| In
the state of Georgia, about 5% of our total electrical energy is provided
by hydroelectric dams. The energy source for a hydroelectric
dam is the potential energy of the water (due to its height above the base
of the dam) that is stored behind the dam. This potential energy
is converted to kinetic energy as the water is allowed to flow out of the
dam. By placing a turbine that is connected to a generator in front
of the flowing water, we are able to produce electricity.
In this week's
experiment, we are going to model this system in the laboratory.
A picture of the turbine generator that will be used for this
activity is shown to the right. This experiment transfers
the potential energy of water from a plastic container that
is placed a height H above the generator to the kinetic energy
of the moving turbine blades in the transparent enclosure.
The generator then transfers this kinetic energy to electrical
energy by spinning a magnetic in the wire coil on the top
of the generator. This electrical energy will be sent to a
computer that will monitor the output. From the energy
measured by the computer, we will plot the dependence of potential
energy on height, as well as calculating the efficiency of
energy transfer in the turbine generator.
As
stated previously, the amount of gravitational potential energy that an
object has should depend upon the height through which it is allowed to
fall. Theoretically, this dependence should be linear, i.e. the amount
of gravitational potential energy an object is equal to some constant times
the height of the object (see derivation at the right). Therefore,
if everything else in the system is linear, this means that the amount
of electrical energy produced should depend linearly on the height of the
water.
The
other issue that we are going to investigate is the efficiency of the total
energy transfer from gravitational potential energy to electrical energy.
As we see in the theory (lower right), the amount of energy in the water
initially is given by
Potential
energy = (mass of the water) x (the acceleration due to gravity)
x (average height of the water)
= mgH
For
our experiment (we will be using 150 mL of water, which has a mass of .150
kg), this equation becomes:
Potential
energy = (.150 kg)x(9.80 m/sec2) x H
= (1.47 kg m/sec2) x H
By
plugging in the height of each individual run, this formula gives us the
total amount of energy in the system at the start. The computer will
measure the amount of electrical energy that is output by the generator.
Thus, we should be able to compute the efficiency of the system using the
formula:
Efficiency
= (electrical energy output)/(potential energy)
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Gravitational
Potential Energy
As
we have already stated, the potential energy is the energy stored in a
system by virtue of forces between objects that are separated by some distance.
Because gravity is a force that is operating on all objects near the surface
of the Earth, there will be gravitational potential energy contained in
any object that is allowed to move toward the Earth under its influence,
i.e. any object that can fall to a lower height will have usable gravitational
potential energy. The amount of potential energy that an object has
depends upon the strength of the force and the amount of distance over
which the force can act. For gravity, this reduces to a very simple
expression. Near the surface of the Earth, the force due to gravity
is a constant. It is merely the mass of the object upon which gravity
is acting times the acceleration due to gravity:
Fgravity
= mass x acceleration due to gravity
= mass x 9.80 m/sec2
Since
the force is a constant, the potential energy is merely this force times
the distance through which the object falls. If we allow H to be
the height through the object will fall, then the potential energy of the
object is:
P.E.
= Fgravity x H = mass x 9.80 m/sec2 x H |
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