A hard rubber ball, not affected by air resistance in its motion, is tossed upward from shoulder height, falls to the sidewalk, rebounds to a somewhat smaller maximum height, and is caught on its way down again. This motion is represented where the successive positions of the ball (A) through (G) are not equally spaced in time. At point (E) the center of the ball is at its lowest point in the motion. The motion of the ball is along a straight line, but the diagram shows successive positions offset to the right to avoid overlapping. Choose the positive $y$ direction to be upward.
($i$) Rank the situations (A) through (G) according to the speed of the ball $\left|v_y\right|$ at each point, with the largest speed first.
($ii$) Rank the same situations according to the velocity of the ball at each point.
($iii$) Rank the same situations according to the acceleration $a_y$ of the ball at each point. In each ranking, remember that zero is greater than a negative value. If two values are equal, show that they are equal in your ranking.

A specimen of a methacrylate plastic is tested in tension at room temperature, producing the stress-strain data listed in the accompanying table. Plot the stress-strain curve and determine the propor tional limit, modulus of elasticity (i.e., the slope of the initial part of the stress-strain curve), and yield stress at 0.2% offset. Is the material ductile or brittle?

$$\begin{matrix} \text{Stress (MPa)} & \text{Strain}\\ \text{8.0} & \text{0.0032}\\ \text{17.5} & \text{0.0073}\\ \text{25.6} & \text{0.0111}\\ \text{31.1} & \text{0.0129}\\ \text{39.8} & \text{0.0163}\\ \text{44.0} & \text{0.0184}\\ \text{48.0} & \text{0.0209}\\ \text{53.9} & \text{0.0260}\\ \text{58.1} & \text{0.0331}\\ \text{62.0} & \text{0.0429}\\ \text{62.1} & \text{Fracture}\\ \end{matrix}$$

A small hydraulic impulse turbine is supplied with water through a penstock with diameter D and length L; the jet diameter is d. The elevation difference between the reservoir surface and nozzle centerline is Z. The nozzle head loss coefficient is K$_{nozzle}$ and the loss coefficient from the reservoir to the penstock entrance is K$_{entrance}$. Determine the water jet speed, the volume flow rate, and the hydraulic power of the jet, for the case where Z = 300 ft, L = 1000 ft, D = 6 in.,K$_{entrance}$ = 0.5, K$_{nozzle}$ =0.04 and d = 2 in., if the pipe is made from commercial steel. Plot the jet power as a function of jet diameter to determine the optimum jet diameter and the resulting hydraulic power of the jet. Comment on the effects of varying the loss coefficients and pipe roughness.

The hot water needs of a household are to be met by heating water at $55^{\circ} \mathrm{F}$ to $180^{\circ} \mathrm{F}$ by a parabolic solar collector at a rate of $5 \mathrm{lbm} / \mathrm{s}$. Water flows through a $1.25$-in-diameter thin aluminum tube whose outer surface is black anodized in order to maximize its solar absorption ability. The centerline of the tube coincides with the focal line of the collector, and a glass sleeve is placed outside the tube to minimize heat losses. If solar energy is transferred to water at a net rate of $350 \mathrm{Btu} / \mathrm{h}$ per ft length of the tube, find the necessary length of the parabolic collector to meet the hot water requirements of this house. Also, find the surface temperature of the tube at the exit.

What is a difference between counseling and psychotherapy?

An ergonomics consultant is engaged by a large consumer products company to see what they can do to increase productivity. The consultant recommends an "employee athlete" program, encouraging every employee to devote 5 minutes an hour to physical activity. The company worries that the gains in productivity will be offset by the loss of time on the job. They'd like to know if the program increases or decreases productivity. To calculate it, they monitor a random sample of 145 employees who word process, calculating their hourly keystrokes both before and after the program is instituted. Here are the data:

A small company, on hearing about the employee athlete program at the large company down the street, decides to try it as well. To measure the difference in productivity, they measure the average number of keystrokes per hour of $23 \mathrm{cmployees}$ before and after the program is instituted. The data follow:

b) Provide a $95 \%$ confidence interval for the mean change in productivity (as measured by keystrokes per hour).

An ergonomics consultant is engaged by a large consumer products company to see what they can do to increase productivity. The consultant recommends an "employee athlete" program, encouraging every employee to devote 5 minutes an hour to physical activity. The company worries that the gains in productivity will be offset by the loss of time on the job. They'd like to know if the program increases or decreases productivity. To calculate it, they monitor a random sample of 145 employees who word process, calculating their hourly keystrokes both before and after the program is instituted. Here are the data:

A small company, on hearing about the employee athlete program at the large company down the street, decides to try it as well. To measure the difference in productivity, they measure the average number of keystrokes per hour of $23 \mathrm{cmployees}$ before and after the program is instituted. The data follow:

a) Is there proof to suggest that the program increases productivity?

Strasburg Loan Company is in the consumer loan business. Strasburg borrows from banks and loans out the money at higher interest rates. Strasburg’s bank requires Strasburg to submit quarterly financial statements to keep its line of credit. Strasburg’s main asset is Notes Receivable. Therefore, Uncollectible-Account Expenses and Allowance for Uncollectible Accounts are important accounts for the company.

Raquel Lanser, the company’s owner, prefers that net income reflect a steady increase in a smooth pattern, rather than an increase in some periods and a decrease in other periods. To report smoothly increasing net income, Lanser underestimates uncollectible-account expenses in some periods. In other periods, Lanser overestimates the expense. She reasons that the income overstatements roughly offset the income understatements over time.

Requirements

1. What is the ethical issue in this situation?
2. Who are the stakeholders? What are the possible consequences of each?
3. Analyze the alternatives from the following standpoints: a. economic, b. legal, c. ethical.
4. What would you do? How would you justify your decision?

The fiscal policy variables G and T are thought to be independent of income level. But this is not how things work in the real world. Since taxes are primarily based on income, larger incomes tend to result in higher taxes. In this issue, we look at how taxes react automatically to changes in autonomous spending to help offset their effects on output. Take into account the subsequent behavioural equations:

$$\begin{aligned} C &=c_0+c_1 Y_D \\ T &=t_0+t_1 Y \\ Y_D &=Y-T \end{aligned}$$

G and I are both constant. Assume that t1 is between 0 and 1. What is the multiplier? Does the economy respond more to changes in autonomous spending when t1 is 0 or when t1 is positive? Explain.

Uniform internal heat generation at $q=5 \times 10^{7} \mathrm{~W} / \mathrm{~m}^{3}$ is occurring in a cylindrical nuclear reactor fuel rod of $50$-$\mathrm{mm}$ diameter, and under steady-state conditions the temperature distribution is of the form $T(r)=a+b r^{2}$, where T is in degrees Celsius and $r$ is in meters, while $a=800^{\circ} \mathrm{~C}$ and $b=-4.167 \times 10^{5} \mathrm{~C} / \mathrm{~m}^{2}$. The fuel rod properties are $k=30 \mathrm{~W} / \mathrm{~m} \cdot \mathrm{~K}, \quad \rho=1100 \mathrm{~kg} / \mathrm{~m}^{3}$, and $c_{p}=800 \mathrm{~J} / \mathrm{~kg} \cdot \mathrm{~K}$. (a) What is the rate of heat transfer per unit length of the rod at $r=0$ (the centerline) and at $r=25 \mathrm{~mm}$ (the surface)? (b) If the reactor power level is suddenly increased to $\dot{q}_{2}=10^{8} \mathrm{~W} / \mathrm{~m}^{3}$, what is the initial time rate of temperature change at $r=0$ and $r=25 \mathrm{~mm}$?

 1 public class ShowCurrentTime {
 2 public static void main(String[] args) {
 3 // Obtain the total milliseconds since midnight, Jan 1, 1970
 4 long totalMilliseconds = System.currentTimeMillis();
 5
 6 // Obtain the total seconds since midnight, Jan 1, 1970
 7 long totalSeconds = totalMilliseconds / 1000;
 8
 9 // Compute the current second in the minute in the hour
10 long currentSecond = totalSeconds % 60;
11
12 // Obtain the total minutes
13 long totalMinutes = totalSeconds / 60;
14
15 // Compute the current minute in the hour
16 long currentMinute = totalMinutes % 60;
17
18 // Obtain the total hours
19 long totalHours = totalMinutes / 60;
20
21 // Compute the current hour
22 long currentHour = totalHours % 24;
23
24 // Display results
25 System.out.println("Current time is " + currentHour + ":"
26 + currentMinute + ":" + currentSecond + " GMT");
27 }
28 }

Current time is 17:31:8 GMT

(Current time) Revise the above program to display the hour using a 12-hour clock. Here is a sample run:

Enter the time zone offset to GMT: -5
The current time is 4:50:34 AM

A balanced budget amendment would allegedly cause instability, according to a common argument. The fiscal policy variables G and T are thought to be independent of income level. But this is not how things work in the real world. Since taxes are primarily based on income, larger incomes tend to result in higher taxes. In this issue, we look at how taxes react automatically to changes in autonomous spending to help offset their effects on output. Take into account the subsequent behavioural equations:

$$\begin{aligned} C &=c_0+c_1 Y_D \\ T &=t_0+t_1 Y \\ Y_D &=Y-T \end{aligned}$$

G and I are both constant. Assume that t1 is between 0 and 1. Suppose that the government starts with a balanced budget and that there is a drop in c0. What happens to Y? What happens to taxes?

An ergonomics consultant is engaged by a large consumer products company to see what they can do to increase productivity. The consultant recommends an "employee athlete" program, encouraging every employee to devote 5 minutes an hour to physical activity. The company worries that the gains in productivity will be offset by the loss of time on the job. They'd like to know if the program increases or decreases productivity. To calculate it, they monitor a random sample of 145 employees who word process, calculating their hourly keystrokes both before and after the program is instituted. Here are the data:

b) What can you conclude? Describe.

Trees offsetting $\mathbf{C O}_2$. Trees can help offset the buildup of $\mathrm{CO}_2$ due to burning coal and other fossil fuels. $\mathrm{CO}_2$ can be absorbed by tree foliage. Trees use the carbon to grow, and release $\mathrm{O}_2$ into the atmosphere. Suppose a refrigerator uses $600 \mathrm{kWh}$ of electricity per year (about $2 \times 10^9 \mathrm{~J}$ ) from a $33 \%$ efficient coal-fired power plant. Burning $1 \mathrm{~kg}$ of coal releases about $2 \times 10^7 \mathrm{~J}$ of energy. Assume coal is all carbon, which when burned in air becomes $\mathrm{CO}_2$. How much coal is burned per year to run this refrigerator?