Energy: Transformation and Conservation

Although energy is a somewhat mysterious concept to apprehend, its presence can be discerned all around in the natural patterns that are a by-product of its transmission, from the turbulent daily weather to the erosion of landscapes over millennia. Energy is well known as a source of light and heat for homes and also to power transport systems and factories.

Other forms of energy are more discrete.  Informally one might consider that anything that “happens” takes place on account of the energy appearing at the event.  It was energy that moved the apple to inspire Isaac Newton to reach his famous conclusions about gravity, just as energy is moving the planets and the stars.  Without energy, all would be still, ultimately cold and lifeless.

Energy is therefore an obvious thread to follow to connect the physical world to its social and economic domains.

It is well recognised that energy which animates all things can take various specific forms which need to be identified:-

  • Potential Energy – that is gained by moving something through a potential field, for example raising a mass in a gravitational field.  The higher the mass the greater is its potential energy.
  • Kinetic Energy – that appears on account of the movement.  The faster a mass is moving, the greater is its kinetic energy.
  • Strain Energy – that is held within matter as it is deformed by applied forces.  The more a particular material is stretched or squashed the greater is its strain energy.
  • Surface Energy – is an energy that determines how sticky or slippery a material surface is.  This is an energy locked into that surface that was derived initially from the energy required to create the surface.

To these items one can add thermal energy, sound, chemical energy, electrical energy, nuclear energy, each with their specific characteristics.

Furthermore, these different forms of energy are governed and linked by a fundamental common principle.   The 1st law of thermodynamics requires a conservation of energy, so that whilst energy may change from one form to another, it cannot be destroyed.  An example of this transformation and conservation of energy is shown for a bouncing ball in the figure below.

 

Bouncing Ball

Figure (1): Example of Transformation and Conservation of Energy[1]

The sequence in this figure begins with the input of energy, perhaps exerted by a muscle or through an explosion to launch a ball into the air.  The ball slows down as it gains height.  The initial kinetic energy of movement is being gradually transformed into a potential energy gained on account of the height of the ball above ground.  This potential energy will reach a maximum before being recycled back into kinetic energy as the ball falls back to earth.  On meeting the ground, the ball is brought rapidly to a halt as the kinetic energy is transformed momentarily into a mechanical strain energy stored within the material of the now deformed ball.  Back this strain energy goes into the kinetics of the first bounce, although some energy will be dissipated as sound and heat in this and subsequent bounces, causing the maximum height attained to diminish.  Finally, the ball will come to rest as all its original kinetic energy is lost to the dissipative processes[2].  Through this sequence, energy is not destroyed but is changed from one form to another.  Understanding this conservation of energy enables one to trace the energy transformations that take place in such a dynamic process.

 Bouncing Ball Energy Transfers
One can picture such a sequence of energy transformations as a flow of energy with time, essentially using the material components with which it interacts as conduits to channel the flow.  In figure (2) we map these conduits schematically into a graphical representation of energy flow.Later, we shall go on to use this method to chart a broader range of energy transformations and interactions.

Figure (2): Energy Flow Network – Equivalent of Figure (1)

The dynamics of the ball following its launch in are strictly controlled by the properties of the gravitational field through which it travels.  Its movement on the moon would be far more exaggerated as there the force of gravity is merely one sixth of that on Earth.

Later we will go onto form an analogy to this physical trajectory to represent the elevation of a Value Surface in an economic potential field.  In this case, the projectile, which would now be a commodity, moves under the action of economic factors such as labour and capital which are deployed over time to boost the value of the goods in question  For this analysis of innovation, it is first necessary to understand a fundamental mechanical “Principle of Least Action” that governs the trajectory of a physical object in the analogous mechanical domain.

 

Notes:

[1] Note that if the ball bounces on the same spot, the kinetic energy at the top of the bounce decreases to zero as the ball is momentarily stationary.  Alternatively, if the ball travels horizontally, then kinetic energy does not decrease to zero as there will be some continuous sideways movement.

[2] Thus fulfilling the 2nd law of thermodynamics which insists that, in this case, the entropy in the universe is increased by a very small amount with each bounce.

 

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