4. Carbon nanotubes are materials that have good
conductivity properties, are light weight and high strength.
The density of a carbon nanotube is 1300 kg/m² the
diameter of a carbon nanotube is 0.68 nm and its elastic
modulus is 1.1 TPa. (a) What is the mass of a nanotube
whose length is 150 nm? (b) What is the elastic modulus
measured in lb/in²? (c) The natural frequency of a nanotube
is $\omega = \sqrt{\frac{EI}{\rho A l^2}}$, where $A$ is its cross sectional area and $l$ is its
cross sectional moment of inertia (second moment of area).
Calculate, in hertz, the natural frequency of a nanotube of
length 150 nm. (d) The resistivity of a carbon nanotube is
approximated as $0.34 \times 10^{-4} \Omega \cdot cm$. What is the resistance of a
nanotube of length 150 nm? (f) What is the voltage drop
across a nanowire of length 150 cm if the current entering
the wire is 2.1 $\mu A$? (Hint; the voltage drop across a wire
that has an entering current of $i$ and has a resistance of $R$ is
$v = iR$, known as Ohm's law, (g) If a nanotube of length 150
nm is placed in parallel with a nanotube of length 80 nm
what is the equivalent resistance of the parallel
combination. The equivalent resistance of resistors in
parallel is
$\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2}$
