Energy Transformations (1) GPE to KE and vice versa; the story of Sisyphus)

Persephone supervising Sisyphus in the Underworld

Sisyphus was famed as the craftiest of men. He was nasty, deceitful and greedy. As a punishment from the gods for his trickery, Sisyphus was made to push a huge rock up a steep hill, but before he could reach the top of the hill, the rock would always roll back down, forcing him to begin again – an endless cycle of energy conservation. The gravitational potential energy gained by pushing the rock up the hill was converted to kinetic energy as the rock rolled down again.

…let’s forget about frictional forces for now, shall we?

Notice that Sisyphus had to push the stone up a hill. The VERTICAL height of the hill is used to calculate the gain in gravitational potential energy, not the length of the slope of the hill.

Sisyphus had to push much harder. Why? How could he reduce his pushing force? What else would have to change?

Next: conserving E, cancelling m gives the expression to show how fast the stone would be

going if it was allowed to fall freely (forget about rolling)Screen Shot 2016-06-27 at 12.30.32

You might think about how much higher the hill would have to be to cause the stone to be going twice as fast at the bottom – this kind of thing crops up in MC all the time.

My ‘hill’ in the diagram is a straight line. In terms of energy conservation, would the shape of the hill matter? The answer is ‘no’, but can you explain why?

The original track to the hilltop fortress of Masada in Israel is shaped like this.

Screen Shot 2016-06-27 at 12.37.36
Looking down

You might like to reflect on this…

Work done = energy transformed (against gravity) = applied force x distance moved in the direction of the force.

 

Renewable and Non-renewable Fuels

An Oil Refinery

All life on earth gets its energy from the sun. Plants and animals can store energy and some of this energy remains with them when they die. It is the remains of these ancient animals and plants that make up fossil fuels.

Energy resources

Fossil fuels are non-renewable energy resources and will one day run out and we can’t replace them. Burning fossil fuels generates polluting  greenhouse gases and we mustn’t continue to rely on them to make the energy we need.

Renewable or infinite energy resources are sources of energy that can be used again and again.

Some resources can be thought of as both renewable and non-renewable.

  • Wood can be used for fuel and is renewable if trees are replanted.
  • Biomass, which is material from living things, can be renewable if plants  – like sugar cane – are replanted.

Over the last 200 years most of our energy has come from non-renewable sources such as oil and coal.

Non-renewable energy resources

Type of fuel Where it is from

Coal (fossil fuel)
  • Formed from fossilised plants.
  • Mined from seams andwiched between layers of rock in the earth.
  • Burnt to provide heat or electricity.
  • Ready-made fuel.
  • It is relatively cheap to mine and to convert into energy.
  • Coal supplies will last longer than oil or gas.
  • When burnt it gives off poisonous gases, including greenhouse gases.
Oil (fossil fuel)
  • A carbon-based liquid formed from fossilised animals.
  • Lakes of oil are sandwiched between seams of rock in the earth.
  • Pipes are sunk down to the reservoirs to pump the oil out.
  • Widely used in industry and transport.
  • Oil is a ready-made fuel.
  • Relatively cheap to extract and to convert into energy.
  • When burnt it gives off poisonous gases, including greenhouse gases.
  • Only a limited supply (ther isn’t very much of it available).
Natural gas (fossil fuel)
  • Methane and some other gases trapped between seams of rock under the earth’s surface.
  • Pipes are sunk into the ground to release the gas.
  • Often used in houses for heating and cooking.
  • Gas is a ready-made fuel.
  • It is a relatively cheap form of energy.
  • It’s a slightly cleaner fuel than coal and oil.
  • When burnt it gives off poisonous gases, including greenhouse gases.
  • Only limited supply of gas.
Nuclear
  • Radioactive minerals such as uranium are mined.
  • Electricity is generated from the energy that is released when the atoms of these minerals are split (fission) or joined together (fusion) in nuclear reactors.
  • A small amount of radioactive material produces a lot of energy.
  • Raw materials are cheap and can last quite a long time.
  • It doesn’t give off atmospheric pollutants.
  • Nuclear reactors are expensive to run.
  • Nuclear waste is very poisonous, and needs to be safely stored for hundereds or thousands of years (storage is extremely expensive).
  • Leakage of nuclear materials is very dangerous. The worst nuclear reactor accident was at Chernobyl, Ukraine in 1986.
Biomass
  • Biomass energy is generated from decaying plant or animal waste.
  • It can also be an organic material which is burnt to provide energy, e.g heat, or electricity.
  • An example of biomass energy is oilseed rape (yellow flowers you see in the UK in summer), which produces oil.
  • After treatment with chemicals it can be used as a fuel in diesel engines.
  • It is a cheap and readily available source of energy.
  • If the crops are replaced, biomass can be a long-term, sustainable energy source (it can be kept going for a long time).
  • When burnt it gives off poisonous gases, including greenhouse gases.
  • If crops are not replanted, biomass is a non-renewable resource.
Wood
  • Obtained from cutting down trees, burnt to generate heat and light.
  • A cheap and readily available source of energy.
  • If the trees are replaced, wood burning can be a long-term energy source.
  • When burnt it gives off poisonous gases, including greenhouse gases.
  • If trees are not replanted wood is a non-renewable resource.

How long will fossil fuels last?

If we all continue to burn fuels “like there’s no tomorrow”, oil and gas reserves may run out within our lifetimes. Coal is expected to last a little bit  longer.

Estimated length of time left for fossil fuels

Fossil fuel Time left
Oil 50 years
Natural gas 70 years
Coal 250 years

Centre of Gravity

 

Wibbly-wobbly men

 

The centre of mass or is the mean or average location of all the mass in a system. In the case of a rigid body the position of the centre of mass is fixed in relation to the body. For example the centre of mass of a pool ball is exactly in the middle of it. In the case of a loose distribution of masses in free space such as pellets scattered from a shotgun or the planets of the solar system the position of the centre of mass is a point in space among them that may or may not correspond to the position of any individual mass.

The concept is useful since sometimes we want to know where exactly to apply a force on a body.

The centre of gravity of a body corresponds to the point where all the gravitational force acts, in other words the single point through which the resultant of the gravitational forces on the component particles of the body acts.

Homogeneous objects. Think about where the c.g of objects like these might lie

  • Centre of gravity of a lamina or flat sheet – drop two plumblines from two separate fixed points – where they cross is the c.g
  • Centre of gravity of an L shaped body- as above but the lines may cross outside of the body
  • Centre of gravity of a snooker cue (a reminder about moments)the sum of all the mass elements and their associated clockwise moments equals the sum of all the mass elements on the other side of the pivot and their associated moments. Result – it balances nearer the thicker end.
  • Centre of gravity of a lab stool – will lie outside the body of the material. Where’s the c.g of a doughnut?

Non- homogeneous objects – a reminder about stable equilibrium and toppling (IGCSE)

  • Bowls – eccentric balls – the ball has an eccentric c.g, thus when bowled, there’ll be a turning moment curling the ball into a curved path
  • London buses – have a very low c.g, so they can be tilted to over 40 degrees and the weight force still acts between the wheels so they won’t topple over
  • Racing carsare subject to very large turning forces, the c.g needs to be very close to the ground otherwise they’d flip over.

For practical purposes, the centre of gravity corresponds exactly to the centre of mass because the gravitational field of the Earth (the gravitational force exerted on every kilogram of mass) is the same at 9.81N kg-1 close to the Earth’s surface

  • Centre of gravity of the Burj Khalifa in Dubai. g = F/m, but is g constant? assuming the structure is homogeneous (it isn’t) there will be an imperceptibly small reduction in g at the c.g, since the centre of the building is so far away from the ground. The c.m will be less than 0.1mm away from the c.g

Four Factors Affecting Resistance

Some old-fashioned electrical components

Resistance is a property of a DEVICE or a COMPONENT. like a lamp, a resistor, a thermistor, a diode and so on. Its value depends on four things.

1. What it’s made of. Metals are good conductors so have lower resistance than an insulator of the same dimensions.

2. Length – the longer, the greater resistance.

3. Area of cross section – the larger the lower.

4. Temperature (metals: higher temperature = higher resistance because the vibration of the metal lattice impedes the drift of the electrons, semiconductors:  like thermistors , resistance decreases with temperature)

Variable resistors or potentiometers control the length of wire we introduce into a circuit  – the volume control on a hi-fi

Thermistors have a high resistance in the cold and a low resistance in the warm. They are used in logic circuits to turn heaters on and off.

LDR’s (light dependent resistors have a high resistance in the dark but a low resistance in the light. As darkness falls, they are used in logic circuits to turn on street lights.

A diode is an electrical one way street, which is useful sometimes in electronic circuits. Current is allowed through a low resistance pathway in one direction, the resistance is very high in the reverse direction so no current flows.