Lecture
11: Potential Energy, Energy Conservation and Power
Part 1: Potential Energy and the Work
Energy Theorem
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Potential energy is the energy associated with
the object’s POSITION in space
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First kind: Gravitational Potential energy, Ug
= mgy, where y is the distance of the object from the zero reference point
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This zero reference point is arbitrary, it is
not a fixed reference point.
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Second kind: Elastic Potential energy, Us
= ½ kx2, where x is the distance from the equilibrium
or zero reference point which refers to the springs unstretched state.
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Work – Potential Energy theorem: Wnet
= -DU
PART 2: Conservation of Energy and
Conservative Forces
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A conservative force is a force that does work
on an object that is independent of the path taken. Therefore, it does
not matter how you get from point A to pint B, because the work done will
be the same regardless of the path taken.
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Gravitational Force and Elastic forces are examples
of conservative forces.
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Total Mechanical Energy E = K + U, just the sum
of the kinetic and the potential energy acting on a system.
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If a system has only conservative forces acting
on it, then the conservation of mechanical energy states: the mechanical
energy of the system is constant, therefore DE
= 0 or Ei = Ef .
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Simply put: the energy of the system anywhere
on its path is constant, the only thing that may change is the type of
energy involved.
PART 3: Conservation of Energy and
Non-conservative forces
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A non-conservative force is a force that does
path-dependent work on an object, that is, to go from point A to B, it
matters what path is taken.
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All dissipative or frictional forces are NON-Conservative.
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Total Energy (includes mechanical energy and
other types of energy like thermal energy) is conserved under all circumstances,
even when non-conservative forces are involved.
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The most general statement of conservation of
energy is: Energy can neither be destroyed nor created, energy is merely
transformed from one form to another.
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For non-conservative forces: DE
= Wnc, the change in energy is equal to the work done by the
non-conservative force.
PART 4: Power
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Power is the rate at which work is done
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Power is a scalar quantity and has units called
WATTS or J/s
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Average Power
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Instantaneous Power