Formation and Structure of Ramified Transportation Networks in an Electromechanical System

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• Last Week Mass
• Mass is the amount of matter
• in an object, i.e. its total energy content
• (nuclear chemical termal energy).
• Em c2
• Inertial mass is sluggishness
• of an object, its resistance to acceleration.
• Fm a (Newtons 2nd
  law)
• Gravitational mass is proportional
• to the weight of an object,
• the gravitational pull on the object.
• W m g
• Inertial mass Gravitational mass Mass

The U.S. National Prototype Kilogram, which
currently serves as the primary standard for
measuring mass in the U.S.
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Importance of a Concept The weight force on
an object is constant on Earth, whereas The
mass of the object (sluggishness) is constant
throughout universe. Therefore, the on concept
of mass is more important than weight.
Importance of a concept range of applicability
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• Discussion of mass continued
• high-energy cosmic rays produce minute quantities
  of matter and antimatter, such as an electron
  positron pair.
• - Small regular waves represent heat, light,
  X-rays. Full left twist (solitons) represents
  matter. Full right twist (antisoliton) represents
  antimatter.

Experimental observation 0f the ceation of
matter in a bubble chamber
Solition machine illustrates the creation of
matter. Here an antisoliton passes through a
soliton.
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• Volume
• Context I drink a cup of tea. Please buy a
  gallon of milk. The volume of a cube with
  dimension r is r3.
• Definitions
• The volume of a solid object measures how much
  space it occupies.
• The volume of irregularly shaped objects can be
  determined by their displacement of a liquid.

Lecture demo Displacement of water by a
butterfly and a sponge.
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• Density
• Context The fog is very dense. The density of
  wood is less than the density of water.
• Definition
• The density of a material is the mass per volume

density mass / volume
Lecture demos Archimedes
In a famous problem, Archimedes was given the
task of determining whether King Hiero's
goldsmith was embezzling gold during the
manufacture of a wreath dedicated to the gods and
replacing it with another, cheaper
alloy.1 Archimedes knew that the irregular
shaped wreath could be smashed into a cube or
sphere, where the volume could be calculated more
easily when compared with the weight the king
did not approve of this. Baffled, Archimedes went
to take a bath and observed from the rise of the
water upon entering that he could calculate the
volume of the crown through the displacement of
the water. Allegedly, upon this discovery,
Archimedes went running though the streets in the
nude shouting, "Eureka! Eureka!" (Greek "I have
found it"). As a result, the term "eureka"
entered common parlance and is used today to
indicate a moment of enlightenment.
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• Discussion of density
• - Density of an object does not depend the shape
  and size of the object, just on the material it
  is made of
• - Density of water 1000kg/m3 1kg/liter
• Density of a solids and fluids depend very
  little of the pressure and the temperature, since
  they are easily compressible.
• However the density of gases depends on the
  pressure (and temperature)
• Density of a gas (molecular weight)
  (pressure) / (gas constant)temperature

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Buoyancy Buoyancy force Weight force of the
displaced fluid Floating on an
interface density of an object is less than the
density of the lower liquid, (but larger than the
density of the upper liquid)
Lecture demos Floating and Sinking pop cans,
Aluminum foil boat in water, Density of Water
vs. Oil, Hot Air Balloon, Lava Lamp, Cartesian
Diver, Density and Three Balloons, Density
Paradox Set, Dry Ice Bubbles (Density of
Gases)
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• Volume
• Definitions
• The volume of a solid object measures how much
  space it occupies.
• The volume of irregularly shaped objects can be
  determined by their displacement of a liquid.

Lecture demo Displacement of water by a
butterfly and a sponge.
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• Density
• .
• Definition
• The density of a material is the mass per volume

density mass / volume
Lecture demos Archimedes