Gravitational potentials

The miderstanding of the quantum mechanics of atoms was pioneered by Bohr, in his theory of the hydrogen atom. This combined the classical ideas on planetary motion—applicable to the atom because of the fomial similarity of tlie gravitational potential to tlie Coulomb potential between an electron and nucleus—with the quantum ideas that had recently been introduced by Planck and Einstein. This led eventually to the fomial theory of quaiitum mechanics, first discovered by Heisenberg, and most conveniently expressed by Schrodinger in the wave equation that bears his name. 

AV is the net change in gravitational potential energy. This term is path independent and depends only on the initial and final heights, h and hj, above some arbitrary reference height with respect to the surface of the earth. 

A body of mass m at a height b above the surface of the Earth has a gravitational potential energy... 

EXAMPLE A.4 Sample exercise Calculating the gravitational potential energy... 

Self-Test A.5A What is the gravitational potential energy of this book (mass 1.5 kg) when it is on a table of height 0.82 m relative to its potential energy when it is on the... 

I 4 Calculate the gravitational potential energy of an object (Example A.3). 

Removing an electron from a nucleus increases the electrical potential energy. Lifting a backpack from the floor to a tabletop increases the gravitational potential energy. 

C06-0008. Which of the following are state functions (a) height of a mountain (b) distance traveled in climbing that mountain (c) energy consumed in climbing the mountain and (d) gravitational potential energy of a climber on top of the mountain... 

The quantum levels of an electron bound to an atom are cmdely analogous to the gravitational potential energies available to a ball on a staircase. As illustrated in Figure 7-12. a ball may sit on any of the steps. If we define the top of the steps to be 5" = 0, the ball has a negative potential energy when it is on any of the lower steps. To move a ball from the bottom of the staircase to step 5 requires the addition of a specific amount of energy,... 

Whereas gravitational potentials are measured in heights, electrical potential differences are measured in volts. For electrons, a point at a more negative electrical potential is uphill from a point at a more positive electrical potential. The parallel between gravitational potential and electrical potential is summarized in Figure 19-10. 

Water flows down a spillway from higher to lower gravitational potential. Electrons flow downhill through a wire from higher to lower negative electrical potential. 

Gravity force can be measured by means of the mass of the water. The direction of the force is, obviously, downwards toward the Earth s center. The gravitational potential of soil water at each position is determined by the elevation of the position relative to some reference level. If we only consider the elevation potential and the related velocity energy, then a water body at a higher elevation will flow to a lower elevation, decreasing the elevation potential but increasing its velocity. 

The cause of flow between these points is the difference in elevation head between them, that is, (Z, - Z2), denoted as dh, which is contributed by the gravitational potential. If is the distance between the two points on the water table, then the djd ratio is known as the hydraulic gradient. 

Gravitational potential energy (associated with the attraction between separated masses)... 

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