POTENTIAL AND KINETIC ENERGY

Energy is something that causes a change to a system, at the macroscopic or microscopic level. There are different forms of energy.

• Kinetic energy: any given body has kinetic energy if it is in motion.
  • KE = 1/2 m v²

  • Fast moving object has more: double speed, get 4x energy

  • Massive object has more: double mass, get 2x energy

  • Units: (remember Lab 1) [kg m² /s²] = joules (1 calorie = 4.186 J)

  A common sense approach to understanding kinetic energy:

  

  A more generalized way to understand kinetic energy:

  
  Summary of Kinetic Energy
  The Figure is not as complicated as you might think. An object which starts at velocity = 0 and is accelerated to some velocity v, will always have an average velocity of v/2.

  Ultimately, we can describe the change in position of an object as a force applied to it by a change in energy or by the amount of work done that is required to move the object. Remember, energy is the capacity to do work. These relations are summarized in the figure below:

  

  Energy can be defined as Force x distance. So the total work needed to move the block as distance DX, is given by FDX and that is equal to the change in energy of the system (which is equal to the difference between the initial and final velocities).

  If you recall lab 2 (and you will encounter this later as well), you already know that the displacement goes as 1/2at² and that velocity goes as a * t. So you can get the 1D kinematic equation above as follows:

  v = a * t

  v² = (at)² = a(at²)

  From before, (at²) =2*d (displacement) and therefore,

  v² = a(2*d) = 2ad

  
  

  
  

Potential energy: Stored energy waiting to be released. Often time potential energy is related to the position of an object in some force field. The most common example is height above the earth's surface.

• A tensioned spring: even at rest it has the potential for creating motion

• Chemical energy: wood, gasoline, dinamite are fuels that can release energy when electrons in atoms and molecules change their configuration

• Electrical Energy: fresh battery

• Electromagnetic radiation: light (ex: Sun)

• Nuclear energy can be released if the configuration of subatomic particles in the nucleus of an atom change

• Gravitational energy:
  • brick moved up to table will release energy when falling (GE --> KE)

  • hydroelectric plant

  • GE = m g h for simplicity we take g to be 10 m/sec². Therefore, if you had a 10 kg object at a height of 10 meters above the earth's surface, its potential energy would be 10 x 10 x 10 = 1000 joules.
  )
  Graphical representation of Potential Energy

The law of the conservation of energy means that energy can neither be created or destroyed, only transformed from one form to another.

• Potential energy may be converted into kinetic energy of motion, and in turn to other forms such as electrical energy. Thus, water behind a dam flows to lower levels through turbines that turn electric generators, producing electric energy plus some unusable heat energy resulting from turbulence and friction. We can relate these ideas to the motions of the planets around the sun:

• Kepler's second law
  • In an elliptical orbit about the Sun, the speed of a planet is related to its distance from the Sun

  • Planet has more gravitational potential energy and least kinetic energy when furthest from Sun

  • Planet has least potential energy and most kinetic energy when closest to the Sun

• Asteroid impact
  • Asteroid hurtles through space at 10 km/s and crashes into Earth

  • Before collision, has kinetic energy and little potential energy

  • Falls toward planet and speeds up

  • After collision, no kinetic energy or potential energy

  • Does the energy disappear? No, energy is transformed

  • Crater, Heat!

  • 1000 ton meteorite releases 5 x 10¹³ J. (1 kiloton TNT = 4.2 x 10¹² J, Hiroshima atomic bomb=6.3 x 10¹³ J) and a 1000 ton meteorite is very small on the scale of objects that do hit the earth.