will pass directly through your home spot on the map. Lock the globe in this position and let the rotation of the Earth do the rest. Be patient and do not turn the globe at a rate greater than that of the turning of the Earth. However, it will take a year for the sun to tell you all it can before it begins to repeat its story. When you look at the globe fixed in this proper orientation you can see half of it lighted by the sun and half of it in shadow. These are the actual halves of the Earth in light or darkness at that moment. An hour later, the circle separating light from shadow has turned westward and its intersection with the equator having moved 15o to the west. On the side of the circle west of you, the sun is rising, on the side east of you, the sun is setting. You can count the hours along the equator between your home meridian and the sunset line and estimate how many hours of sunlight remain that day. Look to the west of you and see how soon the sun will rise there. As you watch the globe day after day, you will become aware of the slow turning of the circle northward or southward, depending upon the time of year.
36.70B Parallel rays of the sun
BE CAREFUL! DO NOT LOOK AT THE SUN THROUGH THE TUBE AS DIRECT SUN RAYS CAN DESTROY THE RETINA OF YOUR EYE.
1. To show that the sun's rays are parallel as they fall on the Earth, on a bright morning, point a piece of pipe or a cardboard tube at the sun so that it casts a small, ring shaped shadow. If at the same moment a person 120o east of you, one third of the way round the world, performs the same experiment, that person points the tube westward at the afternoon sun. Yet that tube and yours approximately parallel. If you point the tube at the sun in the afternoon, and someone far to the west simultaneously does the same in the morning, that tube will approximately parallel to your tube. So when our globes are properly set up, people all over the world who are in sunlight will see them illuminated in just the same way.
2. You can tell from the global sundial how many hours of sunlight any latitude receives on any particular day. Count the number of 15o longitudinal divisions that lie within the lighted circle at the desired latitude. Thus, at 40o north latitude in summer the circle may cover 225o of longitude along the 40th parallel, representing 15 divisions or 15 hours of sunlight. However, in winter the circle may cover only 135o, representing nine divisions or nine hours. As soon as the lighted circle passes beyond either pole, that pole has 24 hours of sunlight a day, and the opposite pole is in darkness.
36.70.5 Building sundials
See diagram 36.70.5
The gnomon is the part of the sundial that produces the shadow. The top edge of the gnomon must slant upward away from the base, or horizontal, at an angle equal to the latitude of the observer and towards the South for an observer in the Southern hemisphere. The gnomon must be aligned along the N-S meridian. The hour lines are marked on the other part of the sundial, called the time plane. The configuration of the gnomon and the time plane identifies the type of sundial that has been constructed. In the diagram, the shaded area represents a sundial. The top edge of the gnomon is parallel to the Earth's axis and the angle, gamma, between the top edge of the gnomon and the horizontal is equal to the latitude of the observation site. A horizontal sundial has the hour lines are marked on a time plane horizontal to the Earth's surface. You can use the data in Table 3 to construct your horizontal sundial. The table contains hour angles for some cities and towns in Queensland, Australia, calculated by using spherical trigonometry. Note how the hour angles vary with latitude.
Table 3: Hour angles for the horizontal sundial
Time a.m. Time p.m. B R
 M T C T L M
11 hours or 13 hours 07.0 06.1 05.5 5.0
07.5 07.1 06.1 05.4
10 hours or 14 hours 17.8 12.9 11.7 10.8 09.5 13.0 12.9 11.5
09 hours or 15 hours 27.6 21.7 19.8 18.2 16.2 27.9 21.7 19.4
08 hours or 16 hours 38.4 37.5 31.9 29.7 26.7 38.8 37.5 31.4
07 hours or 17 hours 59.7 56.0 53.3 50.8 47.3 60.0 56.0 52.7
B = Brisbane, R = Rockhampton, M = Mackay, C = Cairns, T = Toowoomba, L = Longreach, M = Mt Isa
On a square sheet of cardboard draw a line perpendicular to one edge to represent the 12h 00 m hour line. Use a protractor to draw lines spreading out from the 12h 00 m hour line at the angles in the table if you are in one of the places in Table 3. If you live in Queensland outside these places, find out the latitude of your place and estimate the hour angles, e.g. the hour angle corresponding to 11 AM and 1 PM for Maryborough would be somewhere between 7.0o (Brisbane) and 6.1o (Rockhampton). Label the hour lines as in the diagram. Use another piece of cardboard to cut out the gnomon with one angle equal to the latitude of your location. Attach the gnomon to your sundial base along the 12h 00 m hour line with the angle equal to your latitude pointing North. The angle shown in Figure 3 is the latitude of Brisbane. Align the gnomon along the N - S meridian.
36.70.6 Make a pocket sundial
Cut a wire coat hanger in half and set the angle to the latitude of your location. Attach the coat hanger to a cardboard base marked with the hour lines and align the gnomon north south. Use the sundial to investigate the altitude of the sun and the passage of time during the day. Maintain daily records of the progress of sunrise and sunset to the North and South.
36.76 Make a constellarium
A  constellarium is a simple device used in teaching the shapes of various constellations. Use a cardboard or wooden box and remove one end. Draw the shapes of various constellations on pieces of dark coloured cardboard large enough to cover the end of the box. Punch holes on the diagrams where the stars are located in the constellations. Place an electric lamp inside the box. When the lamp is turned on and various cards are placed over the end of the box, the constellations may be seen clearly.
Another way is to obtain several tin cans into which an electric lamp may be fitted. Holes are punched in the bottoms of the cans to represent the stars in various constellations. When the lamp is placed inside a can and switched on, the light shows through the openings and the shape of the constellations may be observed. The cans may be painted to prevent rusting and kept from year to year.
36.76B Umbrella constellarium
See diagram 36.76Bd: Northern hemisphere, Southern hemisphere
Since an umbrella has the shape of the inside of a sphere, it can be made into a constellarium that will illustrate portions of the heavens and how they move. You will need an old umbrella that is large enough for this purpose.
The Northern hemisphere: Using chalk, mark the North Star, or Polaris, next to the centre on the inside of the umbrella. Consult a star map, and mark the star positions for various constellations with crosses. When you have filled in all the polar constellations, you can paste white stars made from gummed labels over the crosses, or you may paint the stars in with white paint. Later you can draw dotted lines with white paint or chalk to join the stars in a given constellation. If the handle of the umbrella is rotated in a counter clockwise direction, you will see how the various stars trace a circular path about the Pole Star.
The Southern hemisphere: South of the equator, the umbrella should be pointed towards the southern celestial pole and we will therefore have to turn it clockwise. As in the Northern hemisphere, the stars will rise in the east and set in the west. In the diagram above you can see some of the more prominent stars and constellations marked on the umbrella.
36.77 Seasonal shift of the sky
As the Earth travels in its orbit around the sun the constellations seem to move across the sky. The materials required for observing the shift are a star chart and a plumb line. Make observations as described in 7.75, except that you make only one set of observations and record the time. At least one month later, repeat the same observations in the same way, at as nearly the same time of night as possible. When you compare the two observations made at the same time of night, what change do you see in one month, or more? How much change would occur in one year, if the same rate continues? What does this mean, when you recall that we tell time by the sun? Will there be a time of year when you cannot see Orion, for example at all? Answer the same questions for the Big Dipper and North Star, if you are north of the equator. What about the Southern Cross if you are south of the equator?
36.78 Tell the time and the date by the stars
Because the stars appear to rotate one full revolution in 24 hours, they can be useful in telling time, at least during those hours of darkness when the stars are visible to us. Because the stars also make one full revolution in a year, they can be used to tell us the time of the year. And so we have not only a star clock, but also a star calendar.
36.78A Star calendar
See diagram 36.78BN: Northern hemisphere | See diagram 36.78BS: Southern hemisphere
The dates round the edge of the star chart for the Northern hemisphere show when the corresponding part of the heavens is due north at midnight. For the Southern hemisphere the dates show the part which is due south at midnight. Knowing this you can easily rotate the star map so that it corresponds to what you see in the sky. If you are north of the equator and you have to rotate the map 15o clockwise from the midnight position, the time is 1 a.m., if you have to rotate it 30o counter clockwise, the time is 10 p.m. South of the equator it is the other way round since you are facing south. If you have to turn the map 15o clockwise from the midnight position it means that the time is 11 p.m. The times determined this way are sun times and they may differ from your local standard time.
36.78B Star clock
Separate sets of diagrams are given below for the northern and Southern hemispheres, one clock for each month. The nine o'clock positions of the star clock's hand are marked of f at the middle of some months. Can you fill in the nine o'clock positions for May, August and November? Try to fill in midnight positions for June, September and December. In the Southern hemisphere, locate roughly the southern celestial pole.
36.91 Star trails in colour
The stars are as colourful as land subjects, but this is not generally known because dark adapted eyes have low sensitivity to colour. High speed colour film and a camera with at least an f 3.5 lens will record the red star Betelgeuse in the constellation Orion, the yellow star Capella in the constellation Auriga, and the gold star Albireo in the constellation Cygnus. The constellation Cassiopeia contains two blue, one white, one golden, and one green star. A good camera that can make time exposures, a rigid tripod, and fast film are all you need. The simple star charts in this book will help you to identify the constellations. Your local public library may have books on amateur astronomy which contain similar charts. Dial indicators that show all the constellations overhead when the dial is set for the month, day, and hour, are also obtainable in some countries. The Earth rotates 15o per hour, or 10 every 4 minutes. To us on the Earth, it is easier to appreciate this movement by assuming that the stars move. Furthermore, the stars appear to rotate around your celestial pole. Each star near the pole traces a tight circle in its movement, and as the distance from the pole increases, the radius of curvature increases until the stars above the equator appear to travel in straight lines. A star is a true point source of light and no movement of the camera can be tolerated unless you want pigtails for star images. All trouble can be avoided if you mount your camera on a rigid tripod, cover the lens with a cardboard, use a long cable release to open the shutter on time or bulb, wait 3 seconds or so for the camera to stop moving, and then remove the cardboard from in front of the lens. At the end of the exposure, again cover the lens with a cardboard before closing the shutter. Commercial processing laboratories will probably not recognize star images for what they are and, unless you instruct them otherwise, will return your negatives unprinted.
36.92 Photograph constellations
See diagram 36.14
1. Photographs of constellations add an aesthetic purpose to photographing star trails. The results make beautiful prints and slides in both black and white and colour, and they prove to be a very effective teaching medium. There are many techniques for photographing constellations, but a favourite is as follows: select a particular constellation, set up the camera, and expose for 30 minutes with high speed black and white film, 400 ASA and a lens opening of f 11, then cover the lens for 2 minutes, open it to f 4, and throw it slightly out of focus, finally, uncover the lens for 3 more minutes. A diffusion screen over the lens for the final exposure works just as well as throwing the lens slightly out of focus. The resulting picture shows a constellation that appears to be plunging through space with a tail following each star.
2. Underexposed and discarded 35 mm film slides can be perforated with a pinpoint in the form of various constellations. The slides can be projected on to a screen or used in a viewer, and students can try to identify the constellations. The slides can also be dropped into a slot made in a mailing tube and held up to the light.
36.93 Photograph satellites
Satellites are a joy to photograph. Use the same camera technique as for star trails, see above. Kodak Tri-X Pan film is an excellent choice. Use Kodak HC-110 developer, diluted 1: 15 at 24oC for 4 minutes. The main problem is to know ahead of time where to aim your camera. There are several sources for this information: many newspapers publish daily the times, the degrees above the western or eastern horizon, and the direction of travel for all visible satellites. Also, local astronomical observatories and amateur astronomical clubs may be able to furnish the required data for you. Satellite photography is particularly rewarding when the satellite path crosses a well known constellation, or if you are extremely lucky, perhaps two satellites will cross within your photograph. It is this unknown factor that continues to attract the amateur, as well as the professional, astronomical photographer.
36.101 Make a spectroscope for materials analysis
See diagram 36.50: Shoe box spectroscope | See 4.134: Colour experiments, diffraction
By using a sensitive instrument called a spectroscope, scientists are often able to analyse the composition of materials located a great distance away. The spectroscope has been used to determine the composition of the sun and other stars and of the atmosphere of many of the planets. Spacemen in the future will use this kind of device to analyse the chemical composition of their immediate surroundings. Light entering a spectroscope is split up by a diffraction grating to form coloured bands, which we call a spectrum. Since each chemical element shows certain characteristic bright Shoe box spectroscope lines in its spectrum the material can thus be easily identified. The materials required are a shoe box, replica grating, see science supply catalogues, some masking tape, and a double edged razor blade broken in two. Cut a hole of about 2 cm diameter in the middle of one end of the box. Use tape to fix a piece of replica grating over the hole from the inside. Cut a 2.5 cm X 0.5 cm slit, which should be parallel to the lines of the grating, in the middle of the other end. Cover the slit from the outside with a finer slit made from two halves of a razor blade, edges facing each other. The two halves are held together and fixed to the box with tape. The width of the slit should be about the same as the thickness of a razor blade and is finally adjusted for the best results, see diagram. Look through the spectroscope at various luminous gases such as neon and argon in lamps or signs. Notice the bright lines in the spectrum, which indicate that each element has its own pattern.
36.106 Satellite launcher
See diagram 36.106
Materials required are a bucket, a football, a coat hanger, or other suitable wire, sinker or weight, a piece of string and a test-tube or a cap of some sort.
Place the ball securely in the bucket. Bend the wire so that about 30 cm of it is straight and the rest is curved into a circular base as shown in the sketch. Using masking tape, secure the circular portion on the ball, allowing the straight, 30 cm portion to stand upright in the centre of the top of the ball. Attach the sinker or weight to the string. Fasten the other end of the string to the test-tube or cap with tape. Invert the cap on top of the upright wire, see diagram. Explain that the ball represents the Earth, and the sinker represents the satellite. All that it takes to set the sinker into motion in any direction is the tap of a finger. Let the students find out what happens when the satellite is launched in the following different ways:
1. With a slight tap, push the sinker up and away from the surface of the ball, as shown in the figure. The sinker moves up and then falls back to the starting point. This is how an object travels when it is projected at low speed straight up from the Earth.
2. With a slight tap, push the sinker of f the surface of the ball at an angle. Show by a diagram what happens. The sinker moves away from the ball and then falls back at some distance from the starting point. The distance spanned depends upon the angle of launching and upon the forcefulness of the tap.
3. With a stronger tap, push the sinker of f the surface of the ball at an angle. Make a diagram of the orbit. The sinker moves away from the ball, circles it, and lands. Evidently, a complete orbit passes through the starting point of the orbit.
36.55 Angle, degree, arc minute, arc second, radian
Angle is the measurement of the inclination of one line to another. An angle is usually measured in degrees, such that 360 degrees (360o) = 1 revolution. The degree is divided into arc minutes, arcmin, such that 1' = 1/60 of a degree, and arc seconds, arcsec, such that 1' = 1/3600 of a degree. Arc minutes and arc seconds are used in astronomy to measure the diameter or separation of astronomical objects. Also, an angle can be measured in radians, an angle at the centre of a circle subtended by an arc equal to the radius of that circle, such that 2 pi radians = 1 revolution. The "second" refers to the second division of time into sixtieths after dividing the hour into minutes.
36.16 Diurnal aberration of a star
An observer at the equator can observe a movement of any star to the east at a rate of 0.32 seconds of arc per day due to the rotation of the Earth on its axis. However, that observed movement reduces to zero as the observer approaches the poles. Diurnal aberration of a star is the direct evidence that the Earth is not fixed in space.
36.107 Kepler's laws of planetary motion (Johann Kepler 1571-1630)
Law 1. The orbit of a planets is an ellipse, with the Sun at one focus of the ellipse.
Law 2. Each planet moves such that a line connecting the planet to the Sun would sweep equal areas in equal times.
Law 3. The ratio of the square of the time of planetary revolution (sidereal period) to the cube of its distance from the Sun is constant for all planets.
36.108 Newton's universal law of gravitation, gravitational constant, G
Any two particles of matter attract each other with a force directly proportional to the product of their masses and inversely proportional to square of the distance between them,
F = m1m2G/d2
F = force of gravitational attraction
m = mass of a particle
d = distance between the particles
G = gravitational constant
G = 6.67259 X 10-11 Nm2kg-2
36.109 Gravitational potential energy
The energy an object possesses because of its position in a gravitational field is called its gravitational potential energy. On the Earth the gravitational acceleration is about 9.8 m/s2. The potential energy of an object at a height h above the ground = the work required to lift the object to that height. The force required to lift the object = its weight, so gravitational potential energy = the weight of an object X times the height it is lifted.
In space, the force approaches zero for large distances. so the gravitational potential energy near a planet is negative because gravity does positive work as a mass approaches. The small mass approaching the large mass of a planet it bound to it unless it can get acces to enough energy to escape. The general form of the gravitational potential energy of mass m is:
PE = -GM1m2/ r
G = the gravitation constant
M = mass of the planet
m = mass of the approaching object
r = distance between the centers of the planet and the approaching object
36.14.1 List of constellations
Latin name, English name
Andromeda, Andromeda
Antlia, Air Pump
Apus, Bird of Paradise
Aquarius (in the Zodiac), Water Bearer
Aquila, Eagle
Ara, Altar
Aries (in the Zodiac), Ram
Auriga, Charioteer
Bootes, Herdsman
Caelum, Chisel
Camelopardalis, Giraffe
Cancer (in the Zodiac), Crab
Canes Venatici, Hunting Dogs
Canis Major, Great Dog
Canis Minor, Little Dog
Capricornus (in the Zodiac), Sea Goat
Carina, Keel
Cassiopeia, Cassiopeia
Centaurus, Centaur
Cepheus, Cepheus
Cetus, Whale
Chamaeleon, Chameleon
Circinus, Compasses
Columba Dove
Coma Berenices, Berenice's Hair
Corona Australis, Southern Crown
Corona Borealis, Northern Crown
Corvus, Crow
Crater Cup
Crux, Southern Cross
Cygnus Swan
Delphinus, Dolphin
Dorado, Swordfish
Draco, Dragon
Equuleus, Little Horse
Eridanus, River Eridanus
Fornax, Furnace
Gemini (in the Zodiac), Twins
Grus, Crane
Hercules, Hercules
Horologium, Clock
Hydra, Sea Serpent
Hydrus, Water Snake
Indus, Indian
Lacerta, Lizard
Leo (in the Zodiac), Lion
Leo Minor, Little Lion
Lepus, Hare
Libra (in the Zodiac), Scales
Lupus, Wolf
Lynx, Lynx
Lyra, Harp
Mensa, Table
Microscopium, Microscope
Monoceros, Unicorn
Musca, Fly
Norma, Level
Octans, 0ctant
Ophiuchus, Serpent Bearer
Orion, Orion
Pavo, Peacock
Pegasus, Winged Horse
Perseus, Perseus
Phoenix, Phoenix
Pictor, Easel
Pisces (in the Zodiac), Fishes
Piscis Austrinus, Southern Fish
Puppis, Ship's Stern
Pyxis, Mariner's Compass
Reticulum, Net
Sagitta, Arrow
Sagittarius (in the Zodiac), Archer
Scorpius (in the Zodiac), Scorpion
Sculptor, Sculptor
Scutum, Shield
Serpens, Serpent
Sextans, Sextant
Taurus (in the Zodiac), Bull
Telescopium, Telescope
Triangulum, Triangle
Triangulum Australe, Southern Triangle
Tucana, Toucan
Ursa Major, Great Bear, Charles's wain
Ursa Minor, Little Bear, Cynosura, Dog's tail (the pole star is alpha in the tail)
Vela, Sails
Virgo (in the Zodiac), Virgin
Volans, Flying Fish
Vulpecula, Fox
36.14.2 Light-year
1. The distance light travels in a year, 9.46 X 1012 km, (5.88 X 1012 miles).
The speed of light is 2.99792458 X 108 ms-1, usual value used = 3 X 108 ms-1.
2. Large distances can be measure by the time light takes to move that distance. The velocity of light is about 300 000 km per second in a vacuum. So distance travelled by a "ray" of light in one year = 300 000 X 365 days, 24 hours X 60 minutes X 60 seconds = 9 460 800 000 000 km. However, based on 365.25 Julian calendar days, each of exactly 24 hours, a light-year = 9,460,730,472,580.8 km or 9.46 X 1012 km (5.88 X 1012 miles).
3. Astronomers use the parsec, linked to the arcsecond. It is about 3.26 light-years.
35.3.0 Abundance of elements in the Earth's crust
Elements can combine to form natural compounds called minerals. For example, oxygen and silicon combine to form silica SiO2 that occurs as the common mineral quartz. Many different versions exist of tables to show the most abundant elements in the Earth's crust.
Element % Mass Element % Mass
Oxygen 46.71 Carbon 0.094
Silicon 27.69 Manganese 0.09
Aluminium 8.07
 Barium 0.05
Iron 35.05
 Sulfur 0.052
Calcium 3.65
 Chlorine 0.045
Sodium 2.75 Nitrogen 0.03
Potassium 2.58
 Chromium 0.035
Magnesium 2.08
 Fluorine 0.029
Titanium 0.62 Zirconium 0.025
Hydrogen gas
 0.14 Nickel 0.019
Phosphorus 0.13 all other elements 0.061
35.3.01 Abundance of elements in the Sun
Element % Mass
Hydrogen
 54.0
Helium
 44.7
Oxygen
 0.8
Carbon
 0.4
Silicon
 0.05
4.142.1 Measure solar ultraviolet radiation
See 36.16: Albedo
After Alflio Parisi and Michael Kimlin, Australian Science Teachers' Journal, 44 (3)
The risk of developing non-melanoma skin cancer is related to the cumulative ultraviolet radiation (UV) exposure. The risk of melanoma increases with the number of sunburns, specially during childhood. The UV waveband consists of UVA (320 to 400 nm), UVB (280 to 320 nm) and UVC (200 to 280 nm) wavelengths. (Note: nm = nanometre = 10 Angstrom units = 10-9 m.) No UVC reaches the Earth's surface because of absorption by oxygen and ozone in the atmosphere. The total solar UV radiation at the Earth's surface consists of a direct component and a diffuse component. The direct component comes in a direct path from the sun. The diffuse component is the radiation scattered by the atmosphere, clouds and the surroundings. The scattering is more significant at the shorter UV wavelengths. The reflected UV radiation is the UV reflected from any surface, e.g. the ground surface. The shorter wavelengths are the most damaging and produce the greatest erythema, redness of the skin due to dilation of the capillaries (sunburn), i.e. the UVB wavelengths. Take two sets of readings per day, at 10.30 am and 1.00 pm over a period of two weeks. Measure the total solar UV irradiance (UVTotal) with the meter pointing upwards. Measure the diffuse UV reflectance with the detector facing two ground surfaces, e.g. dead grass and asphalt. Cover the detector so that it is in shadow. Calculate the percentage reflectance (albedo) of the surface (R%), e.g. 3.3% for dead grass and 3.8% for asphalt: R% = (UVReflected / UVTotal) X 100. Albedo is the reflecting power of a non-luminous body. Plot the total and diffuse reflectance for two readings each day on a bar graph. Note the cloud cover at each measuring time. The total and diffuse UV radiation varies with the cloud cover. On the overcast days the diffuse irradiance forms a high relative proportion of the total UV irradiance. The relative proportions of the diffuse and total UV irradiance also vary with the seasons due to the change in solar zenith angle resulting in a different atmospheric optical path length. So there is a change in the amount of scattering and absorption in the atmosphere. A UV meter can be designed to have a response that approximates the response of human skin to UV radiation measures the erythemal UV irradiance or the UV irradiance weighted with the response of human skin.