What maximum power can be radiated by a 10-cm-diameter solid lead sphere? Assume an emissivity of 1.

A counterweight of mass m = 4.00 kg is attached to a light cord that is wound around a pulley. The pulley is a thin hoop of radius R = 8.00 cm and mass M = 2.00 kg. The spokes have negligible mass. (a) What is the magnitude of the net torque on the system about the axle of the pulley? (b) When the counterweight has a speed v, the pulley has an angular speed $\omega=v / R.$ Determine the magnitude of the total angular momentum of the system about the axle of the pulley. (c) Using your result from part (b) and $\vec{\tau}=d \overrightarrow{\mathbf{L}} / d t,$ calculate the acceleration of the counterweight.

The $\chi^2$ value means nothing on its own-it is used to find the probability that, assuming the hypothesis is true, the observed data set could have resulted from random fluctuations. A low probability suggests that the observed data are not consistent with the hypothesis, and thus the hypothesis should be rejected. A standard cutoff point used by biologists is a probability of 0.05(5%). If the probability corresponding to the $\chi^2$ value is $0.05$ or less, the differences between observed and expected values are considered statistically significant, and the hypothesis (that the genes are unlinked) should be rejected. If the probability is above $0.05$, the results are not statistically significant; the observed data are consistent with the hypothesis. To find the probability, locate your $\chi^2$ value in the $\chi^2$ Distribution Table in Appendix $F$. The "degrees of freedom" (df) of your data set is the number of categories (here, 4 phenotypes) minus 1 , so $\mathrm{df}=3$. Determine which values on the $d f=3$ line of the table your calculated $\chi^2$ value lies between.

Energetic particles, such as protons, can be detected with a silicon detector. When a particle strikes a thin piece of silicon, it creates a large number of free electrons by ionizing silicon atoms. The electrons flow to an electrode on the surface of the detector, and this current is then amplified and detected. In one experiment, each incident proton creates, on average, 35,000 electrons; the electron current is amplified by a factor of 100; and the experimenters record an amplified current of $3.5 \mu \mathrm{A}$. How many protons a re st riking the detector per second?

Find out the lengths of the unknown sides in the following given pairs of similar triangles .

The shaft shown in the figure was designed in A simply supported shaft is shown in the figure. A constant magnitude distributed unit load $p$ is applied as the shaft rotates subject to a time-varying torque that varies from $T_{\min }$ to $T_{\max }$. For the data in the row(s) assigned from

$$\begin{array}{ccrrrrr} \hline Row & l & a & b & Por p & T_{\min } & T_{\max } \\ \hline a & 20 & 16 & 18 & 1000 & 0 & 2000 \\ b & 12 & 2 & 7 & 500 & -100 & 600 \\ c & 14 & 4 & 12 & 750 & -200 & 400 \\ d & 11 & 4 & 8 & 1000 & 0 & 2000 \\ e & 17 & 6 & 12 & 1500 & -200 & 500 \\ f & 24 & 16 & 22 & 750 & 1000 & 2000 \\ \hline \end{array}$$

, find the diameter of shaft required to obtain a safety factor of $2$ in fatigue loading if the shaft is steel of $S_{u t}=$ $745 \mathrm{~MPa}$ and $S_{y}=427 \mathrm{~MPa}$. The dimensions are in $\mathrm{cm}$, the distributed force in $\mathrm{N} / \mathrm{cm}$, and the torque in $\mathrm{N}-\mathrm{m}$. Assume no stress concentrations are present. For the data in the row(s) assigned from

$$\begin{array}{crrrrrr} \hline Row & l & a & {b} & Porp & T_{\min } & T_{\max } \\ \hline a & 20 & 16 & 18 & 1000 & 0 & 2000 \\ b & 12 & 2 & 7 & 500 & -100 & 600 \\ c & 14 & 4 & 12 & 750 & -200 & 400 \\ d & 8 & 4 & 8 & 1000 & 0 & 2000 \\ e & 17 & 6 & 12 & 1500 & -200 & 500 \\ f & 24 & 16 & 22 & 750 & 1000 & 2000 \\ \hline \end{array}$$

, and the corresponding diameter of shaft found in A simply supported shaft is shown in the figure. A constant magnitude distributed unit load $p$ is applied as the shaft rotates subject to a time-varying torque that varies from $T_{\min }$ to $T_{\max }$. For the data in the row(s) assigned from

$$\begin{array}{ccrrrrr} \hline Row & l & a & b & Por p & T_{\min } & T_{\max } \\ \hline a & 20 & 16 & 18 & 1000 & 0 & 2000 \\ b & 12 & 2 & 7 & 500 & -100 & 600 \\ c & 14 & 4 & 12 & 750 & -200 & 400 \\ d & 11 & 4 & 8 & 1000 & 0 & 2000 \\ e & 17 & 6 & 12 & 1500 & -200 & 500 \\ f & 24 & 16 & 22 & 750 & 1000 & 2000 \\ \hline \end{array}$$

, find the diameter of shaft required to obtain a safety factor of $2$ in fatigue loading if the shaft is steel of $S_{u t}=$ $745 \mathrm{~MPa}$ and $S_{y}=427 \mathrm{~MPa}$. The dimensions are in $\mathrm{cm}$, the distributed force in $\mathrm{N} / \mathrm{cm}$, and the torque in $\mathrm{N}-\mathrm{m}$. Assume no stress concentrations are present, design suitable bearings to support the load for at least $3 E 8$ cycles at $2500 \mathrm{~rpm}$. State all assumptions. (a) Using hydrodynamically lubricated bronze sleeve bearings with $O_{N}=30$, $l / d=1.0$, and a clearance ratio of $0.002$. (b) Using deep-groove ball bearings for a $10\%$ failure rate.

With your team, review what you know about seasonal changes on Earth. How do those changes relate to Earth's orbit and the tilt of Earth's axis? Then make a plan for what information about Mars you need to gather to explain seasonal changes on that planet.

a. Sketch the graphs of the functions f and g and find the x-coordinate of the points at which they intersect. b. Compute the area of the region described. f(x)=sinh x, g(x)=tanh x; the region bounded by the graphs of f, g, and x=ln 3

The electric field in a certain region of space obeys $E_y \neq 0$, $E_x=E_z=0$ and $\partial \vec{E} / \partial x \neq 0, \partial \vec{E} / \partial y=\partial \vec{E} / \partial z=0$. (a) The net force on an electric dipole oriented parallel to the $x$ axis in this field is (A) directed along the $x$ axis. (B) directed along the $y$ axis. (C) directed along the $z$ axis. (D) None of the above (b) The net torque on an electric dipole parallel to the $x$ axis in this field is (A) directed along the $x$ axis. (B) directed along the $y$ axis. (C) directed along the $z$ axis. (D) None of the above

Which of the following transformations map the segment $\overline{A B}$ to $\overline{A^{\prime} B^{\prime}}$ in such a way that $\overline{A B} \| \overline{A^{\prime} B^{\prime}}$ ? (There may be more than one correct answer.)

a. Translation

Use 6 to 10 bolded words of your choice from the Chapter Summary to create a concept map. Finish it by providing linking words.

Specify whether each system is autonomous or nonautonomous, and whether it is linear or nonlinear. If it is linear, specify whether it is homogeneous or nonhomogeneous. $d y / d t=3 y z-2 z, \quad d z / d t=2 z+5 y$

Match each description or case by choosing its corresponding disorder: (a) mania, (b) double depression, (c) persistent depressive disorder, (d) major depressive episode, and (e) bipolar I disorder. For the past few weeks, Jennifer has been sleeping a lot. She feels worthless, can't get up the energy to leave the house, and has lost a lot of weight. Her problem is the most common and extreme mood disorder. _____________

What are some symptoms of a mood disorder?