Contents

Simple potential energy, "E_p", may be the product of an object's weight and its distance, "d", above the surface of the earth. This product is expressed in English measurement as foot-pounds. A pound is actually a force, "F", rather than a mass unit, "m", and it is equal to the acceleration of gravity, "g", multiplied by the mass of the object which is expressed in slugs. So E_p = Fd = mgd.

Kinetic energy, "E_k", for an object that has been dropped is equal to the E_p which existed before it was dropped.
E_k = mv² / 2 where v is the velocity when the object impacts upon the earth. E_k at impact is the way the object discharges what was its E_p.

Gravity is a force which extends to infinity (or for as far as the universe extends).

If we were to cause an object to escape from our gravity funnel, it would have to leave the earth's surface with a velocity at least equal to that in its kinetic energy equation, were it to fall from an infinite distance to the planetary surface. In other words, gravity extends to infinity so the maximum kinetic energy the body can have, due to earth's gravity alone, is what would be given to it if it were to fall to earth from an infinite distance.

In the absence of any other force, an object at an infinite distance from earth would not be subjected to earth's gravity, so the gravitational force from earth would be equal to zero at this distance. Once having been given a very small shove toward earth, the object would begin to accelerate along with its surrounding nether that also started with zero velocity toward earth.

So the nether which passes through earth's surface should have the same kinetic energy as an object dropped from an infinite distance. Since the two E_ks are equal, the velocity found for the object E_k should be the same velocity as that of the nether passing through the earth's surface.

So E_p will be equal to the weight (ma) of the object multiplied by an infinite distance. E_k will be equal to the square of its instantaneous velocity multiplied by its mass, "m", divided by two. In the process of discovering the velocity, both "m" and the infinite distance divide out and are no longer part of the equation.

The equation we use with the energy equality is that used to find the average gravity, "g_ave", experienced by an object falling from an infinite distance. Bear in mind that the average gravity varies with the velocity experienced during each part of the fall. The time experienced while at lower gravity will be greater than the time experienced at higher gravity. Thus, we find that "g_ave" is a function of B.
 

Contents - Next