Certain cold stars (called white dwarfs) are stabilized against gravitational collapse by the degeneracy pressure of their electrons. Assuming constant density, the radius R of such an object can be calculated as follows: (a) Write the total electron energy in terms of the radius, the number of nucleons (protons and newtons) N, the number of electrons per nucleon q, and the mass of the electron m. (b) Look up, or calculate, the gravitational energy of a uniformly dense sphere. Express your answer in terms of G (the constant of universal gravitation), R, N, and M (the mass of a nucleon). Note that the gravitational energy is negative. (c) Find the radius for which the total energy, (a) plus (b), is a minimum. (d) Determine the radius, in kilometers, of a white dwarf with the mass of the sun. (e) Determine the Fermi energy, in electron volts, for the white dwarf in (d), and compare it With the rest energy of an electron.(Note that this system is getting dangerously relativistic.

You have been called upon to prevent outbreaks of SSSS in the nursery of a hospital where this strain of S. aureus has been isolated.
a. What will be the main concerns?

A spherical steel pressure vessel (diameter $500\ \mathrm{~mm}$, thickness $10\ \mathrm{~mm}$ ) is coated with brittle lacquer that cracks when the strain reaches $150 \times 10^{-6}$ (see figure). (a) What internal pressure $p$ will cause the lacquer to develop cracks? (Assume $E=205\ \mathrm{GPa}$ and $\nu=0.30$. (b) If the strain is measured at $125 \times 10^{-6}$, what is the internal pressure at that point?

Only about $5 \%$ of the energy in the universe is composed of baryonic matter. Estimate the density of dark matter in the observable universe with a radius of $14$ billion light-years that contains $10^{11}$ galaxies, each with about $10^{11}$ stars like our Sun.

Genes a and b are 21 m.u. apart when mapped in highly inbred strain 1 of corn and 21 m.u. apart when mapped in highly inbred strain 2. But when the distance is mapped by testcrossing the $\mathrm{F}_{1}$ progeny of a cross between strains 1 and 2, the two genes are only 1.5 m.u. apart. What arrangement of genes a and b and any potential rearrangement breakpoints could explain these results?

If a horizontal load applied to the bar $A C$ causes point $A$ to be displaced to the right by an amount $\Delta L,$ determine the normal strain in the wire $A B .$ Originally, $\theta=45^{\circ} .$

Show that the energy density radiated by a blackbody

$$\frac{E_{\text {total }}(T)}{V}=\int_0^{\infty} \rho(\nu, T) d \nu=\int_0^{\infty} \frac{8 \pi h \nu^3}{c^3 e^{h \nu / k_B T}-1} d \nu$$

depends on the temperature as $T^4$. (Hint: Make the substitution of variables $x=h \nu / k_B T$.) The definite integral $\int_0^{\infty}\left[x^3 /\left(e^x-1\right)\right] d x=\pi^4 / 15$. Using your result, calculate the energy density radiated by a blackbody at 1100 . and 6000 . K.

Diego was seriously out of shape the day he joined his friends for a game of touch football. While he was running pell-mell for the ball, his left calf began to hurt. He went to the clinic the next day and was told he had a strain. Diego insisted that this must be wrong, because his joints did not hurt. Clearly, Diego was confusing a strain with a sprain. Explain the difference.

How is the density of a fish controlled? How is the density of a submarine controlled?

How does Escherichia coli O157:H7 end up in ground beef? To what class of pathogenic E. coli does this strain belong? (Section 31.11)

Determine the strain components $\epsilon_n, \epsilon_t$, and $\gamma_{n t}$ at the point if the $n t$-axes are rotated with respect to the $x y$-axes by the amount and in the direction indicated by the angle $\theta$ shown in figure.

The density of iodine is about $6.28 \overline{1}$ times the density of acetone. The density of acetone is about 785 kilograms per cubic meter. What is the density of iodine? Write your answer as a repeating decimal.

In a particular strain of Neurospora, a poky mutation exhibits biparental inheritance, whereas poky mutations in other strains are inherited only from the maternal parent. Explain these results.

The state of strain at the point on the bracket has components $\epsilon_x=400\left(10^{-6}\right), \epsilon_y=-250\left(10^{-6}\right), \gamma_{x y}=$ $310\left(10^{-6}\right)$. Use the strain-transformation equations to determine the equivalent in-plane strains on an element oriented at an angle of $\theta=30^{\circ}$ clockwise from the original position. Sketch the deformed element due to these strains within the $x-y$ plane.