Question

In this "lab" (worksheet), you will explore the geometry of Lorentz transformations, specifically a "boost" from frame S to S^('), and how this changes the coordinates of time and space. You will need one full sheet of graph paper per person. Procedure: Part A - The Spacetime Diagram On graph paper, lay out the S frame with axis ct vertical and x horizontal. For ct, create axis ticks from 0 to 15m in increments of 0.5m. For x, go from 0 to 20m in increments of 0.5m. In this exercise, frame S^(') moves relative to S with speed v=0.6000c. Determine gamma , then use the Lorentz Transformation equations to draw lines for the ct^(') and x^(') axes on your graph. Note that S and S^(') have the same origin at x=x^(')=0 and t=t^(')=0. After you have the ct^(') and x^(') axes drawn, locate and draw lines for x^(')=2.5,5.0,7.5,10.0,12.5, and 15.0m. Again, use the Lorentz Transformation equations to help you do this. Next, locate and draw lines for ct^(')=10.0,7.5,5.0,2.5,-2.5, and -5.0m. Now that you have both sets of axes set up, choose two events ( A and B ) that are simultaneous in frame S. Choose the points so that Delta x>=7m and ct>=4m. Label the points on your graph. Use the Lorentz Transformation equations to calculate the S^(') coordinates of these points. Do your calculated values agree with the grid you drew in steps 3 and 4 ? If not, find your errors and correct them. Using Delta x,cDelta t,Delta x^('), and cDelta t^('), calculate Delta s^(2) and Delta s^('2). Is it invariant? If not, again correct your errors. According to your grid, which event happened first in S^(') ? Which is greater, Delta x or Delta x^(') ? How are they related? Explain this regarding proper length. Now choose two events and B^(') ) that are simultaneous in frame S^('). Choose the points so that Delta x^(')>=7m and ct^(')!=0. Label the points on your graph. Use the Lorentz Transformation equations to calculate the S coordinates of these points. Do you calculated values agree with the S grid? If not, find your errors and correct them. Using Delta x,cDelta t,Delta x^('), and cDelta t^('), calculate Delta s^(2) and Delta s^('2). Is it invariant? If not, again correct your errors. According to your grid, which event happened first in S ? Which is greater, Delta x or Delta x^(') ? How are they related? Explain this regarding proper length. Using a different color, draw the path through spacetime (the world line) for a beam of light emitted from the origin. Verify that both frames measure the speed to be c. Can anyone help me with this lab? Project Caliper Lorentz Transformations - Spacetime Page 1 In this"lab"(worksheet),you will explore the geometry of Lorentz transformations specifically a "boost" from frame S to S', and how this changes the coordinates of time and space. You will need one full sheet of graph paper per person. Procedure: Part A-The Spacetime Diagram 1. On graph paper,lay out the S frame with axis ct vertical and x horizontal.For ct,create axis ticks from 0 to 15 m in increments of 0.5 m.For x,go from 0 to 20 m in increments of 0.5 m 2. In this exercise,frame Smoves relative to S with speed v = 0.6000c.Determine y,then use the Lorentz Transformation equations to draw lines for the ct' and x' axes on your graph. Note that S and S' have the same origin at x = x' = 0 and t = t' = 0. 3. After you have the ct' and x' axes drawn,locate and draw lines for x' = 2.5, 5.0, 7.5, 10.0, 12.5, and 15.0 m. Again, use the Lorentz Transformation equations to help you do this. 4. Next, locate and draw lines for ct'=10.0,7.5,5.0,2.5,-2.5,and -5.0 m 5. Now that you have both sets of axes set up,choose two events(A and B)that are simultaneous in frame S.Choose the points so that Ax 7 m and ct 4 m.Label the points on your graph. 6. Use the Lorentz Transformation equations to calculate the S' coordinates of these points Do your calculated values agree with the grid you drew in steps 3 and 4? if not, find your errors and correct them 7. Using Ax, cAt, Ax', and ct', calculate As2 and s'2. Is it invariant? If not, again correct your errors. 8. According to your grid, which event happened first in S'? 9. Which is greater, Ax or Ax'? How are they related? Explain this regarding proper length. 1o.Now choose two events (A' and B') that are simultaneous in frame S'.Choose the points so that x' 7 m and ct' # 0. Label the points on your graph. 11.Use the Lorentz Transformation equations to calculate the S coordinates of these points.Do you calculated values agree with the S grid? if not, find your errors and correct them. 12. Using Ax, ct, Ax', and ct', calculate s2 and s'2. Is it invariant? If not, again correct your errors. 13.According to your grid,which event happened first in S? 14. Which is greater, x or Ax'? How are they related? Explain this regarding proper length. 15. Using a different color, draw the path through spacetime (the world line) for a beam of light emitted from the origin.Verify that both frames measure the speed to be c

          In this "lab" (worksheet), you will explore the geometry of Lorentz transformations,
specifically a "boost" from frame S to S^('), and how this changes the coordinates of time and
space. You will need one full sheet of graph paper per person.
Procedure:
Part A - The Spacetime Diagram
On graph paper, lay out the S frame with axis ct vertical and x horizontal. For ct, create axis
ticks from 0 to 15m in increments of 0.5m. For x, go from 0 to 20m in increments of 0.5m.
In this exercise, frame S^(') moves relative to S with speed v=0.6000c. Determine gamma , then
use the Lorentz Transformation equations to draw lines for the ct^(') and x^(') axes on your
graph. Note that S and S^(') have the same origin at x=x^(')=0 and t=t^(')=0.
After you have the ct^(') and x^(') axes drawn, locate and draw lines for
x^(')=2.5,5.0,7.5,10.0,12.5, and 15.0m. Again, use the Lorentz Transformation equations
to help you do this.
Next, locate and draw lines for ct^(')=10.0,7.5,5.0,2.5,-2.5, and -5.0m.
Now that you have both sets of axes set up, choose two events ( A and B ) that are
simultaneous in frame S. Choose the points so that Delta x>=7m and ct>=4m. Label the
points on your graph.
Use the Lorentz Transformation equations to calculate the S^(') coordinates of these points.
Do your calculated values agree with the grid you drew in steps 3 and 4 ? If not, find your
errors and correct them.
Using Delta x,cDelta t,Delta x^('), and cDelta t^('), calculate Delta s^(2) and Delta s^('2). Is it invariant? If not, again correct your
errors.
According to your grid, which event happened first in S^(') ?
Which is greater, Delta x or Delta x^(') ? How are they related? Explain this regarding proper length.
Now choose two events  and B^(') ) that are simultaneous in frame S^('). Choose the points so
that Delta x^(')>=7m and ct^(')!=0. Label the points on your graph.
Use the Lorentz Transformation equations to calculate the S coordinates of these points. Do
you calculated values agree with the S grid? If not, find your errors and correct them.
Using Delta x,cDelta t,Delta x^('), and cDelta t^('), calculate Delta s^(2) and Delta s^('2). Is it invariant? If not, again correct your
errors.
According to your grid, which event happened first in S ?
Which is greater, Delta x or Delta x^(') ? How are they related? Explain this regarding proper length.
Using a different color, draw the path through spacetime (the world line) for a beam of light
emitted from the origin. Verify that both frames measure the speed to be c.
Can anyone help me with this lab?
Project Caliper
Lorentz Transformations - Spacetime
Page 1
In this"lab"(worksheet),you will explore the geometry of Lorentz transformations specifically a "boost" from frame S to S', and how this changes the coordinates of time and space. You will need one full sheet of graph paper per person.
Procedure: Part A-The Spacetime Diagram 1. On graph paper,lay out the S frame with axis ct vertical and x horizontal.For ct,create axis ticks from 0 to 15 m in increments of 0.5 m.For x,go from 0 to 20 m in increments of 0.5 m 2. In this exercise,frame Smoves relative to S with speed v = 0.6000c.Determine y,then use the Lorentz Transformation equations to draw lines for the ct' and x' axes on your graph. Note that S and S' have the same origin at x = x' = 0 and t = t' = 0. 3. After you have the ct' and x' axes drawn,locate and draw lines for x' = 2.5, 5.0, 7.5, 10.0, 12.5, and 15.0 m. Again, use the Lorentz Transformation equations to help you do this. 4. Next, locate and draw lines for ct'=10.0,7.5,5.0,2.5,-2.5,and -5.0 m 5. Now that you have both sets of axes set up,choose two events(A and B)that are simultaneous in frame S.Choose the points so that Ax  7 m and ct  4 m.Label the points on your graph. 6. Use the Lorentz Transformation equations to calculate the S' coordinates of these points Do your calculated values agree with the grid you drew in steps 3 and 4? if not, find your errors and correct them 7. Using Ax, cAt, Ax', and ct', calculate As2 and s'2. Is it invariant? If not, again correct your errors. 8. According to your grid, which event happened first in S'? 9. Which is greater, Ax or Ax'? How are they related? Explain this regarding proper length. 1o.Now choose two events (A' and B') that are simultaneous in frame S'.Choose the points so that x'  7 m and ct' # 0. Label the points on your graph. 11.Use the Lorentz Transformation equations to calculate the S coordinates of these points.Do you calculated values agree with the S grid? if not, find your errors and correct them. 12. Using Ax, ct, Ax', and ct', calculate s2 and s'2. Is it invariant? If not, again correct your errors. 13.According to your grid,which event happened first in S? 14. Which is greater, x or Ax'? How are they related? Explain this regarding proper length. 15. Using a different color, draw the path through spacetime (the world line) for a beam of light emitted from the origin.Verify that both frames measure the speed to be c

in this lab worksheet you will explore the geometry of lorentz transformations specifically a boost from frame s to s and how this changes the coordinates of time and space you will need one 30316

Added by Dwayne W.

1.) Five observations taken for two variables follow. xi 4 6 11 3 16 yi 50 40 40 60 30 (a) Develop a scatter diagram with x on the horizontal axis. A scatter plot with 5 points is given. The horizontal axis is labeled: x, and ranges from 0 to 20. The vertical axis is labeled: y, and ranges from 0 to 80. The leftmost point on the plot is at about (3 , 30). Moving right, the second point is above and to the right of the first point. The third point is to the right of the second point. The fourth point is above and to the right of the third point. The fifth point is above and to the right of the fourth point. A scatter plot with 5 points is given. The horizontal axis is labeled: x, and ranges from 0 to 20. The vertical axis is labeled: y, and ranges from 0 to 80. The leftmost point on the plot is at about (3 , 60). Moving right, the second point is below and to the right of the first point. The third point is below and to the right of the second point. The fourth point is to the right of the third point. The fifth point is below and to the right of the fourth point. A scatter plot with 5 points is given. The horizontal axis is labeled: x, and ranges from 0 to 20. The vertical axis is labeled: y, and ranges from 0 to 80. The leftmost point on the plot is at about (3 , 50). Moving right, second point is below and to the right of the first point. The third point is below and to the right of the second point. The fourth point is to the right of the third point. The fifth point is below and to the right of the fourth point. A scatter plot with 5 points is given. The horizontal axis is labeled: x, and ranges from 0 to 20. The vertical axis is labeled: y, and ranges from 0 to 80. The leftmost point on the plot is at about (3 , 48). Moving right, second point is below and to the right of the first point. The third point is above and to the right of the second point. The fourth point is below and to the right of the third point. The fifth point is below and to the right of the fourth point. (b) What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? The scatter diagram indicates that there is relationship between the two variables. (c) Compute the sample covariance. Based on the sample covariance, what can be said about the relationship between the two variables? There is a strong positive linear relationship between the two variables. There is a strong negative linear relationship between the two variables. There is no relationship between the two variables. There is a positive linear relationship between the two variables, but the strength of this relationship cannot be determined based on the sample covariance. There is a negative linear relationship between the two variables, but the strength of this relationship cannot be determined based on the sample covariance. (d) Compute the sample correlation coefficient. (Round your answer to three decimal places.) Based on the sample correlation coefficient, what can be said about the relationship between the two variables? There is a strong positive linear relationship between the two variables. There is a strong negative linear relationship between the two variables. There is no relationship between the two variables. There is a positive linear relationship between the two variables, but the strength of this relationship cannot be determined based on the sample correlation coefficient. There is a negative linear relationship between the two variables, but the strength of this relationship cannot be determined based on the sample correlation coefficient. 2. Suppose the following data set contains the monthly adjusted stock prices for technology company A, and a consumer-goods company B from 2013–2018. Date A B 6/1/2013 43.44 64.71 7/1/2013 49.71 67.54 8/1/2013 53.60 65.98 9/1/2013 54.00 64.00 10/1/2013 60.40 68.44 11/1/2013 64.32 71.99 12/1/2013 67.69 69.55 1/1/2014 60.29 65.40 2/1/2014 63.43 67.68 3/1/2014 67.57 69.38 4/1/2014 74.39 71.08 5/1/2014 79.87 70.11 6/1/2014 85.47 68.17 7/1/2014 87.95 66.05 8/1/2014 94.37 72.73 9/1/2014 93.21 73.29 10/1/2014 99.99 76.42 11/1/2014 110.21 79.84 12/1/2014 102.66 80.43 1/1/2015 109.03 74.35 2/1/2015 119.64 75.64 3/1/2015 116.32 72.77 4/1/2015 117.00 70.58 5/1/2015 121.84 70.14 6/1/2015 117.76 70.01 7/1/2015 113.85 68.61 8/1/2015 105.91 63.66 9/1/2015 103.91 64.82 10/1/2015 112.66 68.89 11/1/2015 111.51 68.09 Date A B 12/1/2015 99.54 72.31 1/1/2016 91.98 74.42 2/1/2016 91.35 73.77 3/1/2016 103.67 75.65 4/1/2016 90.02 73.61 5/1/2016 94.90 75.09 6/1/2016 91.37 78.49 7/1/2016 99.69 80.36 8/1/2016 101.51 81.62 9/1/2016 108.82 83.92 10/1/2016 109.30 81.13 11/1/2016 106.36 77.63 12/1/2016 112.09 79.17 1/1/2017 117.49 82.53 2/1/2017 132.76 86.53 3/1/2017 139.88 85.35 4/1/2017 139.87 82.93 5/1/2017 148.80 82.31 6/1/2017 140.82 83.40 7/1/2017 145.45 85.95 8/1/2017 160.49 89.06 9/1/2017 151.36 86.80 10/1/2017 166.11 81.27 11/1/2017 167.88 84.49 12/1/2017 166.90 89.35 1/1/2018 165.11 83.90 2/1/2018 175.72 73.80 3/1/2018 166.14 74.55 4/1/2018 163.63 72.68 5/1/2018 186.86 83.31 (a) Develop a scatter diagram with company A stock price on the horizontal axis and company B stock price on the vertical axis. A scatter diagram has a horizontal axis labeled "B Adjusted Stock Price" with values from 0 to 100 and a vertical axis labeled "A Adjusted Stock Price" with values from 0 to 200. The scatter diagram has 60 points. A pattern goes up and right from (64, 43) to (89, 187). A scatter diagram has a horizontal axis labeled "A Adjusted Stock Price" with values from 0 to 200 and a vertical axis labeled "B Adjusted Stock Price" with values from 0 to 100. The scatter diagram has 60 points. A pattern goes up and right from (43, 64) to (187, 89). A scatter diagram has a horizontal axis labeled "A Adjusted Stock Price" with values from 0 to 200 and a vertical axis labeled "B Adjusted Stock Price" with values from 0 to 100. The scatter diagram has 60 points. A pattern goes down and right from (43, 89) to (187, 64). A scatter diagram has a horizontal axis labeled "B Adjusted Stock Price" with values from 0 to 100 and a vertical axis labeled "A Adjusted Stock Price" with values from 0 to 200. The scatter diagram has 60 points. A pattern goes down and right from (64, 187) to (89, 43). (b) What appears to be the relationship between these two stock prices? The scatter diagram shows a relationship with company A stock prices associated with higher company B stock prices. (c) Compute the sample covariance. (Round your answer to two decimal places.) Interpret the sample covariance. There is a positive relationship between the two variables. There is a negative relationship between the two variables. There is no relationship between the two variables. (d) Compute the sample correlation coefficient. (Round your answer to two decimal places.) What does this value indicate about the relationship between the stock price of company A and the stock price of company B? There is a moderately strong positive relationship between the two variables. There is a moderately strong negative relationship between the two variables. There is no relationship between the two variables. There is a positive relationship between the two variables, but the strength of this relationship cannot be determined based on the sample correlation coefficient. There is a negative relationship between the two variables, but the strength of this relationship cannot be determined based on the sample correlation coefficient. 3. A random sample of 30 colleges from Kiplinger's list of the best values in private college provided the data shown in the variable named Admit Rate (%) shows the percentage of students that applied to the college and were admitted, and the variable named 4 yr Grad. Rate (%) shows the percentage of students that were admitted and graduated in four years. (a) Develop a scatter diagram with Admit Rate (%) as the independent variable. A scatter diagram has 30 points. The horizontal axis is labeled Admit Rate (%) and ranges from 0 to 100. The vertical axis is labeled 4-yr Grad. Rate (%) and ranges from 0 to 100. The points plotted from the horizontal axis values of 6 to 81 are evenly scattered between the vertical axis values of 62 and 88. A scatter diagram has 30 points. The horizontal axis is labeled Admit Rate (%) and ranges from 0 to 100. The vertical axis is labeled 4-yr Grad. Rate (%) and ranges from 0 to 100. Most of the points follow a trend that starts at the point (6 , 86) and moves downward towards the point (81 , 66). The points become more scattered as the value on the horizontal axis increases. A scatter diagram has 30 points. The horizontal axis is labeled Admit Rate (%) and ranges from 0 to 100. The vertical axis is labeled 4-yr Grad. Rate (%) and ranges from 0 to 100. Most of the points follow a trend that starts at the point (6 , 47) and moves upward towards the point (81 , 89). The points are plotted close together with very little scatter. A scatter diagram has 30 points. The horizontal axis is labeled Admit Rate (%) and ranges from 0 to 100. The vertical axis is labeled 4-yr Grad. Rate (%) and ranges from 0 to 100. Most of the points follow a trend that starts at the point (6 , 89) and moves downward towards the point (81 , 47). The points are plotted close together with very little scatter. What does the scatter diagram indicate about the relationship between the two variables? There appears to be relationship between the two variables. This implies that admission rates are associated with graduation rates. (b) Compute the sample correlation coefficient. (Round your answer to two decimal places.) What does the value of the sample correlation coefficient indicate about the relationship between the Admit Rate (%) and the 4 yr Grad. Rate (%)? The sample correlation coefficient indicates relationship between the two variables.

Adi S.

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