“How to Date a Black girl, Brown girl, Halfie or White girl” written by Junot Diaz

“How to Date a Black girl, Brown girl, Halfie or White girl” written by Junot Diaz

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Morgan Extra Pages Graphing with Excel to be carried out in a computer lab, 3rd floor Calloway Hall or elsewhere The Excel spreadsheet consists of vertical columns and horizontal rows; a column and row intersect at a cell. A cell can contain data for use in calculations of all sorts. The Name Box shows the currently selected cell (Fig. 1). In the Excel 2007 and 2010 versions the drop-down menus familiar in most software screens have been replaced by tabs with horizontally-arranged command buttons of various categories (Fig. 2) ___________________________________________________________________ Open Excel, click on the Microsoft circle, upper left, and Save As your surname. xlsx on the desktop. Before leaving the lab e-mail the file to yourself and/or save to a flash drive. Also e-mail it to your instructor. Figure 1. Parts of an Excel spreadsheet. Name Box Figure 2. Tabs. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 1: BASIC OPERATIONS Click Save often as you work. 1. Type the heading “Edge Length” in Cell A1 and double click the crack between the A and B column heading for automatic widening of column A. Similarly, write headings for columns B and C and enter numbers in Cells A2 and A3 as in Fig. 3. Highlight Cells A2 and A3 by dragging the cursor (chunky plus-shape) over the two of them and letting go. 2. Note that there are three types of cursor crosses: chunky for selecting, barbed for moving entries or blocks of entries from cell to cell, and tiny (appearing only at the little square in the lower-right corner of a cell). Obtain a tiny arrow for Cell A3 and perform a plus-drag down Column A until the cells are filled up to 40 (in Cell A8). Note that the two highlighted cells set both the starting value of the fill and the intervals. 3. Click on Cell B2 and enter a formula for face area of a cube as follows: type =, click on Cell A2, type ^2, and press Enter (note the formula bar in Fig. 4). 4. Enter the formula for cube volume in Cell C2 (same procedure, but “=, click on A2, ^3, Enter”). 5. Highlight Cells B2 and C2; plus-drag down to Row 8 (Fig. 5). Do the numbers look correct? Click on some cells in the newly filled area and notice how Excel steps the row designations as it moves down the column (it can do it for horizontal plusdrags along rows also). This is the major programming development that has led to the popularity of spreadsheets. Figure 3. Entries. Figure 4. A formula. Figure 5. Plus-dragging formulas. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 6. Now let’s graph the Face Area versus Edge Length: select Cells A1 through B8, choose the Insert tab, and click the Scatter drop-down menu and select “Scatter with only Markers” (Fig. 6). 7. Move the graph (Excel calls it a “chart”) that appears up alongside your number table and dress it up as follows: a. Note that some Chart Layouts have appeared above. Click Layout 1 and alter each title to read Face Area for the vertical axis, Edge Length for the horizontal and Face Area vs. Edge Length for the Graph Title. b. Activate the Excel Least squares routine, called “fitting a trendline” in the program: right click any of the data markers and click Add Trendline. Choose Power and also check “Display equation on chart” and “Display R-squared value on chart.” Fig. 7 shows what the graph will look like at this point. c. The titles are explicit, so the legend is unnecessary. Click on it and press the delete button to remove it. Figure 6. Creating a scatter graph. Figure 7. A graph with a fitted curve. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 8. Now let’s overlay the Volume vs. Edge Length curve onto the same graph (optional for 203L/205L): Make a copy of your graph by clicking on the outer white area, clicking ctrl-c (or right click, copy), and pasting the copy somewhere else (ctrl-v). If you wish, delete the trendline as in Fig. 8. a. Right click on the outer white space, choose Select Data and click the Add button. b. You can type in the cell ranges by hand in the dialog box that comes up, but it is easier to click the red, white, and blue button on the right of each space and highlight what you want to go in. Click the red, white, and blue of the bar that has appeared, and you will bounce back to the Add dialog box. Use the Edge Length column for the x’s and Volume for the y’s. c. Right-click on any volume data point and choose Format Data Series. Clicking Secondary Axis will place its scale on the right of the graph as in Fig. 8. d. Dress up your graph with two axis titles (Layout-Labels-Axis Titles), etc. Figure 8. Adding a second curve and y-axis to the graph Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 2: INTERPRETING A LINEAR GRAPH Introduction: Many experiments are repeated a number of times with one of the parameters involved varied from run to run. Often the goal is to measure the rate of change of a dependent variable, rather than a particular value. If the dependent variable can be expressed as a linear function of the independent parameter, then the slope and yintercept of an appropriate graph will give the rate of change and a particular value, respectively. An example of such an experiment in PHYS.203L/205L is the first part of Lab 20, in which weights are added to the bottom of a suspended spring (Figure 9). This experiment shows that a spring exerts a force Fs proportional to the distance stretched y = (y-yo), a relationship known as Hooke’s Law: Fs = – k(y – yo) (Eq. 1) where k is called the Hooke’s Law constant. The minus sign shows that the spring opposes any push or pull on it. In Lab 20 Fs is equal to (- Mg) and y is given by the reading on a meter stick. Masses were added to the bottom of the spring in 50-g increments giving weights in newtons of 0.49, 0.98, etc. The weight pan was used as the pointer for reading y and had a mass of 50 g, so yo could not be directly measured. For convenient graphing Equation 1 can be rewritten: -(Mg) = – ky + kyo Or (Mg) = ky – kyo (Eq. 1′) Procedure 1. On your spreadsheet note the tabs at the bottom left and double-click Sheet1. Type in “Basics,” and then click the Sheet2 tab to bring up a fresh worksheet. Change the sheet name to “Linear Fit” and fill in data as in this table. Hooke’s Law Experiment y (m) -Fs = Mg (N) 0.337 0.49 0.388 0.98 0.446 1.47 0.498 1.96 0.550 2.45 2. Highlight the cells with the numbers, and graph (Mg) versus y as in Steps 6 and 7 of the Basics section. Your Trendline this time will be Linear of course. If you are having trouble remembering what’s versus what, “y” looks like “v”, so what comes before the “v” of “versus” goes on the y (vertical) axis. Yes, this graph is confusing: the horizontal (“x”) axis is distance y, and the “y” axis is something else. 3. Click on the Equation/R2 box on the graph and highlight just the slope, that is, only the number that comes before the “x.” Copy it (control-c is a fast way to Figure 9. A spring with a weight stretching it Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com do it) and paste it (control-v) into an empty cell. Do likewise for the intercept (including the minus sign). SAVE YOUR FILE! 5. The next steps use the standard procedure for obtaining information from linear data. Write the general equation for a straight line immediately below a hand-written copy of Equation 1′ then circle matching items: (Mg) = k y + (- k yo) (Eq. 1′) y = m x + b Note the parentheses around the intercept term of Equation 1′ to emphasize that the minus sign is part of it. Equating above and below, you can create two useful new equations: slope m = k (Eq. 2) y-intercept b = -kyo (Eq. 3) 6. Solve Equation 2 for k, that is, rewrite left to right. Then substitute the value for slope m from your graph, and you have an experimental value for the Hooke’s Law constant k. Next solve Equation 3 for yo, substitute the value for intercept b from your graph and the value of k that you just found, and calculate yo. 7. Examine your linear graph for clues to finding the units of the slope and the yintercept. Use these units to find the units of k and yo. 8. Present your values of k and yo with their units neatly at the bottom of your spreadsheet. 9. R2 in Excel, like r in our lab manual and Corr. in the LoggerPro software, is a measure of how well the calculated line matches the data points. 1.00 would indicate a perfect match. State how good a match you think was made in this case? 10. Do the Homework, Further Exercises on Interpreting Linear Graphs, on the following pages. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com Eq.1 M m f M a g               , (Eq.2) M slope m g       (Eq.3) M b f        Morgan Extra Pages Homework: Graph Interpretation Exercises EXAMPLE WITH COMPLETE SOLUTION In PHYS.203L and 205L we do Lab 9 Newton’s Second Law on Atwood’s Machine using a photogate sensor (Fig. 1). The Atwood’s apparatus can slow the rate of fall enough to be measured even with primitive timing devices. In our experiment LoggerPro software automatically collects and analyzes the data giving reliable measurements of g, the acceleration of gravity. The equation governing motion for Atwood’s Machine can be written: where a is the acceleration of the masses and string, g is the acceleration of gravity, M is the total mass at both ends of the string, m is the difference between the masses, and f is the frictional force at the hub of the pulley wheel. In this exercise you are given a graph of a vs. m obtained in this experiment with the values of M and the slope and intercept (Fig. 2). The goal is to extract values for acceleration of gravity g and frictional force f from this information. To analyze the graph we write y = mx + b, the general equation for a straight line, directly under Equation 1 and match up the various parameters: Equating above and below, you can create two new equations: and y m x b M m f M a g                Figure 1. The Atwood’s Machine setup (from the LoggerPro handout). Figure 2. Graph of acceleration versus mass difference; data from a Physics I experiment. Atwood’s Machine M = 0.400 kg a = 24.4 m – 0.018 R2 = 0.998 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.000 0.010 0.020 0.030 0.040 0.050 0.060  m (kg) a (m/s2) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 2 2 9.76 / 0.400 24.4 /( ) m s kg m kg s g Mm      To handle Equation 2 it pays to consider what the units of the slope are. A slope is “the rise over the run,“ so its units must be the units of the vertical axis divided by those of the horizontal axis. In this case: Now let’s solve Equation 2 for g and substitute the values of total mass M and of the slope m from the graph: Using 9.80 m/s2 as the Baltimore accepted value for g, we can calculate the percent error: A similar process with Equation 3 leads to a value for f, the frictional force at the hub of the pulley wheel. Note that the units of intercept b are simply whatever the vertical axis units are, m/s2 in this case. Solving Equation 3 for f: EXERCISE 1 The Picket Fence experiment makes use of LoggerPro software to calculate velocities at regular time intervals as the striped plate passes through the photogate (Fig. 3). The theoretical equation is v = vi + at (Eq. 4) where vi = 0 (the fence is dropped from rest) and a = g. a. Write Equation 4 with y = mx + b under it and circle matching factors as in the Example. b. What is the experimental value of the acceleration of gravity? What is its percent error from the accepted value for Baltimore, 9.80 m/s2? c. Does the value of the y-intercept make sense? d. How well did the straight Trendline match the data? 2 / 2 kg s m kg m s   0.4% 100 9.80 9.76 9.80 100 . . . %        Acc Exp Acc Error kg m s mN kg m s f Mb 7.2 10 / 7.2 0.400 ( 0.018 / ) 3 2 2           Figure 3. Graph of speed versus time as calculated by LoggerPro as a picket fence falls freely through a photogate. Picket Fence Drop y = 9.8224x + 0.0007 R2 = 0.9997 0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1 1.2 t (s) v (m/s) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 2 This is an electrical example from PHYS.204L/206L, potential difference, V, versus current, I (Fig. 4). The theoretical equation is V = IR (Eq. 5) and is known as “Ohm’s Law.” The unit symbols stand for volts, V, and Amperes, A. The factor R stands for resistance and is measured in units of ohms, symbol  (capital omega). The definition of the ohm is: V (Eq. 6) By coincidence the letter symbols for potential (a quantity ) and volts (its unit) are identical. Thus “voltage” has become the laboratory slang name for potential. a. Rearrange the Ohm’s Law equation to match y = mx + b.. b. What is the experimental resistance? c. Comment on the experimental intercept: is its value reasonable? EXERCISE 3 This graph (Fig. 5) also follows Ohm’s Law, but solved for current I. For this graph the experimenter held potential difference V constant at 15.0V and measured the current for resistances of 100, 50, 40, and 30  Solve Ohm’s Law for I and you will see that 1/R is the logical variable to use on the x axis. For units, someone once jokingly referred to a “reciprocal ohm” as a “mho,” and the name stuck. a. Rearrange Equation 5 solved for I to match y = mx + b. b. What is the experimental potential difference? c. Calculate the percent difference from the 15.0 V that the experimenter set on the power supply (the instrument used for such experiments). d. Comment on the experimental intercept: is its value reasonable? Figure 4. Graph of potential difference versus current; data from a Physics II experiment. The theoretical equation, V = IR, is known as “Ohm’s Law.” Ohm’s Law y = 0.628x – 0.0275 R2 = 0.9933 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 Current, I (A) Potential difference, V (V) Figure 5. Another application of Ohm’s Law: a graph of current versus the inverse of resistance, from a different electric circuit experiment. Current versus (1/Resistance) y = 14.727x – 0.2214 R2 = 0.9938 0 100 200 300 400 500 600 5 10 15 20 25 30 35 R-1 (millimhos) I (milliamperes) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 4 The Atwood’s Machine experiment (see the solved example above) can be done in another way: keep mass difference m the same and vary the total mass M (Fig. 6). a. Rewrite Equation 1 and factor out (1/M). b. Equate the coefficient of (1/M) with the experimental slope and solve for acceleration of gravity g. c. Substitute the values for slope, mass difference, and frictional force and calculate the experimental of g. d. Derive the units of the slope and show that the units of g come out as they should. e. Is the value of the experimental intercept reasonable? EXERCISE 5 In the previous two exercises the reciprocal of a variable was used to make the graph come out linear. In this one the trick will be to use the square root of a variable (Fig. 7). In PHYS.203L and 205L Lab 19 The Pendulum the theoretical equation is where the period T is the time per cycle, L is the length of the string, and g is the acceleration of gravity. a. Rewrite Equation 7 with the square root of L factored out and placed at the end. b. Equate the coefficient of √L with the experimental slope and solve for acceleration of gravity g. c. Substitute the value for slope and calculate the experimental of g. d. Derive the units of the slope and show that the units of g come out as they should. e. Is the value of the experimental intercept reasonable? 2 (Eq . 7) g T   L Figure 6. Graph of acceleration versus the reciprocal of total mass; data from a another Physics I experiment. Atwood’s Machine m = 0.020 kg f = 7.2 mN y = 0.1964x – 0.0735 R2 = 0.995 0.400 0.600 0.800 1.000 2.000 2.500 3.000 3.500 4.000 4.500 5.000 1/M (1/kg) a (m/s2) Effect of Pendulum Length on Period y = 2.0523x – 0.0331 R2 = 0.999 0.400 0.800 1.200 1.600 2.000 2.400 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 L1/2 (m1/2) T (s) Figure 7. Graph of period T versus the square root of pendulum length; data from a Physics I experiment. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 6 In Exercise 5 another approach would have been to square both sides of Equation 7 and plot T2 versus L. Lab 20 directs us to use that alternative. It involves another case of periodic or harmonic motion with a similar, but more complicated, equation for the period: where T is the period of the bobbing (Fig. 8), M is the suspended mass, ms is the mass of the spring, k is a measure of stiffness called the spring constant, and C is a dimensionless factor showing how much of the spring mass is effectively bobbing. a. Square both sides of Equation 8 and rearrange it to match y = mx + b. b. Write y = mx + b under your rearranged equation and circle matching factors as in the Example. c. Write two new equations analogous to Equations 2 and 3 in the Example. Use the first of the two for calculating k and the second for finding C from the data of Fig. 9. d. A theoretical analysis has shown that for most springs C = 1/3. Find the percent error from that value. e. Derive the units of the slope and intercept; show that the units of k come out as N/m and that C is dimensionless. 2 (Eq . 8) k T M Cm s    Figure 8. In Lab 20 mass M is suspended from a spring which is set to bobbing up and down, a good approximation to simple harmonic motion (SHM), described by Equation 8. Lab 20: SHM of a Spring Mass of the spring, ms = 25.1 g y = 3.0185x + 0.0197 R2 = 0.9965 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 0 0.05 0.1 0.15 0.2 0.25 0.3 M (kg) T 2 2 Figure 9. Graph of the square of the period T2 versus suspended mass M data from a Physics I experiment. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 7 This last exercise deals with an exponential equation, and the trick is to take the logarithm of both sides. In PHYS.204L/206L we do Lab 33 The RC Time Constant with theoretical equation: where V is the potential difference at time t across a circuit element called a capacitor (the  is dropped for simplicity), Vo is V at t = 0 (try it), and  (tau) is a characteristic of the circuit called the time constant. a. Take the natural log of both sides and apply the addition rule for logarithms of a product on the right-hand side. b. Noting that the graph (Fig. 10) plots lnV versus t, arrange your equation in y = mx + b order, write y = mx + b under it, and circle the parts as in the Example. c. Write two new equations analogous to Equations 2 and 3 in the Example. Use the first of the two for calculating  and the second for finding lnVo and then Vo. d. Note that the units of lnV are the natural log of volts, lnV. As usual derive the units of the slope and interecept and use them to obtain the units of your experimental V and t. V V e (Eq. 9) t o    Figure 10. Graph of a logarithm versus time; data from Lab 33, a Physics II experiment. Discharge of a Capacitor y = -9.17E-03x + 2.00E+00 R2 = 9.98E-01 0.00 0.50 1.00 1.50 2.00 2.50

Morgan Extra Pages Graphing with Excel to be carried out in a computer lab, 3rd floor Calloway Hall or elsewhere The Excel spreadsheet consists of vertical columns and horizontal rows; a column and row intersect at a cell. A cell can contain data for use in calculations of all sorts. The Name Box shows the currently selected cell (Fig. 1). In the Excel 2007 and 2010 versions the drop-down menus familiar in most software screens have been replaced by tabs with horizontally-arranged command buttons of various categories (Fig. 2) ___________________________________________________________________ Open Excel, click on the Microsoft circle, upper left, and Save As your surname. xlsx on the desktop. Before leaving the lab e-mail the file to yourself and/or save to a flash drive. Also e-mail it to your instructor. Figure 1. Parts of an Excel spreadsheet. Name Box Figure 2. Tabs. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 1: BASIC OPERATIONS Click Save often as you work. 1. Type the heading “Edge Length” in Cell A1 and double click the crack between the A and B column heading for automatic widening of column A. Similarly, write headings for columns B and C and enter numbers in Cells A2 and A3 as in Fig. 3. Highlight Cells A2 and A3 by dragging the cursor (chunky plus-shape) over the two of them and letting go. 2. Note that there are three types of cursor crosses: chunky for selecting, barbed for moving entries or blocks of entries from cell to cell, and tiny (appearing only at the little square in the lower-right corner of a cell). Obtain a tiny arrow for Cell A3 and perform a plus-drag down Column A until the cells are filled up to 40 (in Cell A8). Note that the two highlighted cells set both the starting value of the fill and the intervals. 3. Click on Cell B2 and enter a formula for face area of a cube as follows: type =, click on Cell A2, type ^2, and press Enter (note the formula bar in Fig. 4). 4. Enter the formula for cube volume in Cell C2 (same procedure, but “=, click on A2, ^3, Enter”). 5. Highlight Cells B2 and C2; plus-drag down to Row 8 (Fig. 5). Do the numbers look correct? Click on some cells in the newly filled area and notice how Excel steps the row designations as it moves down the column (it can do it for horizontal plusdrags along rows also). This is the major programming development that has led to the popularity of spreadsheets. Figure 3. Entries. Figure 4. A formula. Figure 5. Plus-dragging formulas. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 6. Now let’s graph the Face Area versus Edge Length: select Cells A1 through B8, choose the Insert tab, and click the Scatter drop-down menu and select “Scatter with only Markers” (Fig. 6). 7. Move the graph (Excel calls it a “chart”) that appears up alongside your number table and dress it up as follows: a. Note that some Chart Layouts have appeared above. Click Layout 1 and alter each title to read Face Area for the vertical axis, Edge Length for the horizontal and Face Area vs. Edge Length for the Graph Title. b. Activate the Excel Least squares routine, called “fitting a trendline” in the program: right click any of the data markers and click Add Trendline. Choose Power and also check “Display equation on chart” and “Display R-squared value on chart.” Fig. 7 shows what the graph will look like at this point. c. The titles are explicit, so the legend is unnecessary. Click on it and press the delete button to remove it. Figure 6. Creating a scatter graph. Figure 7. A graph with a fitted curve. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 8. Now let’s overlay the Volume vs. Edge Length curve onto the same graph (optional for 203L/205L): Make a copy of your graph by clicking on the outer white area, clicking ctrl-c (or right click, copy), and pasting the copy somewhere else (ctrl-v). If you wish, delete the trendline as in Fig. 8. a. Right click on the outer white space, choose Select Data and click the Add button. b. You can type in the cell ranges by hand in the dialog box that comes up, but it is easier to click the red, white, and blue button on the right of each space and highlight what you want to go in. Click the red, white, and blue of the bar that has appeared, and you will bounce back to the Add dialog box. Use the Edge Length column for the x’s and Volume for the y’s. c. Right-click on any volume data point and choose Format Data Series. Clicking Secondary Axis will place its scale on the right of the graph as in Fig. 8. d. Dress up your graph with two axis titles (Layout-Labels-Axis Titles), etc. Figure 8. Adding a second curve and y-axis to the graph Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 2: INTERPRETING A LINEAR GRAPH Introduction: Many experiments are repeated a number of times with one of the parameters involved varied from run to run. Often the goal is to measure the rate of change of a dependent variable, rather than a particular value. If the dependent variable can be expressed as a linear function of the independent parameter, then the slope and yintercept of an appropriate graph will give the rate of change and a particular value, respectively. An example of such an experiment in PHYS.203L/205L is the first part of Lab 20, in which weights are added to the bottom of a suspended spring (Figure 9). This experiment shows that a spring exerts a force Fs proportional to the distance stretched y = (y-yo), a relationship known as Hooke’s Law: Fs = – k(y – yo) (Eq. 1) where k is called the Hooke’s Law constant. The minus sign shows that the spring opposes any push or pull on it. In Lab 20 Fs is equal to (- Mg) and y is given by the reading on a meter stick. Masses were added to the bottom of the spring in 50-g increments giving weights in newtons of 0.49, 0.98, etc. The weight pan was used as the pointer for reading y and had a mass of 50 g, so yo could not be directly measured. For convenient graphing Equation 1 can be rewritten: -(Mg) = – ky + kyo Or (Mg) = ky – kyo (Eq. 1′) Procedure 1. On your spreadsheet note the tabs at the bottom left and double-click Sheet1. Type in “Basics,” and then click the Sheet2 tab to bring up a fresh worksheet. Change the sheet name to “Linear Fit” and fill in data as in this table. Hooke’s Law Experiment y (m) -Fs = Mg (N) 0.337 0.49 0.388 0.98 0.446 1.47 0.498 1.96 0.550 2.45 2. Highlight the cells with the numbers, and graph (Mg) versus y as in Steps 6 and 7 of the Basics section. Your Trendline this time will be Linear of course. If you are having trouble remembering what’s versus what, “y” looks like “v”, so what comes before the “v” of “versus” goes on the y (vertical) axis. Yes, this graph is confusing: the horizontal (“x”) axis is distance y, and the “y” axis is something else. 3. Click on the Equation/R2 box on the graph and highlight just the slope, that is, only the number that comes before the “x.” Copy it (control-c is a fast way to Figure 9. A spring with a weight stretching it Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com do it) and paste it (control-v) into an empty cell. Do likewise for the intercept (including the minus sign). SAVE YOUR FILE! 5. The next steps use the standard procedure for obtaining information from linear data. Write the general equation for a straight line immediately below a hand-written copy of Equation 1′ then circle matching items: (Mg) = k y + (- k yo) (Eq. 1′) y = m x + b Note the parentheses around the intercept term of Equation 1′ to emphasize that the minus sign is part of it. Equating above and below, you can create two useful new equations: slope m = k (Eq. 2) y-intercept b = -kyo (Eq. 3) 6. Solve Equation 2 for k, that is, rewrite left to right. Then substitute the value for slope m from your graph, and you have an experimental value for the Hooke’s Law constant k. Next solve Equation 3 for yo, substitute the value for intercept b from your graph and the value of k that you just found, and calculate yo. 7. Examine your linear graph for clues to finding the units of the slope and the yintercept. Use these units to find the units of k and yo. 8. Present your values of k and yo with their units neatly at the bottom of your spreadsheet. 9. R2 in Excel, like r in our lab manual and Corr. in the LoggerPro software, is a measure of how well the calculated line matches the data points. 1.00 would indicate a perfect match. State how good a match you think was made in this case? 10. Do the Homework, Further Exercises on Interpreting Linear Graphs, on the following pages. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com Eq.1 M m f M a g               , (Eq.2) M slope m g       (Eq.3) M b f        Morgan Extra Pages Homework: Graph Interpretation Exercises EXAMPLE WITH COMPLETE SOLUTION In PHYS.203L and 205L we do Lab 9 Newton’s Second Law on Atwood’s Machine using a photogate sensor (Fig. 1). The Atwood’s apparatus can slow the rate of fall enough to be measured even with primitive timing devices. In our experiment LoggerPro software automatically collects and analyzes the data giving reliable measurements of g, the acceleration of gravity. The equation governing motion for Atwood’s Machine can be written: where a is the acceleration of the masses and string, g is the acceleration of gravity, M is the total mass at both ends of the string, m is the difference between the masses, and f is the frictional force at the hub of the pulley wheel. In this exercise you are given a graph of a vs. m obtained in this experiment with the values of M and the slope and intercept (Fig. 2). The goal is to extract values for acceleration of gravity g and frictional force f from this information. To analyze the graph we write y = mx + b, the general equation for a straight line, directly under Equation 1 and match up the various parameters: Equating above and below, you can create two new equations: and y m x b M m f M a g                Figure 1. The Atwood’s Machine setup (from the LoggerPro handout). Figure 2. Graph of acceleration versus mass difference; data from a Physics I experiment. Atwood’s Machine M = 0.400 kg a = 24.4 m – 0.018 R2 = 0.998 0.00 0.20 0.40 0.60 0.80 1.00 1.20 1.40 0.000 0.010 0.020 0.030 0.040 0.050 0.060  m (kg) a (m/s2) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com 2 2 9.76 / 0.400 24.4 /( ) m s kg m kg s g Mm      To handle Equation 2 it pays to consider what the units of the slope are. A slope is “the rise over the run,“ so its units must be the units of the vertical axis divided by those of the horizontal axis. In this case: Now let’s solve Equation 2 for g and substitute the values of total mass M and of the slope m from the graph: Using 9.80 m/s2 as the Baltimore accepted value for g, we can calculate the percent error: A similar process with Equation 3 leads to a value for f, the frictional force at the hub of the pulley wheel. Note that the units of intercept b are simply whatever the vertical axis units are, m/s2 in this case. Solving Equation 3 for f: EXERCISE 1 The Picket Fence experiment makes use of LoggerPro software to calculate velocities at regular time intervals as the striped plate passes through the photogate (Fig. 3). The theoretical equation is v = vi + at (Eq. 4) where vi = 0 (the fence is dropped from rest) and a = g. a. Write Equation 4 with y = mx + b under it and circle matching factors as in the Example. b. What is the experimental value of the acceleration of gravity? What is its percent error from the accepted value for Baltimore, 9.80 m/s2? c. Does the value of the y-intercept make sense? d. How well did the straight Trendline match the data? 2 / 2 kg s m kg m s   0.4% 100 9.80 9.76 9.80 100 . . . %        Acc Exp Acc Error kg m s mN kg m s f Mb 7.2 10 / 7.2 0.400 ( 0.018 / ) 3 2 2           Figure 3. Graph of speed versus time as calculated by LoggerPro as a picket fence falls freely through a photogate. Picket Fence Drop y = 9.8224x + 0.0007 R2 = 0.9997 0 2 4 6 8 10 12 0 0.2 0.4 0.6 0.8 1 1.2 t (s) v (m/s) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 2 This is an electrical example from PHYS.204L/206L, potential difference, V, versus current, I (Fig. 4). The theoretical equation is V = IR (Eq. 5) and is known as “Ohm’s Law.” The unit symbols stand for volts, V, and Amperes, A. The factor R stands for resistance and is measured in units of ohms, symbol  (capital omega). The definition of the ohm is: V (Eq. 6) By coincidence the letter symbols for potential (a quantity ) and volts (its unit) are identical. Thus “voltage” has become the laboratory slang name for potential. a. Rearrange the Ohm’s Law equation to match y = mx + b.. b. What is the experimental resistance? c. Comment on the experimental intercept: is its value reasonable? EXERCISE 3 This graph (Fig. 5) also follows Ohm’s Law, but solved for current I. For this graph the experimenter held potential difference V constant at 15.0V and measured the current for resistances of 100, 50, 40, and 30  Solve Ohm’s Law for I and you will see that 1/R is the logical variable to use on the x axis. For units, someone once jokingly referred to a “reciprocal ohm” as a “mho,” and the name stuck. a. Rearrange Equation 5 solved for I to match y = mx + b. b. What is the experimental potential difference? c. Calculate the percent difference from the 15.0 V that the experimenter set on the power supply (the instrument used for such experiments). d. Comment on the experimental intercept: is its value reasonable? Figure 4. Graph of potential difference versus current; data from a Physics II experiment. The theoretical equation, V = IR, is known as “Ohm’s Law.” Ohm’s Law y = 0.628x – 0.0275 R2 = 0.9933 0 0.1 0.2 0.3 0.4 0 0.1 0.2 0.3 0.4 0.5 0.6 Current, I (A) Potential difference, V (V) Figure 5. Another application of Ohm’s Law: a graph of current versus the inverse of resistance, from a different electric circuit experiment. Current versus (1/Resistance) y = 14.727x – 0.2214 R2 = 0.9938 0 100 200 300 400 500 600 5 10 15 20 25 30 35 R-1 (millimhos) I (milliamperes) Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 4 The Atwood’s Machine experiment (see the solved example above) can be done in another way: keep mass difference m the same and vary the total mass M (Fig. 6). a. Rewrite Equation 1 and factor out (1/M). b. Equate the coefficient of (1/M) with the experimental slope and solve for acceleration of gravity g. c. Substitute the values for slope, mass difference, and frictional force and calculate the experimental of g. d. Derive the units of the slope and show that the units of g come out as they should. e. Is the value of the experimental intercept reasonable? EXERCISE 5 In the previous two exercises the reciprocal of a variable was used to make the graph come out linear. In this one the trick will be to use the square root of a variable (Fig. 7). In PHYS.203L and 205L Lab 19 The Pendulum the theoretical equation is where the period T is the time per cycle, L is the length of the string, and g is the acceleration of gravity. a. Rewrite Equation 7 with the square root of L factored out and placed at the end. b. Equate the coefficient of √L with the experimental slope and solve for acceleration of gravity g. c. Substitute the value for slope and calculate the experimental of g. d. Derive the units of the slope and show that the units of g come out as they should. e. Is the value of the experimental intercept reasonable? 2 (Eq . 7) g T   L Figure 6. Graph of acceleration versus the reciprocal of total mass; data from a another Physics I experiment. Atwood’s Machine m = 0.020 kg f = 7.2 mN y = 0.1964x – 0.0735 R2 = 0.995 0.400 0.600 0.800 1.000 2.000 2.500 3.000 3.500 4.000 4.500 5.000 1/M (1/kg) a (m/s2) Effect of Pendulum Length on Period y = 2.0523x – 0.0331 R2 = 0.999 0.400 0.800 1.200 1.600 2.000 2.400 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 L1/2 (m1/2) T (s) Figure 7. Graph of period T versus the square root of pendulum length; data from a Physics I experiment. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 6 In Exercise 5 another approach would have been to square both sides of Equation 7 and plot T2 versus L. Lab 20 directs us to use that alternative. It involves another case of periodic or harmonic motion with a similar, but more complicated, equation for the period: where T is the period of the bobbing (Fig. 8), M is the suspended mass, ms is the mass of the spring, k is a measure of stiffness called the spring constant, and C is a dimensionless factor showing how much of the spring mass is effectively bobbing. a. Square both sides of Equation 8 and rearrange it to match y = mx + b. b. Write y = mx + b under your rearranged equation and circle matching factors as in the Example. c. Write two new equations analogous to Equations 2 and 3 in the Example. Use the first of the two for calculating k and the second for finding C from the data of Fig. 9. d. A theoretical analysis has shown that for most springs C = 1/3. Find the percent error from that value. e. Derive the units of the slope and intercept; show that the units of k come out as N/m and that C is dimensionless. 2 (Eq . 8) k T M Cm s    Figure 8. In Lab 20 mass M is suspended from a spring which is set to bobbing up and down, a good approximation to simple harmonic motion (SHM), described by Equation 8. Lab 20: SHM of a Spring Mass of the spring, ms = 25.1 g y = 3.0185x + 0.0197 R2 = 0.9965 0.0000 0.2000 0.4000 0.6000 0.8000 1.0000 0 0.05 0.1 0.15 0.2 0.25 0.3 M (kg) T 2 2 Figure 9. Graph of the square of the period T2 versus suspended mass M data from a Physics I experiment. Click to buy NOW! PDF-XChange Viewer www.docu-track.com Click to buy NOW! PDF-XChange Viewer www.docu-track.com EXERCISE 7 This last exercise deals with an exponential equation, and the trick is to take the logarithm of both sides. In PHYS.204L/206L we do Lab 33 The RC Time Constant with theoretical equation: where V is the potential difference at time t across a circuit element called a capacitor (the  is dropped for simplicity), Vo is V at t = 0 (try it), and  (tau) is a characteristic of the circuit called the time constant. a. Take the natural log of both sides and apply the addition rule for logarithms of a product on the right-hand side. b. Noting that the graph (Fig. 10) plots lnV versus t, arrange your equation in y = mx + b order, write y = mx + b under it, and circle the parts as in the Example. c. Write two new equations analogous to Equations 2 and 3 in the Example. Use the first of the two for calculating  and the second for finding lnVo and then Vo. d. Note that the units of lnV are the natural log of volts, lnV. As usual derive the units of the slope and interecept and use them to obtain the units of your experimental V and t. V V e (Eq. 9) t o    Figure 10. Graph of a logarithm versus time; data from Lab 33, a Physics II experiment. Discharge of a Capacitor y = -9.17E-03x + 2.00E+00 R2 = 9.98E-01 0.00 0.50 1.00 1.50 2.00 2.50

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Who Were the Redeemers?

Who Were the Redeemers?

The Redeemers were an democratically eclectic group of people constituted … Read More...
Chapter 06 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 6 Reading Quiz Question 17 Part A Which of the following represents an example of intraspecific exploitation competition? ANSWER: Chapter 6 Reading Quiz Question 3 Part A A species’s realized niche _____. ANSWER: Chapter 6 Reading Quiz Question 2 Part A Two species of ant compete for limited resources in a front yard, until only one species is able to remain. This is an example of _____. ANSWER: Hungry and fighting for a meal, a jackal quickly consumes the carcass of a young antelope while fighting off the feeding efforts of a vulture. Two species of worker ants converge on pieces of a donut left behind from the people in the park. The leaves of the huge hickory tree overshadow the young hickory tree saplings struggling for light just below. Spotting a fresh source of grasses, the large male bison moves over to graze, pushing the smaller bison out of the way. is smaller than the fundamental niche because of the constraints of competition is broader than a species’s fundamental niche does not overlap with similar species includes environmental conditions that are not included in the fundamental niche Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 20 Part A In which of the following situations would we expect a parasite to spread the fastest? ANSWER: Chapter 6 Reading Quiz Question 6 Part A Many plants have evolved adaptations to discourage herbivore feeding. Which one of the following is an example of such coevolution between bison and prairie plants? ANSWER: Chapter 6 Reading Quiz Question 5 Part A When predators selectively prey on the old and sick members of a prey population, they _____. ANSWER: mutualism intraspecific competition the competitive exclusion principle niche differentiation concentrated hosts with slowly moving vectors widely dispersed hosts with rapidly moving vectors concentrated hosts with rapidly moving vectors widely dispersed hosts with slow-moving vectors the ability to regrow after a wildfire thorns the production of nutritious fruits longer and thicker roots Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 21 Part A Cattle egrets are large white birds that follow grazing cattle. The cattle disturb the grass and stir up insects upon which the egrets feed. The cattle do not seem to mind the birds and gain nothing from this relationship. This relationship between cattle and cattle egrets is a type of _____. ANSWER: Chapter 6 Reading Quiz Question 8 Part A Which of the following is a mutualistic relationship that has a significant effect on an entire ecological community? ANSWER: Chapter 6 Reading Quiz Question 7 Part A Which one of the following relationships would be considered a win/win? ANSWER: cause the overall health of the prey population to increase illustrate the process of prey switching increase the likelihood of parasitic infections of the prey cause the overall health of the prey population to decrease parasitism commensalism mimicry mutualism Polar bears are the top predator influencing the abundance of seals and sea lions in a region. Hermit crabs inhabit the abandoned shells of marine snails that died long ago. Fungus-plant root associations benefit most of the plants living in a prairie. Mosquitoes function as a vector in the widespread transmission of malaria to people living in Ecuador. Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 23 Part A In examining a terrestrial food web, we expect that the _____. ANSWER: Chapter 6 Reading Quiz Question 22 Part A Energy is lost as it moves from one trophic level to the next because _____. ANSWER: Chapter 6 Reading Quiz Question 11 Part A The research on the reintroduction of wolves into Yellowstone National Park reveals that in this ecosystem, wolves represent _____. ANSWER: mutualism predation parasitism commensalism biomass of primary consumers exceeds the biomass of producers number of secondary consumers exceeds the number of producers biomass of primary consumers exceeds the biomass of secondary consumers number of tertiary consumers exceeds the number of secondary consumers one trophic level does not consume the entire trophic level below it some of the calories consumed drive cellular activities and do not add mass some ingested materials are undigested and eliminated All of the listed responses are correct. Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 10 Part A Overhunting of deer followed by a very difficult winter caused the deer population on an island to drop by 80%. In the next two years, visitors to the island were surprised to see many young trees sprouting up at the edges of the forest. This change in the number of saplings as a result of the decline of the deer population represents _____. ANSWER: Chapter 6 Reading Quiz Question 24 Part A The May 18, 1980, eruption of Mount Saint Helens blasted away soil and produced massive mudflows that scoured the adjacent region down to bare rock. Pumice rock that covered the area is eroding down to smaller gravel. This situation represents _____. ANSWER: Chapter 6 Reading Quiz Question 15 Part A In some ecosystems, succession increases the chance of disturbance. In these ecosystems, _____. a keystone producer a keystone herbivore a vital primary consumer a keystone predator a trophic cascade a decline in trophic level efficiency the emergence of a new ecological community a loss of a trophic level from a food web primary succession with the removal of all ecological legacies secondary succession with the removal of all ecological legacies secondary succession with several ecological legacies primary succession with several ecological legacies Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 7 5/21/2014 8:01 PM ANSWER: Chapter 6 Reading Quiz Question 12 Part A A forest is logged, leaving behind the seeds and saplings of many shrubs and trees. These seeds and saplings represent _____. ANSWER: Chapter 6 Reading Quiz Question 13 Part A During primary succession, populations of different species replace one another over time because of _____. ANSWER: Chapter 6 Reading Quiz Question 14 Part A Which one of the following represents a climax community in southern Alaska? ANSWER: ecosystems begin again with primary succession climax communities are expected climax communities may not occur disturbances usually result in virtually no ecological legacy ecological legacies a climax community primary succession pioneer species migration facilitation competition All of the listed responses are correct. Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 9 Part A In general, _____. ANSWER: Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 19 points. the group of species associated with a white spruce forest lichens and mosses that colonize exposed rock birch and alder trees herbs and a few low shrubs that replace lichens and mosses food webs usually have 8-10 trophic levels food webs are interconnected food chains food chains consist of many interrelated food webs food webs consist of either consumers or producers Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 7 5/21/2014 8:01 PM

Chapter 06 Reading Questions Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Chapter 6 Reading Quiz Question 17 Part A Which of the following represents an example of intraspecific exploitation competition? ANSWER: Chapter 6 Reading Quiz Question 3 Part A A species’s realized niche _____. ANSWER: Chapter 6 Reading Quiz Question 2 Part A Two species of ant compete for limited resources in a front yard, until only one species is able to remain. This is an example of _____. ANSWER: Hungry and fighting for a meal, a jackal quickly consumes the carcass of a young antelope while fighting off the feeding efforts of a vulture. Two species of worker ants converge on pieces of a donut left behind from the people in the park. The leaves of the huge hickory tree overshadow the young hickory tree saplings struggling for light just below. Spotting a fresh source of grasses, the large male bison moves over to graze, pushing the smaller bison out of the way. is smaller than the fundamental niche because of the constraints of competition is broader than a species’s fundamental niche does not overlap with similar species includes environmental conditions that are not included in the fundamental niche Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 20 Part A In which of the following situations would we expect a parasite to spread the fastest? ANSWER: Chapter 6 Reading Quiz Question 6 Part A Many plants have evolved adaptations to discourage herbivore feeding. Which one of the following is an example of such coevolution between bison and prairie plants? ANSWER: Chapter 6 Reading Quiz Question 5 Part A When predators selectively prey on the old and sick members of a prey population, they _____. ANSWER: mutualism intraspecific competition the competitive exclusion principle niche differentiation concentrated hosts with slowly moving vectors widely dispersed hosts with rapidly moving vectors concentrated hosts with rapidly moving vectors widely dispersed hosts with slow-moving vectors the ability to regrow after a wildfire thorns the production of nutritious fruits longer and thicker roots Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 21 Part A Cattle egrets are large white birds that follow grazing cattle. The cattle disturb the grass and stir up insects upon which the egrets feed. The cattle do not seem to mind the birds and gain nothing from this relationship. This relationship between cattle and cattle egrets is a type of _____. ANSWER: Chapter 6 Reading Quiz Question 8 Part A Which of the following is a mutualistic relationship that has a significant effect on an entire ecological community? ANSWER: Chapter 6 Reading Quiz Question 7 Part A Which one of the following relationships would be considered a win/win? ANSWER: cause the overall health of the prey population to increase illustrate the process of prey switching increase the likelihood of parasitic infections of the prey cause the overall health of the prey population to decrease parasitism commensalism mimicry mutualism Polar bears are the top predator influencing the abundance of seals and sea lions in a region. Hermit crabs inhabit the abandoned shells of marine snails that died long ago. Fungus-plant root associations benefit most of the plants living in a prairie. Mosquitoes function as a vector in the widespread transmission of malaria to people living in Ecuador. Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 23 Part A In examining a terrestrial food web, we expect that the _____. ANSWER: Chapter 6 Reading Quiz Question 22 Part A Energy is lost as it moves from one trophic level to the next because _____. ANSWER: Chapter 6 Reading Quiz Question 11 Part A The research on the reintroduction of wolves into Yellowstone National Park reveals that in this ecosystem, wolves represent _____. ANSWER: mutualism predation parasitism commensalism biomass of primary consumers exceeds the biomass of producers number of secondary consumers exceeds the number of producers biomass of primary consumers exceeds the biomass of secondary consumers number of tertiary consumers exceeds the number of secondary consumers one trophic level does not consume the entire trophic level below it some of the calories consumed drive cellular activities and do not add mass some ingested materials are undigested and eliminated All of the listed responses are correct. Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 10 Part A Overhunting of deer followed by a very difficult winter caused the deer population on an island to drop by 80%. In the next two years, visitors to the island were surprised to see many young trees sprouting up at the edges of the forest. This change in the number of saplings as a result of the decline of the deer population represents _____. ANSWER: Chapter 6 Reading Quiz Question 24 Part A The May 18, 1980, eruption of Mount Saint Helens blasted away soil and produced massive mudflows that scoured the adjacent region down to bare rock. Pumice rock that covered the area is eroding down to smaller gravel. This situation represents _____. ANSWER: Chapter 6 Reading Quiz Question 15 Part A In some ecosystems, succession increases the chance of disturbance. In these ecosystems, _____. a keystone producer a keystone herbivore a vital primary consumer a keystone predator a trophic cascade a decline in trophic level efficiency the emergence of a new ecological community a loss of a trophic level from a food web primary succession with the removal of all ecological legacies secondary succession with the removal of all ecological legacies secondary succession with several ecological legacies primary succession with several ecological legacies Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 7 5/21/2014 8:01 PM ANSWER: Chapter 6 Reading Quiz Question 12 Part A A forest is logged, leaving behind the seeds and saplings of many shrubs and trees. These seeds and saplings represent _____. ANSWER: Chapter 6 Reading Quiz Question 13 Part A During primary succession, populations of different species replace one another over time because of _____. ANSWER: Chapter 6 Reading Quiz Question 14 Part A Which one of the following represents a climax community in southern Alaska? ANSWER: ecosystems begin again with primary succession climax communities are expected climax communities may not occur disturbances usually result in virtually no ecological legacy ecological legacies a climax community primary succession pioneer species migration facilitation competition All of the listed responses are correct. Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 7 5/21/2014 8:01 PM Chapter 6 Reading Quiz Question 9 Part A In general, _____. ANSWER: Score Summary: Your score on this assignment is 0.0%. You received 0 out of a possible total of 19 points. the group of species associated with a white spruce forest lichens and mosses that colonize exposed rock birch and alder trees herbs and a few low shrubs that replace lichens and mosses food webs usually have 8-10 trophic levels food webs are interconnected food chains food chains consist of many interrelated food webs food webs consist of either consumers or producers Chapter 06 Reading Questions http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 7 5/21/2014 8:01 PM

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Which plants in this figure must all be heterozygous?purple-flowered plants in the F1 generation white-flowered plants in the P generation purple-flowered plants in the F2 generation purple-flowered plants in the P generation

Which plants in this figure must all be heterozygous?purple-flowered plants in the F1 generation white-flowered plants in the P generation purple-flowered plants in the F2 generation purple-flowered plants in the P generation

purple-flowered plants in the F1 generation Which plants in this … Read More...
Chapter 06 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Concept Review: Species Interactions Can you identify the type of species interaction that each label describes? Part A Drag each description to the appropriate bin. ANSWER: Activity: Food Webs Click here to complete this activity. Then answer the questions. Part A In an ecosystem, phytoplankton are _____. ANSWER: Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 9 5/21/2014 8:01 PM Correct Autotrophs, such as phytoplankton, are producers. Part B An earthworm that feeds on the remains of plants and animals is acting as a _____. ANSWER: Correct The earthworm is feeding on the remains of dead organisms. Part C When a human eats a steak, the human is acting as a _____. ANSWER: Correct By feeding on a primary consumer, the human is acting as a secondary consumer. Part D A cow eating grass is an example of a _____. ANSWER: Correct By feeding on a producer, the cow is acting as a primary consumer. Part E primary consumers tertiary consumers detritivores producers secondary consumers tertiary consumer secondary consumer producer detritivore primary consumer primary consumer detritivore secondary consumer producer tertiary consumer detritivore producer tertiary consumer secondary consumer primary consumer Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 9 5/21/2014 8:01 PM A seal that just ate a clam is eaten by a shark. The shark is acting as a _____. ANSWER: Correct The shark that ate the seal that ate the clam that ate the algae is the tertiary consumer. Activity: Pyramids of Production Click here to complete this activity. Then answer the questions. Part A _____ are secondary consumers. ANSWER: Correct Secondary consumers are animals that eat other animals; thus, they are carnivores. Part B Approximately _____% of the energy at one trophic level is passed on to the next highest trophic level. ANSWER: Correct Approximately 5–10% of the energy at one trophic level is passed on to the next highest trophic level. producer primary consumer tertiary consumer secondary consumer detritivore Producers Herbivores Plants Cows Carnivores 0–5 5–10 10–15 15–20 90–100 Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 9 5/21/2014 8:01 PM Part C 10,000 kcal of producer could support approximately _____ kcal of tertiary consumer. ANSWER: Correct This is the number of kcal of tertiary consumer that could be supported. Activity: Primary Succession Click here to complete this activity. Then answer the question. Part A Which of these is a starting point for primary succession? ANSWER: Correct Such a surface lacks any life and is thus a starting point for primary succession. Part B The first colonizing organisms during primary succession tend to be: ANSWER: 1,000 100 10 1 0 a surface exposed by a retreating glacier abandoned farmland an abandoned city a neglected yard none of these is a starting point for primary succession small shrubs trees lichens and mosses herbs Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 9 5/21/2014 8:01 PM Correct After the glacier retreats, bare ground is eventually colonized by lichens and mosses. Part C Which one of the following is a general characteristic of plants that are early colonizers during primary succession? ANSWER: Correct After the glacier retreats, bare ground is eventually colonized by lichens and mosses, then by deciduous trees with wind-borne seeds. Concept Review: Secondary Succession Can you order the steps of secondary succession? Part A Order the labels in the flowchart to complete the model of secondary succession as observed in a deciduous forest of eastern North America. ANSWER: Current Events: In Yellowstone, Killing One Kind of Trout to Save Another (New York Times, 8/23/2011) Read this New York Times article and then answer the questions. In Yellowstone, Killing One Kind of Trout to Save Another (8/23/2011) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Which of the following would be the best discovery regarding the Judas fish? ANSWER: plants are able to fix their own nitrogen plants can outcompete other plants that invade the area plants have wind-dispersed seeds plants are shade-tolerant Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 9 5/21/2014 8:01 PM Part B Which of the following is true? ANSWER: Part C Why is protecting cutthroat trout in Yellowstone so important? ANSWER: Part D Which of the following is true? ANSWER: Part E Why don’t bears in Yellowstone eat lake trout? ANSWER: Part F How did rainbow trout become established worldwide? ANSWER: Learning where lake trout feed. Learning where lake trout hibernate. Learning where lake trout spawn. Learning where lake trout migrate to during fall. Officials are working only in certain areas to eliminate lake trout. Officials are working to eliminate lake trout throughout Wyoming. Officials are working to eliminate lake trout throughout the Great Lakes. All states in the U.S. are working to eliminate lake trout. Because many other species depend on cutthroat trout. Because local people depend on cutthroat trout for food. Because Yellowstone is the only place cutthroat trout are found. Because cutthroat trout are listed as a threatened species. Cutthroat trout are to Yellowstone Lake as rainbow trout are to Yellowstone Lake. Cutthroat trout are to Yellowstone Lake as Asian carp are to the Great Lakes. Lake trout are to Yellowstone Lake as see lamprey are to the Great Lakes. Lake trout are to the Great Lakes as Asian carp are to the Yellowstone Lake. They don’t like the taste. They cannot find them. Lake trout skin is too tough. Lake trout are too small for bears to be interested. Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 9 5/21/2014 8:01 PM Current Events: In Thailand, Love of Food Carries Deadly Risks (New York Times, 4/25/2011) Read this New York Times article and then answer the questions. In Thailand, Love of Food Carries Deadly Risks (4/25/2011) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Rather than stop eating fish, what should Thai people do to eliminate the risk of liver fluke infection? ANSWER: Part B Liver flukes are transmitted through which of the following? ANSWER: Part C Getting rid of which of the following would help decrease the population of liver flukes? ANSWER: Part D Pla som is a unique dish because it is what? ANSWER: Part E Due to warming oceans caused by climate change. Natural process of migration. Accidental introduction via ships. Purposeful stocking. Consume ethyl alcohol while eating fish. Add more garlic. Cook it thoroughly. Pick the flukes out by hand. urine saliva feces blood rats mosquitoes frogs snails pickled frozen fermented blanched Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 9 5/21/2014 8:01 PM You have liver flukes. What are your chances of getting liver cancer? ANSWER: Part F You are a scientist studying liver flukes in Thailand. Where should you look for them? ANSWER: ABC News Video: The Cuttlefish Watch the ABC News video (2:20 minutes). Then answer the questions below. Part A The changes to the cuttlefish’s skin are related to _______. ANSWER: Correct Part B Camouflage contributes to the cuttlefish’s survival by enabling it to _______. 1-5% 5-10% 10-15% 15-20% The northwestern part of the country. The southeastern part of the country. The southwestern part of the country. The northeastern part of the country. camouflage elimination of waste reproductive strategies feeding behavior Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 9 5/21/2014 8:01 PM ANSWER: Correct Part C Cuttlefish placed in a sandy environment with white rocks will camouflage their skin in a pattern called _______. ANSWER: Correct Part D In the presence of a black-and-white striped background, a cuttlefish was observed to _______. ANSWER: Correct Part E Which question was raised but not answered in the video? ANSWER: Correct Score Summary: Your score on this assignment is 48.5%. You received 16 out of a possible total of 33 points. sneak up on prey mimic poisonous species hide from predators warn potential predators that it is poisonous universal camouflage disruptive camouflage warning coloration camouflage tide-pool camouflage move its arm to match the orientation of the stripes turn completely white and hide in the white stripe turn completely black and hide in the black stripe exhibit the exact striping pattern of its surroundings Why does the cuttlefish change its skin pattern? What happens when a cuttlefish is placed in an unnatural environment? Is the cuttlefish able to grow a protective shell? How do cuttlefish camouflage themselves even though they are colorblind? Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 9 5/21/2014 8:01 PM

Chapter 06 Homework Due: 11:59pm on Friday, May 23, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Concept Review: Species Interactions Can you identify the type of species interaction that each label describes? Part A Drag each description to the appropriate bin. ANSWER: Activity: Food Webs Click here to complete this activity. Then answer the questions. Part A In an ecosystem, phytoplankton are _____. ANSWER: Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 1 of 9 5/21/2014 8:01 PM Correct Autotrophs, such as phytoplankton, are producers. Part B An earthworm that feeds on the remains of plants and animals is acting as a _____. ANSWER: Correct The earthworm is feeding on the remains of dead organisms. Part C When a human eats a steak, the human is acting as a _____. ANSWER: Correct By feeding on a primary consumer, the human is acting as a secondary consumer. Part D A cow eating grass is an example of a _____. ANSWER: Correct By feeding on a producer, the cow is acting as a primary consumer. Part E primary consumers tertiary consumers detritivores producers secondary consumers tertiary consumer secondary consumer producer detritivore primary consumer primary consumer detritivore secondary consumer producer tertiary consumer detritivore producer tertiary consumer secondary consumer primary consumer Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 2 of 9 5/21/2014 8:01 PM A seal that just ate a clam is eaten by a shark. The shark is acting as a _____. ANSWER: Correct The shark that ate the seal that ate the clam that ate the algae is the tertiary consumer. Activity: Pyramids of Production Click here to complete this activity. Then answer the questions. Part A _____ are secondary consumers. ANSWER: Correct Secondary consumers are animals that eat other animals; thus, they are carnivores. Part B Approximately _____% of the energy at one trophic level is passed on to the next highest trophic level. ANSWER: Correct Approximately 5–10% of the energy at one trophic level is passed on to the next highest trophic level. producer primary consumer tertiary consumer secondary consumer detritivore Producers Herbivores Plants Cows Carnivores 0–5 5–10 10–15 15–20 90–100 Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 3 of 9 5/21/2014 8:01 PM Part C 10,000 kcal of producer could support approximately _____ kcal of tertiary consumer. ANSWER: Correct This is the number of kcal of tertiary consumer that could be supported. Activity: Primary Succession Click here to complete this activity. Then answer the question. Part A Which of these is a starting point for primary succession? ANSWER: Correct Such a surface lacks any life and is thus a starting point for primary succession. Part B The first colonizing organisms during primary succession tend to be: ANSWER: 1,000 100 10 1 0 a surface exposed by a retreating glacier abandoned farmland an abandoned city a neglected yard none of these is a starting point for primary succession small shrubs trees lichens and mosses herbs Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 4 of 9 5/21/2014 8:01 PM Correct After the glacier retreats, bare ground is eventually colonized by lichens and mosses. Part C Which one of the following is a general characteristic of plants that are early colonizers during primary succession? ANSWER: Correct After the glacier retreats, bare ground is eventually colonized by lichens and mosses, then by deciduous trees with wind-borne seeds. Concept Review: Secondary Succession Can you order the steps of secondary succession? Part A Order the labels in the flowchart to complete the model of secondary succession as observed in a deciduous forest of eastern North America. ANSWER: Current Events: In Yellowstone, Killing One Kind of Trout to Save Another (New York Times, 8/23/2011) Read this New York Times article and then answer the questions. In Yellowstone, Killing One Kind of Trout to Save Another (8/23/2011) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Which of the following would be the best discovery regarding the Judas fish? ANSWER: plants are able to fix their own nitrogen plants can outcompete other plants that invade the area plants have wind-dispersed seeds plants are shade-tolerant Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 5 of 9 5/21/2014 8:01 PM Part B Which of the following is true? ANSWER: Part C Why is protecting cutthroat trout in Yellowstone so important? ANSWER: Part D Which of the following is true? ANSWER: Part E Why don’t bears in Yellowstone eat lake trout? ANSWER: Part F How did rainbow trout become established worldwide? ANSWER: Learning where lake trout feed. Learning where lake trout hibernate. Learning where lake trout spawn. Learning where lake trout migrate to during fall. Officials are working only in certain areas to eliminate lake trout. Officials are working to eliminate lake trout throughout Wyoming. Officials are working to eliminate lake trout throughout the Great Lakes. All states in the U.S. are working to eliminate lake trout. Because many other species depend on cutthroat trout. Because local people depend on cutthroat trout for food. Because Yellowstone is the only place cutthroat trout are found. Because cutthroat trout are listed as a threatened species. Cutthroat trout are to Yellowstone Lake as rainbow trout are to Yellowstone Lake. Cutthroat trout are to Yellowstone Lake as Asian carp are to the Great Lakes. Lake trout are to Yellowstone Lake as see lamprey are to the Great Lakes. Lake trout are to the Great Lakes as Asian carp are to the Yellowstone Lake. They don’t like the taste. They cannot find them. Lake trout skin is too tough. Lake trout are too small for bears to be interested. Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 6 of 9 5/21/2014 8:01 PM Current Events: In Thailand, Love of Food Carries Deadly Risks (New York Times, 4/25/2011) Read this New York Times article and then answer the questions. In Thailand, Love of Food Carries Deadly Risks (4/25/2011) Registration with The New York Times provides instant access to breaking news on NYTimes.com. To register, go to http://www.nytimes.com/register. Visit http://www.nytimes.com/content/help/rights/terms/terms-of-service.html to review the current NYT Terms of Service. Part A Rather than stop eating fish, what should Thai people do to eliminate the risk of liver fluke infection? ANSWER: Part B Liver flukes are transmitted through which of the following? ANSWER: Part C Getting rid of which of the following would help decrease the population of liver flukes? ANSWER: Part D Pla som is a unique dish because it is what? ANSWER: Part E Due to warming oceans caused by climate change. Natural process of migration. Accidental introduction via ships. Purposeful stocking. Consume ethyl alcohol while eating fish. Add more garlic. Cook it thoroughly. Pick the flukes out by hand. urine saliva feces blood rats mosquitoes frogs snails pickled frozen fermented blanched Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 7 of 9 5/21/2014 8:01 PM You have liver flukes. What are your chances of getting liver cancer? ANSWER: Part F You are a scientist studying liver flukes in Thailand. Where should you look for them? ANSWER: ABC News Video: The Cuttlefish Watch the ABC News video (2:20 minutes). Then answer the questions below. Part A The changes to the cuttlefish’s skin are related to _______. ANSWER: Correct Part B Camouflage contributes to the cuttlefish’s survival by enabling it to _______. 1-5% 5-10% 10-15% 15-20% The northwestern part of the country. The southeastern part of the country. The southwestern part of the country. The northeastern part of the country. camouflage elimination of waste reproductive strategies feeding behavior Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 8 of 9 5/21/2014 8:01 PM ANSWER: Correct Part C Cuttlefish placed in a sandy environment with white rocks will camouflage their skin in a pattern called _______. ANSWER: Correct Part D In the presence of a black-and-white striped background, a cuttlefish was observed to _______. ANSWER: Correct Part E Which question was raised but not answered in the video? ANSWER: Correct Score Summary: Your score on this assignment is 48.5%. You received 16 out of a possible total of 33 points. sneak up on prey mimic poisonous species hide from predators warn potential predators that it is poisonous universal camouflage disruptive camouflage warning coloration camouflage tide-pool camouflage move its arm to match the orientation of the stripes turn completely white and hide in the white stripe turn completely black and hide in the black stripe exhibit the exact striping pattern of its surroundings Why does the cuttlefish change its skin pattern? What happens when a cuttlefish is placed in an unnatural environment? Is the cuttlefish able to grow a protective shell? How do cuttlefish camouflage themselves even though they are colorblind? Chapter 06 Homework http://session.masteringenvironmentalscience.com/myct/assignmentPrintV… 9 of 9 5/21/2014 8:01 PM

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Do an internet search to find the weirdest animal ( 25 animals) Information need included: 1- name of animals. 2-description. (Your own words) 3-why do you thing it’s weird?

Do an internet search to find the weirdest animal ( 25 animals) Information need included: 1- name of animals. 2-description. (Your own words) 3-why do you thing it’s weird?

S.no Name of the animal Description and Reasons of thinking … Read More...
Earlier in the history of Western medicine, surgeons did not know the immune function of the thymus gland and it was sometimes removed in children. What symptoms would you now predict these patients might display afterward? Select one: a. increased inflammatory and allergic responses to foreign material including viruses b. reduced ability to recognize foreign material and distinguish it from body proteins c. serious problems following receiving blood transfusions of any type of blood d. complete rejection of all normal body tissues e. failure to produce any white blood cells

Earlier in the history of Western medicine, surgeons did not know the immune function of the thymus gland and it was sometimes removed in children. What symptoms would you now predict these patients might display afterward? Select one: a. increased inflammatory and allergic responses to foreign material including viruses b. reduced ability to recognize foreign material and distinguish it from body proteins c. serious problems following receiving blood transfusions of any type of blood d. complete rejection of all normal body tissues e. failure to produce any white blood cells

Info@checkyourstudy.com                                                                                                                                                                                       : reduced ability to recognize foreign material and distinguish … Read More...
Faculty of Science Technology and Engineering Department of Physics Senior Laboratory Faraday rotation AIM To show that optical activity is induced in a certain type of glass when it is in a magnetic field. To investigate the degree of rotation of linearly polarised light as a function of the applied magnetic field and hence determine a parameter which is characteristic of each material and known as Verdet’s constant. BACKGROUND INFORMATION A brief description of the properties and production of polarised light is given in the section labelled: Notes on polarisation. This should be read before proceeding with this experiment. Additional details may be found in the references listed at the end of this experiment. Whereas some materials, such as quartz, are naturally optically active, optical activity can be induced in others by the application of a magnetic field. For such materials, the angle through which the plane of polarisation of a linearly polarised beam is rotated () depends on the thickness of the sample (L), the strength of the magnetic field (B) and on the properties of the particular material. The latter is described by means of a parameter introduced by Verdet, which is wavelength dependent. Thus:  = V B L Lamp Polariser Solenoid Polariser Glass rod A Solenoid power supply Viewing mirror EXPERIMENTAL PROCEDURE The experimental arrangement is shown in the diagram. Unpolarised white light is produced by a hot filament and viewed using a mirror. • The light from the globe passes through two polarisers as well as the specially doped glass rod. Select one of the colour filters provided and place in the light path. Each of these filters transmits a relatively narrow band of wavelengths centred around a dominant wavelength as listed in the table. Filter No. Dominant Wavelength 98 4350 Å 50 4500 75 4900 58 5300 72 B 6060 92 6700 With the power supply for the coil switched off, (do not simply turn the potentiometer to zero: this still allows some current to flow) adjust one of the polarisers until minimum light is transmitted to the mirror. Minimum transmission can be determined visually. • Decide which polariser you will work with and do not alter the other one during the measurements. • The magnetic field is generated by a current in a solenoid (coil) placed around the glass rod. As the current in the coil is increased, the magnitude of the magnetic field will increase as shown on the calibration curve below. The degree of optical activity will also increase, resulting in some angle of rotation of the plane of polarisation. Hence you will need to rotate your chosen polariser to regain a minimum setting. 0 1 2 3 4 5 0.00 0.02 0.04 0.06 0.08 I (amps) B (tesla) Magnetic field (B) produced by current (I) in solenoid • Record the rotation angle () for coil currents of 0,1,2,3,4 and 5 amps. Avoid having the current in the coil switched on except when measurements are actually being taken as it can easily overheat. If the coil becomes too hot to touch, switch it off and wait for it to cool before proceeding. • Plot  as a function of B and, given that the length of the glass rod is 30 cm, determine Verdet’s constant for this material at the wavelength () in use. • Repeat the experiment for each of the wavelengths available using the filter set provided. • Calculate the logarithm for each V and  and tabulate the results. By plotting log V against log , determine the relationship between V and . [Hint: m log(x) = log (xm) and log(xy) = log(x) + log(y)]. • Calculate the errors involved in your determination of V. The uncertainty in a value of B may be taken as the uncertainty in reading the scale of the calibration curve) • The magnetic field direction can be reversed by reversing the direction of current flow in the coil. Describe the effect of this reversal and provide an explanation. Reference Optics Hecht.

Faculty of Science Technology and Engineering Department of Physics Senior Laboratory Faraday rotation AIM To show that optical activity is induced in a certain type of glass when it is in a magnetic field. To investigate the degree of rotation of linearly polarised light as a function of the applied magnetic field and hence determine a parameter which is characteristic of each material and known as Verdet’s constant. BACKGROUND INFORMATION A brief description of the properties and production of polarised light is given in the section labelled: Notes on polarisation. This should be read before proceeding with this experiment. Additional details may be found in the references listed at the end of this experiment. Whereas some materials, such as quartz, are naturally optically active, optical activity can be induced in others by the application of a magnetic field. For such materials, the angle through which the plane of polarisation of a linearly polarised beam is rotated () depends on the thickness of the sample (L), the strength of the magnetic field (B) and on the properties of the particular material. The latter is described by means of a parameter introduced by Verdet, which is wavelength dependent. Thus:  = V B L Lamp Polariser Solenoid Polariser Glass rod A Solenoid power supply Viewing mirror EXPERIMENTAL PROCEDURE The experimental arrangement is shown in the diagram. Unpolarised white light is produced by a hot filament and viewed using a mirror. • The light from the globe passes through two polarisers as well as the specially doped glass rod. Select one of the colour filters provided and place in the light path. Each of these filters transmits a relatively narrow band of wavelengths centred around a dominant wavelength as listed in the table. Filter No. Dominant Wavelength 98 4350 Å 50 4500 75 4900 58 5300 72 B 6060 92 6700 With the power supply for the coil switched off, (do not simply turn the potentiometer to zero: this still allows some current to flow) adjust one of the polarisers until minimum light is transmitted to the mirror. Minimum transmission can be determined visually. • Decide which polariser you will work with and do not alter the other one during the measurements. • The magnetic field is generated by a current in a solenoid (coil) placed around the glass rod. As the current in the coil is increased, the magnitude of the magnetic field will increase as shown on the calibration curve below. The degree of optical activity will also increase, resulting in some angle of rotation of the plane of polarisation. Hence you will need to rotate your chosen polariser to regain a minimum setting. 0 1 2 3 4 5 0.00 0.02 0.04 0.06 0.08 I (amps) B (tesla) Magnetic field (B) produced by current (I) in solenoid • Record the rotation angle () for coil currents of 0,1,2,3,4 and 5 amps. Avoid having the current in the coil switched on except when measurements are actually being taken as it can easily overheat. If the coil becomes too hot to touch, switch it off and wait for it to cool before proceeding. • Plot  as a function of B and, given that the length of the glass rod is 30 cm, determine Verdet’s constant for this material at the wavelength () in use. • Repeat the experiment for each of the wavelengths available using the filter set provided. • Calculate the logarithm for each V and  and tabulate the results. By plotting log V against log , determine the relationship between V and . [Hint: m log(x) = log (xm) and log(xy) = log(x) + log(y)]. • Calculate the errors involved in your determination of V. The uncertainty in a value of B may be taken as the uncertainty in reading the scale of the calibration curve) • The magnetic field direction can be reversed by reversing the direction of current flow in the coil. Describe the effect of this reversal and provide an explanation. Reference Optics Hecht.

Top of Form Abstract.     Faraday Effect or Faraday … Read More...