from last time… Why are bones (mostly covalent bonds) much stronger to compression and tension than to twisting or bending? And given that your tibias have a cross sectional area of about 3 cm 2, and a Young’s modulus of about 1.6  N.m 2, how much do your tibias compress when you get up in the morning?

When you compress or stretch a material you are compressing or stretching bonds, but not changing the direction of them. This is like compressing or stretching springs – push or pull them far enough and they will break, but they can stretch somewhat. Covalent bonds are strongly directional – when you twist or apply a shear force, so that atoms slide past each other you have to change the direction of the bonds. The direction can only change slightly before the bonds break. Almost all bone fractures are due to torsion or shear forces.

Given that your tibias have a cross sectional area of about 3 cm 2, and a Young’s modulus of about 1.6  N.m 2, how much do your tibias compress when you get up in the morning? Use the young’s modulus – Y = we want  x, so rearrange:  x = = ~ 0.03mm

The story so far: solids are held together by primary bonds, which are due to the interaction of electrons. a solid summary… Bond typeconductivitystrength ionicpoorBrittle – weak to shear covalentpoorBrittle – weak to shear metallicexcellantDuctile and malleable

Fluids are held together by secondary bonds (which are also due to electron interactions!) Bonds Primary MetallicIonicCovalent Secondary van der Waals Hydrogen

Secondary bonds are weak bonds, usually between molecules. They are electrostatic in nature, and are due to the interaction of electric dipoles (a thing with a positive end and a negative end – two poles). Very common in fluids – especially in water, also common in biological molecules like proteins and DNA. They are also called van der Waals bonds, and hydrogen bonding is a common type.

an example - water H 2 O is a dipole – the end of the molecule with the oxygen is slightly negative compared to the end with the hydrogens. remember capillary motion and surface tension - these are due to van der Waals bonds! + - O H H O H H O H H O H H + -

Hydrogen bonds Hydrogen bonds are a special type of van der Waal bond – they are weak bonds that occur between a hydrogen on a polar molecule (the positive side) and another atom which is a bit negative. They are electrostatic in nature and can be fairly strong compared to other van der Waals bonds. They help hold us together!

Lecture 8: Fluids 1 You are always in a fluid! The entire surface of the Earth is surrounded by fluid – air and water. Fluid = liquids and gases – anything that flows and takes the shape of its container. Solid, discrete objects – mass and force are used to determine behaviour (velocity, acceleration, etc). Fluids are (approximately) continuous - so we use density and pressure to determine what’s happening in a fluid.

Density and Pressure Density:  = Units?kg.m -3 Pressure: p =N.m -2 = PaUnits? Other common units include atmospheres, mmHg and PSI (1 atm = 760 mmHg = 14.7 PSI = 1.01  10 5 Pa). Note: pressure is a scalar – it does not have a direction.

Pressure Sometimes pressures are given as absolute pressures and sometimes as gauge pressures. A gauge pressure is the pressure above normal atmospheric pressure. Blood pressure (120 mmHg) Tyre pressure (17 kPa) Barometric pressure (102 kPa) Gauge or absolute? Gauge Absolute

Hydrostatic Pressure..is pressure due to a static fluid – e.g. atmospheric pressure, or pressure under water. It’s the pressure due to the weight of stuff above. Area = A Height, h The force due to the fluid above is F = W = mg =  Vg =  Ahg The pressure is p = F/A =  Ahg/A =  hg

Area = A Height, h The force due to the fluid above is F = W = mg =  Vg =  Ahg The pressure is p = F/A =  Ahg/A =  hg What sort of pressure is this? This is a gauge pressure! The absolute pressure is the fluid pressure -  hg – plus the atmospheric pressure above. p =  gh + P o PoPo

Pause for thought #1 A dam is to be enlarged by excavating a section of mountain to increase the surface area (and hence volume) of the damn by a factor of 2, leaving the depth the same. The retaining wall which holds the water in needs to be increased in strength by a factor of: a)4 b)2 c)no change needed now discuss it

and the answer is: c) no change is needed The pressure on the dam wall depends only on the depth of water behind it, not on the volume – P =  gh. what would happen when you paddled in the ocean if pressure depended on volume? your feet would be crushed!

Archimedes and Buoyancy A completely submerged body displaces its own volume in fluid. So we can use this to accurately measure the volume of something oddly shaped (e.g. people), then by weighing them find their density. A body fully or partly submerged, is buoyed up (experiences an upward force) equal to the weight of water that it displaces. In equilibrium, a floating object experiences a buoyant force equal to its own weight.

W = m diver g =  diver V diver g F b = m water displaced g =  water V diver g If  diver =  water – neutral buoyancy, diver floats at same depth. If  diver >  water – W > F b and diver sinks down. If  diver <  water – W < F b, and diver floats upwards. Fully Submerged:

Partly submerged: Floating (at equilibrium) partly submerged: F b = W So m water displaced g = m body g W = m duck g F b = m water displaced g

Pause for thought #2 Two people order drinks, one with ice and one without. A few ice cubes are put in one cup and then both cups are filled to the same level. Which cup weighs more? a)the one with ice b)the one without ice c)neither – they weigh the same now discuss it

and the answer is: c) neither – they weigh the same Ice floats because it is less dense than water. A floating object displaces its own weight in fluid, so as long as the ice floats, and the fluid levels are the same, the cups will weight the same.

a calculation to try… The density of air at 20 o C is 1.2 kg.m -3, the density of hydrogen is kg.m -3. What minimum volume of hydrogen is required to lift an airship if its total mass, including payload, is 12,000 kg? Hydrogen

W = m H g+ m ship g F b = W = m air displaced g Start off by assuming that approximately all the volume is taken up by hydrogen (not a bad approximation). For the airship to float we require that W  F b. Use m =  V: W = mg =  H.V H.g + m ship.g F b = m air displaced g =  air.V air displaced.g =  air.V H.g Using the limiting case, W = F b:  H.V H.g + m ship.g =  air.V H.g Rearranging a bit: V H = m /(  air -  H ) = 12,000 / ( ) = 10,800 m 3

Pascal’s principle A change in pressure applied to an enclosed incompressible fluid is transmitted evenly and undiminished to all parts of the fluid and its container. What’s it good for? Hydraulic levers (like dentist chairs), brakes, tools, jacks, etc! PP PP

something to think about… The Cartesian diver is an upside down test-tube in a plastic bottle full of water. You can also make one using a pen lid. Why does it sink when you squeeze the bottle? A Cartesian diver