Frazer does Physics: October 2011

October 28, 2011

5.9 & 5.10 Solids, Liquids (and gases)

5.9 Recall that particles in a liquid have a random motion within a close-packed irregular structure.
5.10 Recall that particles in a solid vibrate about fixed positions within a close-packed regular structure.

State Changes

All of the state changes are shown in the diagram below

5.8 Boiling

Understand that a substance can change state from a liquid to gas by the process of evaporation or boiling.

If the temperature of liquid atoms increases even more the particles eventually have enough energy to break the inter-molecular bonds between the atoms, the particles now fly around at very high speeds (several hundred kilometers per hour) and fill any container they are placed in. this is the gaseous state. The state change between a liquid and a gas is called boiling.

5.7 Melting

Understand that a substance can change state from solid to liquid by the process of melting.

We know that all materials are made of atoms, in a solid state these atoms attract each other and are locked together by the inter-molecular forces between them. But, even in a solid state the atoms are not completely still; they still vibrate on a fixed position.

If these atoms are given more internal (kinetic) energy, the particles vibrate faster and further, if the temperature continues to increase to a point where the inter-molecular forces between particles are not strong enough to hold the structure together, but are strong enough to prevent the atoms from flying apart from each other; a liquid is born. This process of going from a solid state to a liquid is called melting or fusion.

October 23, 2011

5.6 Pressure Difference

Recall and use the relationship for pressure difference:

$Pressure\: difference=height\times density\times g$

$\Delta p=h\rho g$

Δp = pressure of the fluid (N/m² or Pa)
h = Height of the fluid above loci (depth) (m)
ρ = density of the fluid (kg/m³)
g = gravitational field strength (N/kg)

Proof

The bottom hole of this column squirts water the furthest
This is because the water at the bottom has more pressure
In the formula: Δp = hρg, ρ and g are both constant at all loci, but h is larger lower down \Δp = large.

Questions

The pressure gauge on a submarine in a river was reading 100kPa when it was the surface. If a sailor notices that the gauge is now reading 250kPa, how deep is he? How would the answer change if he were diving in sea water that is slightly denser that fresh water?
Note: ρ_{fresh water} = 1,000kg/m³

$\Delta p=h\rho g$

$150,000Pa=h\times 1,000kg/m^{3}\times 10N/kg$

If the submarine was in sea water he would be slightly shallower than 15m.

A diver on Saturn’s moon Titan is 50m below the surface of a lake of liquid methane, what is the increase in pressure on him due to his depth in the methane? The density of liquid methane is 0.42g/cm³. The acceleration of gravity on Titan is 1.4m/s².
We are told that the pressure of the atmosphere on Titan is 1600mbar. What is the total pressure on the diver (in kPa)?
Note: 1000mbar = 1bar = 100,000Pa.

$\rho = 0.43g/cm^{3}=420kg/m^{3}$
$\Delta p=50\times 420\times 1.4$
$\Delta p=29,400Pa=29.4kPa$

$Total\: Pressure=19.4kPa+160kPa$
$Total\: Pressure=189.4kPa$

5.5 Equal Pressure

Understand that the pressure at a point in a gas or liquid which is at rest acts equally in all directions

Magdeburg Hemispheres

When the pressure inside the sphere is equal to the atmospheric pressure outside, the hemispheres can easily be pulled apart because there is no external force holding the hemispheres together, but if a vacuum is introduced inside the sphere, the pressure atmospheric pressure pushing against the sphere is much greater than the pressure pushing outwards, so the resultant force clamps the sphere closed…

If you’re confused… I tried my best to explain the pressure as a group of men.

1. No vacuum
There are 50 people inside the sphere trying to push the sphere open and 50 outside trying to keep it shut; obviously the sphere will remain in a stable state as neither side has more strength, but when 2 extra people are introduced (the people holding onto the handles) all of a sudden the side trying to open the sphere has more force than the opposing team. So the sphere comes loose and all the little people can escape.

2. Vacuum
Inside the vacuum there are no longer 50 people inside trying to break open the sphere, but the 50 people outside (representing the atmosphere) are still there so the sphere remains firmly closed, and when 2 people are introduced to attempt to open the sphere, the sphere remains closed because those two people alone don’t have enough strength to fight against the 50 people working against them.

5.4 Pressure

Recall and use the relationship between pressure, force and area:

$Pressure=\frac{force}{area}$

$p=\frac{F}{A}$

NB: 1N/m² = 1Pa

Using the Formula

Calculate the pressure generated by an ordinary shoe heel (person of mass 40kg, heel 5cm x 5cm), an elephant (of mass 500kg, foot of 20cm diameter) and a high-heeled shoe (person of mass 40kg, heel area 0.5cm²). Which ones will damage a wooden floor that starts to yield at a pressure of 4000 kPa?

1. Ordinary shoe heel

$p=\frac{F}{A}$

$F=40kg\times 10N/kg=400N$

$A=0.05m\times 0.05m=0.0025m^{2}$

$p=160,000N/m^{2}$

2. Elephant

$p=\frac{F}{A}$

$F=500kg\times 10N/kg=5000N$
$A=\pi r^{2}=\pi 0.1^{2}=0.01\pi$
$p=5000/0.01\pi$

$p\approx 159kPa$

3. High-heeled shoe

$p=\frac{F}{A}$
$F=40kg\times 10N/kg=400N$

$A=0.5cm^{2}=0.00005m^{2}$

Clearly one can see that the high-heeled show will do the most damage to the floor.

October 6, 2011

5.3 Determining Density

Describe how to determine density using direct measurements of mass and volume.

Density of a regular solid

Measure the mass using a balance
Measure the width, length and height using a ruler
Calculate volume (V = w x l x h)
Calculate density (ρ = m/V)

Density of a liquid

Measure mass of empty measuring cylinder using a balance
Measure mass of liquid and measuring cylinder
Subtract 1. from 2. to calculate the mass of the liquid
Measure volume of liquid (using measuring cylinder)

NB: measure to the bottom of the meniscus

Calculate density (ρ = m/V)

Results: Oil

m = 15.74g
V = 18.00cm³
ρ = 15.74/18 = 0.87g/cm³

Density of an irregular solid

Measure mass using balance
Measure volume using the ‘displacement’ method

(submerge solid in ‘Eureka can’ and measure overflow)

Calculate density (ρ = m/V)

Results: Stone

m = 146g
V = 42cm³
ρ = 146/42 = 3.5g/cm³

5.2 Density

Recall and use the relationship between density, mass and volume:

$Density = mass\div volume$

$\rho = m\div V$

ρ = Density [kg/m³] or [g/cm³]
m = mass [kg] or [g]
V = Volume [m³] or [cm³]

NB:
ρ = rho (Greek letter)
1kg = 1000g
1m = 100cm
1m³ = 100,000cm³
1g/cm³ = 1000kg/m³

Topic 5 Solids, Liquids and Gases Keywords

Absolute Zero: The lowest possible temperature. 0K = -273°C.
Brownian Motion: The slow, random motion of large, visible particles such as smoke particles. Explained by postulating much smaller, faster particles that are not visible, such as air particles, that collide with the large particles and make them move.
Density ρ, (g/cm³) or (kg/m³): The mass, in kilograms, of one metre cubed of a substance.
Diffusion: Molecules moving from an area of high concentration to an area of low concentration.
Flexible Container: A container that changes its shape depending on the pressure inside or outside it. The volume is variable and the pressure is constant. Examples are syringes and pistons.
Ideal Gas: A theoretical model of a gas that describes gas molecules by using the Kinetic Theory. The molecules are assumed to collide elastically with the walls of the container they are in.
Kelvin (K): The units of absolute temperature. 273K = 0°C
Kinetic Theory/Particle Model: A model of solids, liquids and gases that explains the observed properties of the materials by postulating that they are made up of lots of tiny, hard, incompressible spheres. At higher temperatures the spheres move faster.
Mass (kg): Amount of material in an object, measured in kilograms
Pressure (Pa) or (N/m²): The effect of a force spread out over an area. Pressure = Force/area, p=F/A
Rigid Container: A container that will keep a fixed shape regardless of the pressure inside or outside it. The volume is constant and the pressure is variable. Examples are rigid metal cans and glass bottles.
Volume: The space occupied by an object in three dimensions measured in m³, For cuboids, V = l x h x w.

October 4, 2011

Energy Formulae summary

Here is a list of all the formula mentioned in this topic:

$Efficiency=\frac{Useful\: Energy\: output}{Total\: Energy\: input} \left (\times 100 \right )$

$Wd=F\times d$

$KE=\frac{mv^{2}}{2}$

$P=\frac{E}{t}\: or\: \frac{Wd}{t}$

$Total\: Energy\: output=Total\: Energy\: input$

Quantities and Units

Energy = Joules (J)
Wd = Work done (J)
GPE = Gravitational Potential Energy (J)
KE = Kinetic Energy (J)
F = force (N, Newtons)
d = distance moved in the direction of the force (m, metres)
m = mass (kg)
g = gravitational field strength (N/kg) NB: G on earth = 10N/kg
h = height (m)
v = velocity (m/s)
P = power (W, Watts)
t = time (s)

End of Energy Topic

4.17 Energy Advantages

Describe the advantages and disadvantages of methods of large-scale electricity production from various renewable and non-renewable resources.

Energy Source	Advantages of Use	Disadvantages of Use
Fossil Fuels	Fuels readily available, easy to make electricity.	Fuels are non-renewable, produce C0₂ and so add to global warming, acid rain. Oil spills damage environment.
Nuclear	Creates large amounts of energy, is reliable and relatively cheap to set up. Produces no C0₂.	Expensive to decommission power stations after use. Waste is produced that is dangerous for long periods. Reactors that are not cooled will overheat and release waste.
Wind	Produces no C0₂. Once setup takes little maintenance. Renewable.	Expensive to set up. Installations may be noisy and seen as ugly. Unreliable as you cannot count on the wind all the time.
Wave	Produces no C0_2.Small devices can produce large amounts of electricity. Out to sea means out of sight. There are large areas unused across the globe. Renewable.	Easily destroyed by bad weather. Electricity produced needs to be transferred over long distances. Expensive to set up.
Tidal	Reliable as the tides are predictable as they depend on the Sun and Moon. Produces no C0_2.Renewable.	Few areas are suitable of being dammed. The dam restricts movement of sea life. Silt will build up. tides vary in strength throughout the day. Expensive to set up.
Hydroelectric	Produce no C0₂. Once set up have little maintenance cost. Create useful water resources. Can be turned on and off instantly. Renewable.	Expensive to build. Destroy ecosystems. If dams break damaging flooding will occur. Most areas in the world that can be used are being used.
Geothermal	Virtually emission free. Some reduce sulphur emissions. Simple systems are easy to maintain. No fuel costs. Renewable.	Expensive to set up. Expensive drilling through hot rocks. Limited areas in the world where hot areas are close to the surface.
Biomass	Produces no long term C02. Renewable as trees can be regrown	Limited areas of land available. Reduces the production of food.
Solar Heating	Produce no C0₂. Renewable. Light is free.	Unreliable as the sun does not shine all the time. No sun at night.
Solar (Photovoltaic) Cells	Produce no C0₂. Renewable. Light is free. Can be small to be used instead of batteries.	Unreliable as the sun does not shine all the time. No sun at night. Expensive to set up.