Page 39 - Science at the nanoscale

RPS: PSP0007 - Science-at-Nanoscale
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June 9, 2009
2.4. Motion at the Nanoscale
to form rather complex macromolecular structures. This mode of
assembly is known as self-assembly, and will be discussed further
in Chapter 7. Such random stochastic processes are the basis of all
chemical reactions, and indeed of the biochemistry of life itself.
So far we have been describing physics at the nanoscale using
purely classical physics. However, quantum mechanical effects
become significant when we consider even smaller entities such
as the electron. Indeed changes in energy levels occur when elec-
trons are confined to nano-sized objects, altering the electronic
and optical properties of the material. We shall address these
issues in the next chapter.
Further Reading
Edward L. Wolf, Nanophysics and Nanotechnology (Wiley, Germany,
2004).
Richard A. L. Jones, Soft Machines — Nanotechnology and Life (OUP,
2004).
W. R. Browne, B. L. Feringa, “Making molecular machines work”,
Nature Nanotechnology 1, Oct 2006, 25.
Exercises
1. A steel bridge spanning a river is 100 m long and fixed only at
the two ends. Calculate (i) the speed of sound in the bridge;
(ii) the resonant frequency of the bridge. Can a class of stu-
dents oscillate this bridge by jumping on it in a coordinated
matter? (iii) If this steel bridge is 1 km long instead, what
might happen if a battalion of soldiers march in step across
it? (iv) If a micro-model of this steel bridge is made 1µm long, 29 ch02
what would be its fundamental frequency, and the next two
harmonics?
2. (i) Estimate the terminal velocity of a skydiver falling from a
plane. State all assumptions made. (ii) The terminal veloc-
ity of a skydiver has actually been measured to be about 200
km/h (or 55 m/s). For a heavy object, the air resistance is pro-
2
portional to the falling body’s velocity squared (i.e. cv , where
c is a constant). Using this information, determine the value of
c and write down the equation of motion for the skydiver of
mass 70 kg. (iii) For a bug 100 µm in size, estimate its terminal
velocity in air. Assume the bug is just able to float in water.