Word and Excel Practice Exercise: Proposed Solution, Summaries of Acting

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Word and Excel Practice Exercise:

Proposed Solution

September ##,

APSC-

Jane Doe

Student #: ########

Doe | i

Table of Contents

List of Figures ................................................................................................................................................. i

List of Tables .................................................................................................................................................. i

Question 1: Specific Weight of Lake Ontario ................................................................................................ 1

Example Response .................................................................................................................................... 1 Overview of Required Content ................................................................................................................. 3

Question 2: Resistance in a Circuit ............................................................................................................... 4

Example Response .................................................................................................................................... 4 Overview of Required Content ................................................................................................................. 7

References .................................................................................................................................................... 7

List of Figures

Figure 1: A plot showing the pressure distribution of Lake Ontario with respect to depth from the surface........................................................................................................................................................... 2 Figure 2: A plot of the instantaneous power and square of current in the circuit. ...................................... 5 Figure 3: The residual plot for the regression analysis of the circuit. ........................................................... 6 Figure 4: Schematic of circuit including voltage source and resistive load .................................................. 6

List of Tables

Table 1: The recent data containing the pressure measurements at various depths below the surface. ... 1 Table 2: The historical pressure and depth measurements taken by the American engineer..................... 1 Table 3: The historical pressure and depth measurements in metric units. ................................................ 2 Table 4: The circuit data over the course of 3.6s.......................................................................................... 4 Table 5: A summary of the results from a regression analysis of the circuit data........................................ 5 Table 6: The mean and standard error of the residuals is zero within error, which is the expected result. 6

Table 3: The historical pressure and depth measurements in metric units.

Sensor Depth (m) Sensor Depth Error (± m) Pressure (kPa) Pressure Error (± kPa) 22.3 0.9 191 12 49.4 0.9 457 14

Both these data sets were plotted in order to determine the relationship between the pressure and the depth beneath the surface, as shown in Figure 1.

Figure 1: A plot showing the pressure distribution of Lake Ontario with respect to depth from the surface.

Linear trendlines were then added to each data series in order to determine the slopes and intercepts of the two relationships, as shown by the equations on the plot. The slopes of the relationships are equal to the specific weights of Lake Ontario for each data set. It should be noted that there appears to be a consistent difference between the historical data and the recent data in that the historical data appears to be shifted down. This discrepancy is likely due to a calibration error in the pressure measurement device used by the American engineer. The analysis of the pressure and depth measurements suggest that the specific weight of water in Lake Ontario is 9.80 𝑘𝑁/𝑚^3 and 9.81 𝑘𝑁/𝑚^3 for the recent and historical data sets respectively. As neither of these values agree within the limits uncertainty of the specific weight of ocean water, it can be concluded that the specific weight of Lake Ontario is less than that of ocean water. This difference can be attributed to the fact that ocean water possesses increased salt content than the fresh water in Lake Ontario, resulting in a higher specific weight.

Specific weight is the weight per unit volume whereas density is the mass per unit volume. Specific weight is therefore proportional to the density of the fluid, as given by Equation 2 [1].

𝛾 = 𝜌𝑔 (2)

Precent = 9.80 zrecent + 3.

Phistorical= 9.81 zhistorical - 27.

0

100

200

300

400

500

600

700

0 10 20 30 40 50 60 70

Pressure (kPa)

Sensor Depth (m)

Recent Data Historical Data

where 𝛾 is the specific weight (in N/m^3 ), 𝜌 is the density (in kg/m^3 ), and 𝑔 is the acceleration due to gravity (in m/s^2 ). As the buoyance force acting on a boat is proportional to both the volume of displaced water and the specific weight of the water, a boat must sit lower in Lake Ontario than the ocean due to the fact that more water must be displaced to account for the lower the specific weight of Lake Ontario.

Overview of Required Content (note to the student, not part of the sample solution)

You must include the following:

• Table of recently collected data
• Table of historical data in imperial units and converted historical data in metric (SI) units
• Scatter plot of depth vs. pressure with appropriate formatting

You should also include following information in your summary paragraphs:

• Statement of the specific weight of Ontario for both data sets (9.80 𝑘𝑁/𝑚^3 for the recent data and 9.81 𝑘𝑁/𝑚^3 for the historical data)
• Subsequent conclusion that Lake Ontario specific weight is less than ocean, mainly due to the salt content of ocean water
• Explanation for lower trendline for the historical data (likely due to bad calibration of measurement device by the American engineer or other plausible explanations, use discretion)
• Explanation that density is mass per unit volume whereas specific weight is weight per unit volume (thus they are related by the acceleration due to gravity)
• Boat must sit lower in Lake Ontario to displace more water and make up for the lower specific weight of lake water while still creating the same force
• If an explanation of the intercept is given (not required) the student should indicate a value of zero is expected because the intercept represents atmospheric pressure which is zero when taking gauge pressure measurements.

The relationship given by Equation 3 was used to determine the resistance of the load through graphical and statistical methods. To determine resistance graphically, a plot of power and current measurements was constructed to determine the slope of the relationship, as shown in Figure 2.

Figure 2: A plot of the instantaneous power and square of current in the circuit.

Through graphical analysis, the resistance of the load was determined from the slope to be 100.19 Ω.

A regression analysis was then performed to statistically determine the slope and intercept of the line as well as its uncertainty. The results of the regression are shown in Table 5.

Table 5: A summary of the results from a regression analysis of the circuit data..

Resistance, R (Ω)

Resistance Standard Error (±Ω) Intercept (W)

Intercept Standard Error (±W) 100.2 1.7 0 2

In order to determine the validity of the regression, a residual plot was created to shown the normality of the residuals. It was concluded that the relationship under study was indeed linear as the residuals were normally distributed with no apparent pattern, as shown in Figure 3.

P = 100.19I^2 + 0.

1.000 1.100 1.200 1.300 1.400 1.500 1.600 1.

Power [W]

Square of Current [A^2 ]

R = 100.2 Ω

V = 128.8 V

I = 1.29 A

Figure 3: The residual plot for the regression analysis of the circuit.

The mean and standard error of the residuals was also examined, and the results are tabulated in Table

6. The mean of the residuals is zero within error, which is an expected result.

Table 6: The mean and standard error of the residuals is zero within error, which is the expected result.

Mean Standard Error 0 0.

The presence of normally distributed residuals indicates that the statistically derived resistance of 100.2 ± 1.7Ω is acceptable. The equation of the trendline shown in Figure 2, 𝑃 = 100.19𝐼^2 − 0.153, contains information on the intercept of the relationship. This intercept possesses no physical meaning and should be equal to zero as there can be no power dissipated in a circuit with no current passing through it. The intercept determined through regression is consistent with this theoretical value as the origin falls within its limits of uncertainty. A schematic was then constructed to depict the elements of the circuit, as shown in Error! Reference source not found..

Figure 4: Schematic of circuit including voltage source and resistive load.

0

2

4

Residuals^ 1.000^ 1.100^ 1.200^ 1.300^ 1.400^ 1.500^ 1.600^ 1.

Square of Current [A^2 ]