Lesson 14 Potential Energy

In 1711 Ruđer Bošković, a diplomat, architect, scientist, and writer, proposed the idea that all matter is made up of point masses, and when masses are far apart, force acts between the two masses. Bošković was in fact correct. For example if a force is graphed against position, the zeroes of the graph are points of no force or equilibrium. However, these points of equilibrium are both stable and unstable. A positive force is repulsive while a negative force is attractive. Therefore, a point with a negative force on the left and a positive force on the right is at unstable equilibrium while a point with a positive force on the left and a negitive force on the right is at stable equilibrium. Here is an image of Bošković's work below:

 From these findings, it was believed that atoms are bound into stable webs of matter, however, this was not a scientific idea because it could not be readily tested. In the following centuries, John Dalton discovered atoms while Michael Faraday studied fields of force. From these advances it was found that every piece of matter in a solid is in stable equilibrium, unlike the webs of stability predicted by Bošković.

The total amount of energy never decreases because energy is strictly and absolutely conserved. Potential energy depends on position, such as a tank of gasoline, where the positions of the atoms in the molecules of the gasoline determine the potential energy becasue an atoms potential energy depends on its position in the matter it's bound to. Potential energy can be both positive and negative without changing effect where F = -du/dx. The higher above earth an object is, the more gravitational potential energy the object has because potential energy changes with the objects position. Therefore, the closer to the ground an object is, the less potential energy it has.

Gasoline:

Kinetic energy is related to speed, where the faster an object travels the more kinetic energy it has while the slower an object travels the less kinetic energy it has.

Any body can trade potential energy for kinetic energy by trading position for speed.

Here is a video that displays the conservation of energy as potential energy tranfers into kinetic energy:



Molecules in oil have great potential enrgy, as the atoms are bound together by the electrical force between atoms. When the oil atoms are ignited, the molecules rearrange themselves into other forms of matter with less potential energy.

Here is a video that displays the enormous amount of potential energy of oil molecules:



On the other hand, a fire hose has initial potential energy as the wtaer enters the hose, kinetic as the water leaves the hose, and potential energy as gravity influences the path of the water. Work can be described as a change in energy:

Take the lifting of a vessel from one height to another:
          
               Rf
W = integral (Fdr)                            F = G m Me
               RE                                                 r^2
              
                Rf
     = integral (G m Me  dr)
                RE        r^2
                        
                           Rf
     = GmMe integral (dr/r^2)
                           RE

                          Rf
      = -GmMe/r |
                          RE

       =  -GmMe/Rf - (-GmMe/RE)

    u = -GmMe/r

W = uf - uE of the change in potential energy

If the ball is lifted to infinity it has a potential energy of 0, and also on the surface or at ground level.

(-GmMe/RE) + 1/2 (mv^2) = 0  because kinetic energy must balance out potential energy.

Therefore, in the case of a rocket leaving the earth's surface u + k = 0 to escape from the earth and reach infinity where:

V = sqrt ( 2 G Me/Re ) and the rocket will escape is traveling at 11 km/sec

In the case of a firefighter:

Potential Energy = mgh                                      m = 90kg of firefighter
                                                                             J = 10 m/s^2
                                                                             The height of the burning building is 30m
                            = 27000J
420 = 1 calorie of heat

About 6400 calories

However 1 food Calorie is equivalent to 1000 heat calories, therefore it would take to firefighter about 6.4 Calories of food storage.

Work = Force x Height

The human body is actually very inneficient because it uses most of its stored energy to mantain basic bodily functions. In the terms of physics, potential energy is relative to the ground, therefore if one climbs a ladder and returns to the ground, no net work has been accomplished.

Here is a video that describes the distinct difference between kinetic and potential energy: