First Principles - Sustainable Design: The Science of Sustainability and Green Engineering - page 53

Green Physics Example 2

(a) An aerosol weighing 2 g is emitted from a stack straight up into the atmo-

sphere with an initial velocity of 5 m s − 1 . Calculate the kinetic energy immediately
following the stack emission. Ignore air friction and external forces (e.g., winds).

µ

Solution From equation (2.1) we can calculate the kinetic energy:
E kinetic = 10 − 7 kg m 2 s − 2

(b) What are the kinetic energy and potential energy at the maximum height for
this example?

1 2 1

10 − 9 kg)(5m s − 1 ) 2

2 m

v =

2 (2

× = 5 ×

Solution Wherever we find the point of maximum height, by definition the
velocity is zero, so a close look at equation (2.1) shows that the kinetic energy
must also be zero. By definition, at the maximum height, all the kinetic energy
has been converted to potential energy. So the value found earlier for the kinetic
energy immediately after the emission is now the value for the potential energy
of the system: that is, 5 × 10 − 7 kg m 2 s − 2 .

(c) What is the total energy in this example at the elevation where the particle
velocity has fallen to 0.5 m s − 1 ?

Solution Even though some (even most) of the kinetic energy has been
converted to potential energy, the total energy of the system remains at 5 10 − 7 ×

kg m 2 s − 2 .

Sidebar: Applying the Synthovation/Regenerative Model:
Gestalt Thinking
Pax Scientific in San Rafael, California is leveraging lessons from the spiral flow
of water and air in nature to create innovative fans and impellers that are more
energy efficient. Jay Harman of Pax has discovered “streamlining principles”
based on his observation of the twisted spiral form of seashells, eddies in a
stream, and spiral galaxies. The similarities suggested to Harmon that these
patterns were representative of the geometric fundamentals of motion.
The understanding and application of this geometry has led to the basic
shapes of impellers, pumps, and fans, which are 30% more efficient in their
energy use in terms of producing less heat and noise than traditional designs.
Pax is now in the process of extending the application to the automotive
industry as well as the commercial heating and cooling industry and licensing
the technology for use in cooling fans for devices as diverse as refrigerators