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Physics textbook answers & solutions

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Most popular questions for Physics Textbooks

The maintenance costs associated with a machine are \(\$ 2,000\) per year for the first 10 years and \(\$ 1,000\) per year thereafter. The machine has an infinite life. If interest is 10 percent, what is the present worth of the annual disbursements? a) \(\$ 16,145\) c) \(\$ 21,300\) b) \(\$ 19,678\) d) \(\$ 92,136\)

Einstein Solid (a) Classical Einstein (or "Boltzmann") Solid: Consider a three-dimensional simple harmonic oscillator with mass \(m\) and spring constant \(k\) (i.e., the mass is attracted to the origin with the same spring constant in all three directions). The Hamiltonian is given in the usual way by $$ H=\frac{\mathbf{p}^{2}}{2 m}+\frac{k}{2} \mathbf{x}^{2} $$ \(\triangleright\) Calculate the classical partition function $$ Z=\int \frac{\mathbf{d p}}{(2 \pi \hbar)^{3}} \int \mathrm{d} \mathbf{x} e^{-\beta H(\mathbf{p}, \mathbf{x})} $$ Note: in this exercise \(\mathbf{p}\) and \(\mathbf{x}\) are three-dimensional vectors. \(\triangleright\) Using the partition function, calculate the heat capacity $3 k_{B}$. D Conclude that if you can consider a solid to consist of \(N\) atoms all in harmonic wells, then the heat capacity should be \(3 N k_{B}=3 R\), in agreement with the law of Dulong and Petit. (b) Quantum Einstein Solid: Now consider the same Hamiltonian quantummechanically. D Calculate the quantum partition function $$ Z=\sum_{j} e^{-\beta E_{j}} $$ where the sum over \(j\) is a sum over all eigenstates. \(\triangleright\) Explain the relationship with Bose statistics. D Find an expression for the heat capacity. D Show that the high-temperature limit agrees with the law of Dulong and Petit. \(\triangleright\) Sketch the heat capacity as a function of temperature. (See also Exercise \(2.7\) for more on the same topic)

Examine the consequences of mutual forces between point charges not bcing directed along the joining line.

What is the percent uncertainty in the measurement 5.48±0.25 m?
A proton moves in a helical path at speed \(v=4.0\) $\times 10^{7} \mathrm{m} / \mathrm{s}$ high above the atmosphere, where Earth's magnetic field has magnitude \(B=1.0 \times 10^{-6} \mathrm{T}\). The proton's velocity makes an angle of \(25^{\circ}\) with the magnetic field. (a) Find the radius of the helix. [Hint: Use the perpendicular component of the velocity.] (b) Find the pitch of the helix-the distance between adjacent "coils." [Hint: Find the time for one revolution; then find how far the proton moves along a field line during that time interval.]
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