Download determining potentiel energy values

DETERMINING POTENTIEL ENERGY VALUES
Potential is the specific potential energy. That is, when potential energy depends on some quantity
associated with object in question, potential is potential energy per unit of that quantity. For example,
gravitational potential is gravitational potential energy per unit of mass. Electrostatic potential is the
electrostatic potential energy per unit of charge. The nature of potential is that the zero point is
arbitrary; it can be set like the origin of a coordinate system. That is not to say that it is insignificant;
once the zero of potential is set, then every value of potential is measured with respect to that zero.
Another way of saying it is that it is the change in potential which has physical significance. The zero of
electric potential (voltage) is set for convenience, but there is usually some physical or geometric logic to
the choice of the zero point. For a single point charge or localized collection of charges, it is logical to set
the zero point at infinity. But for an infinite line charge, that is not a logical choice, since the local values
of potential would go to infinity. For practical electrical circuits, the earth or ground potential is usually
taken to be zero and everything is referenced to the earth.
Gravitional potential energy
We first consider a particle with mass m moving vertically along a y axis (the positive direction is
upward). As the particle moves from point yi to point yf, in the gravitational force Fg does work on it. To
find the corresponding change in the gravitational potential energy of the particle-Earth system, we use
the below equation. In this equation we integrate along y axis instead of x axis because the gravitational
force acts vertically and we substitute –mg for the force symbol F, because Fg has the magnitude mg and
is directed down the y axis.
Only changes ∆U in gravitational potential energy (or any other type of potential energy) are physically
meaningful. However , to simplify a calculation or a discussion , we sometimes would like say that a
certain gravitational potential value U is associated with certain particle-Earth system when the particle
is at a certain height y. to do so, we rewrite equation
Then we take the Ui to be the gravitational potential energy of the system when it is in reference
configuration in which the particles is at a reference point yi . usually we take UI =0. Doing this changes
the equation
Elastic potential energy
First, we consider the block-spring system shown in the figure, with the block moving on the end of a
spring of spring constant k.As the block moves from point xi to point xf, the spring force Fx= -kx does
work on the block. To find the corresponding s change in the elastic potential energy of the block-spring
system, we substitute –kx for F(x) in the below equation
To associate a potential energy value U with the block at the
position x, we choose the reference configuration to be when
the spring is its relaxed length and the block is at xi = 0. Then the
elastic potential energy Ui is 0, and the equation becomes
which gives us
Electric potential energy
Potential energy can be defined as the capacity for doing work which arises from position or
configuration. In the electrical case, a charge will exert a force on any other charge and potential energy
arises from any collection of charges. For example, if a positive charge Q is fixed at some point in space,
any other positive charge which is brought close to it will experience a repulsive force and will therefore
have potential energy. The potential energy of a test charge q in the vicinity of this source charge will
be:
The general expression for the electric potential as a result of a point charge Q can be obtained by
referencing to a zero of potential at infinity.
In electricity, it is usually more convenient to use the electric potential energy per unit charge, just
called electric potential or voltage. Difference between electrostatic potentials between two points is
the voltage. Voltage is the amount of potential energy change for 1 coulomb of charge moving from first
point to the second. If you have a vacuum tube, effectively giving you no resistance, an electron
traveling across 1V gap would gain kinetic energy equal to potential energy drop, which is the charge of
electron * 1V, or in units of electron charge, this is energy of 1 electron-volt (eV). In a circuit, however,
all this energy is dissipated as heat. If one coulomb of charge moves across 1V of potential, 1J of heat
has been produced. Since current is charge flow per unit time, current time voltage gives you amount of
energy going into heat per unit of time, or power.