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The center of gravity is at the same location as the center of mass for systems where the acceleration due to gravity is virtually equal for all points in the system. Therefore, in this Exploration we will talk about and calculate the center of mass. Restart.

The goal when making a mobile is for the center of mass to be below the string attached to the ceiling. Otherwise, there will be a net torque on the mobile about its center of mass until this condition is met.

Consider a mobile made of two blocks as shown in the animation. The mass of the blue block is 0.050 kg. Assume that the rods and string connecting the blocks are light enough to be neglected (position is given in meters). The goal when making a mobile is for the center of mass to be below the string attached to the ceiling. Otherwise, there will be a net torque on the mobile about its center of mass until this condition is met. Consider a mobile made of two blocks as shown in the animation. The mass of the blue block is 0.050 kg. Assume that the rods and string connecting the blocks are light enough to be neglected (position is given in meters).

a. What is the mass of the green block in order for the mobile to be balanced in Animation 1?

To answer this question, consider the conditions of equilibrium. The net torque on the horizontal rod about the point where it is attached to the string connected to the ceiling must equal zero. Therefore, the magnitude of the torque on the rod due to the tension in the right string must be equal to the magnitude of the torque on the rod due to the tension in the left string.

b. Suppose you want to replace the green block with another two-block system just like the first one, but with less massive blocks as shown in Animation 2. What are the masses of the red and orange blocks?

This is very similar to the previous question, except that you are applying the conditions of equilibrium to the rod connecting the red and orange blocks. However, when you solve the equation, net torque = 0, you have a problem. The masses of BOTH the red and orange blocks are unknown. Before, for the green and blue blocks, you knew the mass of the blue block and could solve for the mass of the green.

c. You need another relationship between the red and orange blocks to help you out. Since we replaced the green block with the red and orange ones, how are the masses of these three blocks related?

d. Ok, this is getting fun. Suppose that you now replace the orange block with another identical two- block system as shown in Animation 3. What are the masses of the yellow and purple blocks?

e. Where is the center of mass of the system of four blocks?

Since you know the masses of the blocks, measure the x, y coordinates of each block and calculate the coordinates of the center of mass.

f. Now click on the animation to locate the point that you just calculated. Is it directly beneath the string that connects the mobile to the ceiling? It should be!

Note that adding a new system of blocks to the left end each time did not change the x coordinate of the center of mass; however, it did cause the y coordinate to decrease since each system of blocks hung lower and lower. However, shifting the y coordinate of the center of mass did not change the equilibrium status of the mobile.

Worksheet for Exploration 13.2: Static Friction on a Horizontal Beam

You hold a piece of wood by pushing it horizontally against a wall as shown in the animation (position is given in meters).

The finger/hand contributes to the frictional force in exactly the same way as the wall does.

a. What forces act on the wood? Draw a free-body diagram for the wood showing the forces at their proper locations. Compare your diagram to the one shown in Animation 2. (sketch onto the above figure).

b. What is the force(s) in the +y direction that counteracts the weight of the wood in this example? Note that this force is parallel to the surface of the wall and wood where they are in contact. (dont forget that the hand on the right does exactly what the wall on the left does).

c. What do we call the parallel component of a contact force?

In Animation 3 you can adjust the magnitude of the push by clicking and dragging on the white circle at the tip of the vector representing the force of your hand on the wood. The maximum frictional force (shown as a red vector) adjusts accordingly. At the instant where the actual frictional force (black vector) equals the maximum frictional force (red vector), the beam will still be in equilibrium. In this case this is the least force that you can push the wood and have it remain in equilibrium. If you push it with less force, the meter stick will fall.

In Animation 4 you can adjust the magnitude of the push so that it is less than the minimum push required for the wood to remain in equilibrium. If the maximum possible static frictional force is less than the actual frictional force needed for equilibrium, the piece of wood will fall. In the animation if you adjust fs max < fs, the resulting situation depicted in the animation is unphysical since the piece of wood will actually fall. Worksheet for Exploration 13.3: Distributed Load A box sits on a board of negligible weight. Two supports exert forces on the left and right ends of the board (position is given in meters). The arrows represent the relative sizes of the two force vectors, but their length does not represent their actual magnitudes. Restart. a. How does the force of each support on the board depend on where the box is located? You can drag the box from the left to right to view the forces of the supports on the board. i. To answer part a, you should consider net force and net torque on the board. Suppose the box is exactly half way between the center and the right support. b. What is the ratio of the magnitude of the force of the right support on the board to the magnitude of the force of the left support on the board? Consider a situation where the board has significant weight. c. What then might the force vectors look like when the box is sitting above one of the supports, say for example the left support? Check using Animation 2. d. What is the ratio of the weight of the board to the weight of the box in this case? Worksheet for Exploration 13.4: The Stacking of Bricks How can you stack four uniform bricks (or blocks or meter sticks) one on top of another so that they extend as far over a table as possible and yet remain stable? Rules: You can drag and move bricks horizontally with your mouse (position is given in tenths of inches; hence each brick is a foot long). The stability of each brick is color coded: green: the brick is in stable equilibrium yellow: the center of gravity of the brick, or a group of bricks, is right above the edge of the supporting brick red: the brick is unstable; it will fall in real life. The center of gravity for each brick is shown as a small blue dot. The current mouse position (relative to the top left edge of the table) is shown in the upper part of the animation in the Text Field. If you press "show c.g." button, the center of gravity for the brick subsystems (top brick, top two bricks, top three bricks and all four bricks, respectively) will be shown as a small circle with an arrow. The length of the arrow is proportional to the gravitational force for each balanced subsystem. In addition, The left edge of each brick is in red The position of the center of gravity of each brick is in blue The position of the center of gravity is in black when show c.g. is selected a. What is the stability condition for an object overhanging a table? i. Hint: the object is the total mass sitting on the table. b. How should each brick be positioned relative to the brick underneath it? Be explicit and refer to the center of gravity. Hint: start at the top and work down. c. Can the top brick have its entire length beyond the edge of the table? d. Challenge: come up with a mathematical description for the overhang of each individual brick and the total overhang. i. Once you have an expression you may be able to determine the farthest to the right that the top brick can be (if you have a large stack of bricks one on top of the other).

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The 250-word summary should identify demographic, social and behavioural factors that are associated with routine check-up attendance in a statistically valid, clear and concise manner that can be understood by someone with minimal knowledge of epidemiology and biostatistics. You must identify a group or groups of people where a targeted campaign would be of most benefit.
Results:
The BRFSS:

A short summary of the study design of the BRFSS and a brief discussion of its limitations (no more than 250 words (Marks: 6)
Find a peer-reviewed primary quantitative research study in the literature that investigates the determinants of routine check-up attendance. Compare the designs between the study described in that paper and BRFSS (not more than 150 words). (Marks: 4)

Description of the population and analysis:

1) By analysing the BRFSS dataset, answer the following questions:

In your dataset, what percentage of participants reported routine check-up attendance? (Marks: 5)
Create a table of routine check-up attendance and 3 demographic factors, one of which must be binary, one numerical and one multi-category categorical (either nominal or ordinal). (Marks: 15)

Each cell should contain the appropriate summary measure and 95% confidence interval
The final column in the table should contain the p-value for statistical tests of difference or independence (i.e., tests that we covered in week 6). Footnotes should be used to indicate which statistical tests were used.

2) Examine the association between 4 social and/or behavioural factors and routine check-up attendance:

In an appropriate manner, present the results of analysis into the effect of four social and/or behavioural factors on routine check-up attendance. You must analyse a binary, numeric, nominal and ordinal factor. (Marks: 20)

For each factor you should report:

Variable name and data type
Name of measure calculated
Results of statistical analysis performed
Statistical interpretation
The Stata output (including visible code) e.g.

For one of the identified factors, you should explore the possibility of confounding or effect modification by sex. (Marks: 10)

Perform appropriate analysis
Present STATA output (including visible code)

Report the results in a table
Interpret your result

Conduct a multivariable regression and present the results of the adjusted regression model by including the four factors you examined in your analysis of social and behavioural factors. (Marks: 10)

Present STATA output (including visible code)
Report the results in a table.
Interpret your result

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Subscales for h2 A. Physician’s Empathy
B. Information Provision

C. Respect and Dignity

Remember, you use t-tests when you have a categorical variable like gender predicting a continuous variable. In this case, all of your variables are continuous, so you would use correlations because correlations are for when you are hypothesizing that two continuous variables are related.

The first step for testing your hypotheses is to construct composite variables in SPSS that are composed of the mean score across the items for each construct. So for your Patient Empathy scale you would average those two items together.

H1: The degree to which individuals feel general stigmatization about mental health is positively related to how much self-stigma they feel.

H2: People who experience negative doctor-patient communication are more likely to engage in self-stigmatizing beliefs and behaviors related to their health condition compared to positive doctor-patient communication.

Subscales for h2 A. Physician’s Empathy

B. Information Provision

C. Respect and Dignity

Method

Study Design

This study made use of a quantitative design using a questionnaire to measure doctor-patient diagnosis communication and how it can impact self-stigmatization.

Participants

The study had 200 Adults living with a mental health diagnosis as its participants. To guarantee a thorough understanding of mental health stigmatization, a broad sample of participants was recruited from various sources for adequate representation. The survey was aimed at including people from a variety of age groups, genders, nationalities, and socioeconomic backgrounds to collect views from a wide spectrum of people on stigmatizing mental health.

Participants were recruited through the Western Illinois University emailing list, and online platforms, including social media, were also used to recruit participants. The age group for this research is adults over 18 and therefore would not need parental consent to participate in this study.

Procedure

Participants will be asked to complete a survey that assesses their experiences with doctor-patient communication, self-stigmatization, and mental health outcomes. The survey will include validated measures such as The Stigma and Self-Stigma Scale (SASS) which was developed by Corrigan, Markowitz, Watson, Rowan, and Kubiak in 2003, this scale will be used to measure both their general stigma and self-stigmatization subscales and The Patient-Doctor Communication Scale by Haskard, DiMatteo, and Heritage (2009). These scales were edited to fit the study. The study will take each participant 5 minutes to complete.

Measures

General stigmatization scale

Participants’ perception of general stigmatization was measured using the first half of the Stigma and Self-Stigma Scale (SASS). This scale measures the perceived stigma by people living with mental health illnesses. 4 questions were used to measure this scale, the questions were gotten from Docksey et al. (2022)

Self-Stigmatization scale

Participants’ perception of self-stigmatization was measured using the second half of the Stigma and Self-Stigma Scale (SASS). This scale will be measuring the internalization of stigma and negative beliefs towards oneself because of their mental health illness. There were 5 questions used to measure this scale, the questions were obtained from Docksey et al., (2022).

Doctor-patient communication

Participants’ perception of their doctor-patient communication was measured by the Patient-Doctor Communication scale (PD-COM). This scale measures the quality of communication between patients and their healthcare providers.

This scale has 15 items that can be measured using a questionnaire that assesses various aspects of communication, including patients’ perceptions of their healthcare provider’s attentiveness, communication skills, and responsiveness to their needs.

DATA

Yes = 1, No = 0

Male 1. Female 2, prefer not to say 0, gender queer 3

(1) Strongly Agree (2) Agree 3 somewhat agree (4) Neutral 5 somewhat disagree (6) Disagree (7) Strongly Disagree

great 1, good 2, somewhat good3 , fine4, somewhat bad 5, bad6 , terrible 7.

APPENDIX

Dear participant, thank you for agreeing to be a part of this study. This questionnaire is strictly for research purposes, and any answer you provide will be highly confidential. Your response will be greatly appreciated. Please tick the appropriate box that best represents your stance or write the answer most appropriate to you. Note that there are no right or wrong answers.

1. How old are you? ___________

2. Have you ever been diagnosed with a mental health disorder? a) Yes b) No

Stigma and Self-Stigma Scale (SASS):

“Please indicate the extent to which you believe the following statements towards your about mental health disorder”:

Section I: Stigma Subscale

A) Anticipated Stigma Subscale

1. Because of my mental health disorder, I would worry other people would think that I am weak

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree.

2. Because of my mental health disorder, I would worry other people would avoid talking to me.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

3. Because of my mental health disorder, I would worry other people would think I was exaggerating my difficulties.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

4. Because of my mental health disorder, I would worry that other people might think that I was “not really ill”.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

B) Self-stigma

5. I feel ashamed because of my mental health disorder.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

6. If I cannot solve my own problems because of my mental health disorder, I would feel bad about myself.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

7. I feel weak because of my mental health disorder.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

8. I feel like no one would want to get close to me because of my mental health disorder,

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

9. I would feel a failure if I became mentally incapacitated because of my mental health disorder,

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

Patient-Doctor Communication (PD-COM) SCALE:

Dear participants, we kindly request you focus on patient-doctor interactions during a mental health diagnosis while using this doctor-patient communication scale. This will help us gather specific and valuable information on the quality of Doctor-Patient interaction during a mental health diagnosis.

These are the following scales to take note of while filling out the questionnaire. a) Evaluate the initial communication between you and your doctor during a mental health diagnosis. b) focus on the communication around the diagnosis and the sufficiency of the information provided by the health care practitioner that influenced your understanding of your mental health diagnosis. c) evaluate the doctor’s ability to provide enough empathy and emotional support during the mental health diagnosis interaction. By focusing on these specific areas of doctor-patient communication, we aim to get a better understanding of the strengths and weaknesses of healthcare professionals specifically during a mental health diagnosis. Thank you for your participation and valuable contribution.

Section II: Communication Quality Subscale

Please rate your experiences with your doctor in the following areas of communication quality.

A. Physician’s Empathy

The doctor shows understanding and concern for my well-being.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

The doctor actively listens to my concerns and feelings.

· (a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

B. Information Provision

The doctor explains my health condition and treatment options clearly.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

The doctor provides information in a way that I can easily understand.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

C. Respect and Dignity

The doctor treats me with respect and dignity, regardless of my health condition.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

The doctor acknowledges my autonomy and rights in decision-making.

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

Section III: Overall Assessment

Overall, how would you rate the quality of communication with your doctor?

(a) Strongly Agree (b) Agree (c) Neutral (d) Disagree (e) Strongly Disagree

Section IV: Additional Comments (Optional)

Please provide any additional comments or suggestions regarding your doctor’s communication quality.

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Year

Earnings

1990

(8% Loss)

1995

23%

2000

26%

2005

31%

2010

18%

Address all of the following questions:

· What was the average return for the stock over the period of 1990 through 2010?

· What was the standard deviation for the stock over this period?

· Assume that you currently have a portfolio that returns 19.5%. If you add this stock to the current portfolio, what will happen to the average return on the portfolio?

· Should Allied invest in the stock? Justify your response.

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on the last part write – a) What ONE thing did you learn interesting about the variable from examining the table or chart?

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on the last part write – a) What ONE thing did you learn interesting about the variable from examining the table or chart?

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