8) A heavy steel ball is attached to a light rod to make a pendulum. The pendulum begins at rest at instant A, as shown. The ball is then pulled to one side and held at rest. At instant B, the pendulum is released from rest. It swings down and passes its original height at instant C, as shown. The total mechanical energy of the pendulum is greatest at: a) Point B b) Point C c) Equal at both instants d) Since the mass of the ball and the height it is raised to before it is released is not given it is impossible to determine.

8) A heavy steel ball is attached to a light rod to make a pendulum. The pendulum begins at rest at instant A, as shown. The ball is then pulled to one side and held at rest. At instant B, the pendulum is released from rest. It swings down and passes its original height at instant C, as shown. The total mechanical energy of the pendulum is greatest at: a) Point B b) Point C c) Equal at both instants d) Since the mass of the ball and the height it is raised to before it is released is not given it is impossible to determine.

8) A heavy steel ball is attached to a light … Read More...
struts AB and AC in the figure shown below can transmit only axial tensile or compressive force . If the force F= 1250 n determine ; a) the force in strut AB. b) the force in strut AC. c) the tension in cable.

struts AB and AC in the figure shown below can transmit only axial tensile or compressive force . If the force F= 1250 n determine ; a) the force in strut AB. b) the force in strut AC. c) the tension in cable.

 
A 1000-turn loop (radius = 0.038 m) of wire is connected to a (25 ) resistor as shown in the figure. A magnetic field is directed perpendicular to the plane of the loop. The field points into the paper and has a magnitude that varies in time as B = gt, where g = 0.25 T/s. Neglect the resistance of the wire. What is the magnitude of the potential difference between points a and b?

A 1000-turn loop (radius = 0.038 m) of wire is connected to a (25 ) resistor as shown in the figure. A magnetic field is directed perpendicular to the plane of the loop. The field points into the paper and has a magnitude that varies in time as B = gt, where g = 0.25 T/s. Neglect the resistance of the wire. What is the magnitude of the potential difference between points a and b?

As a student of ECON1005, suppose you were asked to assist a co-worker in investigating whether there is an association between gender and annual salary of researchers in your country. Data was gathered from researchers in your country in your country. MINITAB was used to generate stem-and-leaf diagrams for the salaries of both the female and male researchers. See Exhibit 1 below. Exhibit 1 Stem-and-Leaf Display: Salary Female, Salary Male Stem-and-leaf of Salary Female N = 15 Leaf Unit = 1000.0 1 5 8 5 6 1345 (3) 7 148 7 8 389 4 9 2245 (a) Calculate the mean salary for both the female and the male researchers. All relevant working must be clearly shown. (b) Calculate the standard deviation of the salaries for both the female and the male researchers. All relevant working must be clearly shown. (c) Comment on your answers for parts (c) and (d), in relation to the purpose of your study, that is, the association between gender and annual salary of researchers in your country. MINITAB was used to generate box-and-whisker diagrams for the salaries of both the female and male researchers. See Exhibit 2 below. Exhibit 2 (d) With reference to the box-and-whisker diagrams, compare the salaries of the researchers selected in your sample, by gender. Ensure that you comment on the skewness, the median, the interquartile range, the minimum and the maximum values of both diagrams. MINITAB was used to generate the descriptive statistics for all the 35 researchers selected in the sample. See Exhibit 3 below. Exhibit 3 Descriptive Statistics: ResearcherSalary Variable N N* Mean SE Mean TrMean StDev Minimum Q1 Median Q3 Salary 35 0 82951 2266 83200 13404 58100 74800 83800 94300 Variable Maximum Salary 104500 (e) What does TrMean represent? Comment on the value of the TrMean and show how this value was calculated. (f) For further analysis, a table is drawn showing the number of females and the number of males whose salaries were below the median salary and equal to or above the median salary. Complete the table below: Salary < $83800 Salary ? $83800 Total Female Male Total 35 (g) Using your table in part (h), determine the probability that a randomly selected researcher from your sample, is a female OR has a salary < $83800. (h) Using your table in part (h), determine the probability that a randomly selected researcher from your sample, is a female AND has a salary < $83800. (i) Given that a randomly selected researcher from your sample is a female, what is the probability that her annual salary is < $83800? (j) Are the events “female researcher” and “salary < $83800” mutually independent events? Support your answer with relevant calculations or explanations.

As a student of ECON1005, suppose you were asked to assist a co-worker in investigating whether there is an association between gender and annual salary of researchers in your country. Data was gathered from researchers in your country in your country. MINITAB was used to generate stem-and-leaf diagrams for the salaries of both the female and male researchers. See Exhibit 1 below. Exhibit 1 Stem-and-Leaf Display: Salary Female, Salary Male Stem-and-leaf of Salary Female N = 15 Leaf Unit = 1000.0 1 5 8 5 6 1345 (3) 7 148 7 8 389 4 9 2245 (a) Calculate the mean salary for both the female and the male researchers. All relevant working must be clearly shown. (b) Calculate the standard deviation of the salaries for both the female and the male researchers. All relevant working must be clearly shown. (c) Comment on your answers for parts (c) and (d), in relation to the purpose of your study, that is, the association between gender and annual salary of researchers in your country. MINITAB was used to generate box-and-whisker diagrams for the salaries of both the female and male researchers. See Exhibit 2 below. Exhibit 2 (d) With reference to the box-and-whisker diagrams, compare the salaries of the researchers selected in your sample, by gender. Ensure that you comment on the skewness, the median, the interquartile range, the minimum and the maximum values of both diagrams. MINITAB was used to generate the descriptive statistics for all the 35 researchers selected in the sample. See Exhibit 3 below. Exhibit 3 Descriptive Statistics: ResearcherSalary Variable N N* Mean SE Mean TrMean StDev Minimum Q1 Median Q3 Salary 35 0 82951 2266 83200 13404 58100 74800 83800 94300 Variable Maximum Salary 104500 (e) What does TrMean represent? Comment on the value of the TrMean and show how this value was calculated. (f) For further analysis, a table is drawn showing the number of females and the number of males whose salaries were below the median salary and equal to or above the median salary. Complete the table below: Salary < $83800 Salary ? $83800 Total Female Male Total 35 (g) Using your table in part (h), determine the probability that a randomly selected researcher from your sample, is a female OR has a salary < $83800. (h) Using your table in part (h), determine the probability that a randomly selected researcher from your sample, is a female AND has a salary < $83800. (i) Given that a randomly selected researcher from your sample is a female, what is the probability that her annual salary is < $83800? (j) Are the events “female researcher” and “salary < $83800” mutually independent events? Support your answer with relevant calculations or explanations.

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Problem 2.6 A 1000 VA 230 V / 115 V transformer has been tested to determine its equivalent circuit. The results of the tests are shown below. a. Find the equivalent circuit for this transformer refered to the low voltage side of the transformer. b. Find the transformer’s voltage regulation at rated conditions and at (1) 0.8 pf lag, (2) 1.0 pf, and (3) 0.8 pf lead.

Problem 2.6 A 1000 VA 230 V / 115 V transformer has been tested to determine its equivalent circuit. The results of the tests are shown below. a. Find the equivalent circuit for this transformer refered to the low voltage side of the transformer. b. Find the transformer’s voltage regulation at rated conditions and at (1) 0.8 pf lag, (2) 1.0 pf, and (3) 0.8 pf lead.

0 2p 1 2 Figure 1: PlotCycloidArc(8.5) Math98 HW4 The cylcoid is the plane curve traced out by a point on a circle as the circle rolls without slipping on a straight line.1 In this exercise we will use MATLAB to create an animation of a circle rolling on a straight line, while a point on the circle traces the cycloid. a. Implement a MATLAB function of the form function PlotCycloidArc(ArcLength). This function takes in a positive number ArcLength and displays a snapshot of the cirle rolling (without slipping) on the x-axis while a point on the cirlce traces the cycloid. The circle is initially centered at (0,1) and has radius 1, and the initial tracing point is taken to be (0, 0). An example output is shown in the above figure. As in the figure, plot the cycloid arc black, the circle blue, and use a red dot for the tracing point. Hint: If the circle has rolled for a length of arc t  0, the coordinates of the tracing point are (t−sin t, 1−cos t). b. Implement a MATLAB function of the form function CycloidMovie(NumHumps,NumIntervals). This function will output an animation of the circle rolling along a line while a point on the circle traces the cycloid. This function inputs two natural numbers NumHumps and NumIntervals representing the number of periods (or humps) of the cycloid and the number or frames per hump that will be used to make the animation, respectively. Use the getframe command to save frames outputted from PlotCycloidArc and the movie command to play them back together as a movie. Use the axis command to view the frames on the rectan- gle [0, 2NumHumps] × [0, 5/2]. Also label the ticks 0, 2, . . . , 2NumHumps on the x axis with the strings 1See Wikipedia for more on the cycloid. 0, 2, . . . , 2NumHumps and do the same for 1, 2 on the y axis (see the figure above). Label the movie ’Cycloid Animation’. Submit MATLAB code for both parts a and b and a printout the figures obtained by the commands PlotCycloidArc(8.5), PlotCycloidArc(12), and CycloidMovie(3,10).

0 2p 1 2 Figure 1: PlotCycloidArc(8.5) Math98 HW4 The cylcoid is the plane curve traced out by a point on a circle as the circle rolls without slipping on a straight line.1 In this exercise we will use MATLAB to create an animation of a circle rolling on a straight line, while a point on the circle traces the cycloid. a. Implement a MATLAB function of the form function PlotCycloidArc(ArcLength). This function takes in a positive number ArcLength and displays a snapshot of the cirle rolling (without slipping) on the x-axis while a point on the cirlce traces the cycloid. The circle is initially centered at (0,1) and has radius 1, and the initial tracing point is taken to be (0, 0). An example output is shown in the above figure. As in the figure, plot the cycloid arc black, the circle blue, and use a red dot for the tracing point. Hint: If the circle has rolled for a length of arc t  0, the coordinates of the tracing point are (t−sin t, 1−cos t). b. Implement a MATLAB function of the form function CycloidMovie(NumHumps,NumIntervals). This function will output an animation of the circle rolling along a line while a point on the circle traces the cycloid. This function inputs two natural numbers NumHumps and NumIntervals representing the number of periods (or humps) of the cycloid and the number or frames per hump that will be used to make the animation, respectively. Use the getframe command to save frames outputted from PlotCycloidArc and the movie command to play them back together as a movie. Use the axis command to view the frames on the rectan- gle [0, 2NumHumps] × [0, 5/2]. Also label the ticks 0, 2, . . . , 2NumHumps on the x axis with the strings 1See Wikipedia for more on the cycloid. 0, 2, . . . , 2NumHumps and do the same for 1, 2 on the y axis (see the figure above). Label the movie ’Cycloid Animation’. Submit MATLAB code for both parts a and b and a printout the figures obtained by the commands PlotCycloidArc(8.5), PlotCycloidArc(12), and CycloidMovie(3,10).

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