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.

Fill in the blanks.

Hardening of the arteries:_____________.

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.

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

The composite shaft shown consists of a solid stainless steel shaft (1) and a brass tube (2) that are connected at flange $B$ and securely attached to rigid supports at $A$ and $C$. Stainless steel shaft (1) has a diameter of $2.25$ in., a length of $L_1=40 \mathrm{in}$., and a shear modulus of $12,500 \mathrm{ksi}$. Brass tube (2) has an outside diameter of $3.500$ in., a wall thickness of $0.219$ in., and a shear modulus of $5,600 \mathrm{ksi}$. A concentrated torque of $T_B=60 \mathrm{kip}$-in. is applied to flange $B$. If the shear stresses in both (1) and (2) are to be equal in magnitude, what is the length $L_2$ required for tube (2)?

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

Through what structure do the vertebral arteries run?

Use the following terms to create a concept map: rock, igneous rock, sedimentary rock, metamorphic rock, and rock cycle.

Do the annual variations in Earth-Sun distance adequately account for seasonal temperature changes? Explain .

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.

How do Landsat satellites collect and analyze data to map Earth's surface? (Chapter 2)

Discuss how the disorder strabismus affects vision.

When a pregnant woman receives a blow to the abdomen, doctors must check for pelvic free fluid (FF), which is associated with internal injury. A fast and inexpensive way to do this is with an ultrasound. But sometimes an ultrasound gives the wrong result. A more expensive and invasive test is available, which never gives the wrong result. To check the accuracy of the ultrasound test, 328 pregnant women who had received a blow to the abdomen were given both tests. The results are given in the table below.

a. A false positive occurs when a test shows a positive result but is wrong. How many false positives were there? Explain the meaning of a false positive for the woman tested.

b. A false negative occurs when a test shows a negative result but is wrong. How many false negatives were there? Explain the meaning of a false negative for the woman tested.

c. Looking only at those who had FF, what proportion got a positive ultrasound? This is called the sensitivity of the test.

d. Looking only at those who did not have FF, what proportion got a negative ultrasound? This is called the specificity of the test.

e. Looking only at those who got a positive ultrasound, what proportion actually had FF? This is called the positive predictive value (PPV).

f. Looking only at those who got a negative ultrasound, what proportion actually did not have FF? This is called the negative predictive value (NPV).

g. What do you see as the major statistical strengths and weaknesses of the ultrasound test for FF? Share your ideas with your classmates. Resolve any differences.

Abigail Grace has a $900,000 fully diversified portfolio. She subsequently inherits ABC Company common stock worth$100,000. Her financial adviser provided her with the fol- lowing estimates:

$$\begin{array}{|lll|} \hline & \textbf{Expected Monthly Returns} & \textbf{Standard Deviation of Monthly Returns} \\ \hline \textbf{Original Portfolio} & 0.67\% & 2.37\% \\ \hline \textbf{ABC Company} & 1.25 & 2.95 \\ \hline \end{array}$$

The correlation coefficient of ABC stock returns with the original portfolio returns is .40.

a. The inheritance changes Grace’s overall portfolio and she is deciding whether to keep the ABC stock. Assuming Grace keeps the ABC stock, calculate the: i. Expected return of her new portfolio which includes the ABC stock. ii. Covariance of ABC stock returns with the original portfolio returns. iii. Standard deviation of her new portfolio which includes the ABC stock.

b. If Grace sells the ABC stock, she will invest the proceeds in risk-free government securities yielding .42% monthly. Assuming Grace sells the ABC stock and replaces it with the government securities, calculate the: i. Expected return of her new portfolio which includes the government securities. ii. Covariance of the government security returns with the original portfolio returns. iii. Standard deviation of her new portfolio which includes the government securities.

c. Determine whether the beta of her new portfolio, which includes the government securities, will be higher or lower than the beta of her original portfolio.

d. Based on conversations with her husband, Grace is considering selling the $100,000 of ABC stock and acquiring$100,000 of XYZ Company common stock instead. XYZ stock has the same expected return and standard deviation as ABC stock. Her husband comments, “It doesn’t matter whether you keep all of the ABC stock or replace it with $100,000 of XYZ stock.” State whether her husband’s comment is correct or incorrect. Justify your response.

e. In a recent discussion with her financial adviser, Grace commented, “If I just don’t lose money in my portfolio, I will be satisfied.” She went on to say, “I am more afraid of losing money than I am concerned about achieving high returns.” Describe one weak- ness of using the standard deviation of returns as a risk measure for Grace.