In the country of Wiknam, there is only one firm that produces and sells soccer ball. Initially international trade is prohibited in the country. The following equations describe the monopolist’s demand, marginal revenue, total cost and marginal cost: Demand: P = 10 – Q Marginal Revenue: MR = 10 – 2Q Total Cost: TC = 3 + Q + 0.5Q2 Marginal Cost: MC = 1 + Q Q stands for quantity and P is the price measured in Wiknamian dollars. a) [20 marks] How many soccer balls does the monopolist produce? At what price are they sold? What is the monopolist’s profit? Show all your calculations. b) [10 marks] One day, the King of Wiknam decrees that henceforth, there will be free trade- either imports or exports- of soccer balls at the world price of $6. The firm now becomes a price taker in a competitive market. What happens to domestic production of soccer balls? What happens to domestic consumption? Does Wiknam export or import soccer balls? c) [10 marks] Suppose that the world price was not $6, but instead, happens to be exactly the same as the domestic price without trade as determined in part a) above. Would allowing trade change anything for the Wiknamian economy? Explain

In the country of Wiknam, there is only one firm that produces and sells soccer ball. Initially international trade is prohibited in the country. The following equations describe the monopolist’s demand, marginal revenue, total cost and marginal cost: Demand: P = 10 – Q Marginal Revenue: MR = 10 – 2Q Total Cost: TC = 3 + Q + 0.5Q2 Marginal Cost: MC = 1 + Q Q stands for quantity and P is the price measured in Wiknamian dollars. a) [20 marks] How many soccer balls does the monopolist produce? At what price are they sold? What is the monopolist’s profit? Show all your calculations. b) [10 marks] One day, the King of Wiknam decrees that henceforth, there will be free trade- either imports or exports- of soccer balls at the world price of $6. The firm now becomes a price taker in a competitive market. What happens to domestic production of soccer balls? What happens to domestic consumption? Does Wiknam export or import soccer balls? c) [10 marks] Suppose that the world price was not $6, but instead, happens to be exactly the same as the domestic price without trade as determined in part a) above. Would allowing trade change anything for the Wiknamian economy? Explain

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Three forces FA, FB and FC are applied to a beam as shown in the figure. (a) Determine the moment of force FC about point O using the cross product definition of moment (M = r x F) (10 points) (b) Determine the moment of force FB about point A using the rectangular components of the force (that is, do not use the cross product) (5 points) (c) Resolve force FA into a force and a couple at point C

Three forces FA, FB and FC are applied to a beam as shown in the figure. (a) Determine the moment of force FC about point O using the cross product definition of moment (M = r x F) (10 points) (b) Determine the moment of force FB about point A using the rectangular components of the force (that is, do not use the cross product) (5 points) (c) Resolve force FA into a force and a couple at point C

PHET ElectroMagnetism Key to this Document Instructions are in black. Experimental questions that you need to solve through experimentation with an online animation are in green highlighted. Important instructions are in red highlighted. Items that need a response from you are in yellow highlighted. Please put your answers to this activity in RED. Part I- Comparing Permanent Magnets and Electromagnets: 1. Select the simulation “Magnets and Electromagnets.” It is at this link: http://phet.colorado.edu/new/simulations/sims.php?sim=Magnets_and_Electromagnets 2. Move the compass slowly along a semicircular path above the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 3. Move the compass along a semicircular path below the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 4. What do you suppose the compass needles drawn all over the screen tell you? 5. Use page 10 in your book to look up what it looks like when scientists use a drawing to represent a magnetic field. Describe the field around a bar magnet here. 6. Put the compass to the left or right of the magnet. Click “flip polarity” and notice what happens to the compass. Using the compass needle as your observation tool, describe the effect that flipping the poles of the magnet has on the magnetic field. 7. Click on the electromagnet tab along the top of the simulation window. Place the compass on the left side of the coil so that the compass center lies along the axis of the coil. <--like this 8. Move the compass along a semicircular path above the coil until you’ve put it on the opposite side of the coil. Then do the same below the coil. Notice what happens to the compass needle. Compare this answer to the answer you got to Number 2 and 3. 9. Compare the shape of the magnetic field of a bar magnet to the magnetic field of an electromagnet. 10. Use the voltage slider to change the direction of the current and investigate the shape of the magnetic field the coil using the compass after you’ve let the compass stabilize. Summarize, the effect that the direction of current has on the shape of the magnetic field around an electrified coil of wires. 11. What happens to the current in the coil when you set the voltage of the battery to zero? 12. What happens to the magnetic field around the coil when you set the voltage of the battery to zero? Part II – Investigating relationships- No Answers are written on this document after this point. All three data tables, graphs and conclusion statements go on the Google Spreadsheet that you can download from Ms. Pogge’s website. Experimental Question #1: How does distance affect the strength of the magnetic field around an electromagnet? 1. Using the Electromagnet simulation, click on “Show Field Meter.” 2. Set the battery voltage to 10V where the positive is on the right of the battery (slide the switch all the way to the right). 3. Magnetic field strength (symbol B on the top line of the meter) is measured in gauss (G). You’ll only need to record the value on the top line of the Field Meter. 4. Position zero will be right on top of the coil. Negative number positions will be to the left and positive number positions to the right of the coil. 5. Move the field meter one compass needle to the right and record the value of B at position 1. 6. This data table below will be used to help you fill in the first spreadsheet you downloaded from Ms. Pogge’s website. You will end up with 3 data tables, 3 graphs and 3 conclusion statements in your document, one for each mini-experiment you are doing. a. NOTE: Be sure to take all of your values along the horizontal axis of the coil. You’ll know you’re on the axis because the B-y measurement of the magnetic field is zero along the axis. Compass position (no units) Magnetic Field Strength ( )<--Fill in units! -5 (5 needles to the left of coil) Don’t fill in the table here...do it on the Google Spreadsheet you downloaded -4 -3 -2 -1 0 (middle of coil) 1 2 3 4 5 (5 needles to right of coil) 7. In your Google Spreadsheet: Graph the compass position on the horizontal (x) axis and magnetic field magnitude on the vertical (y) axis. 8. Make sure to label the axes and title the graph. Share this spreadsheet with your teacher. 9. Analyze your graph to discover how the two variables are related, and report the relationship between magnetic field strength and position using 1-3 complete sentences. Experimental Question #2: How does the number of coils affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the number of coils. Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet. Experimental Question #3: How does the amount of current affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the Current. (Recall that voltage is directly proportional to current….Ohm’s Law.) Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet.

PHET ElectroMagnetism Key to this Document Instructions are in black. Experimental questions that you need to solve through experimentation with an online animation are in green highlighted. Important instructions are in red highlighted. Items that need a response from you are in yellow highlighted. Please put your answers to this activity in RED. Part I- Comparing Permanent Magnets and Electromagnets: 1. Select the simulation “Magnets and Electromagnets.” It is at this link: http://phet.colorado.edu/new/simulations/sims.php?sim=Magnets_and_Electromagnets 2. Move the compass slowly along a semicircular path above the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 3. Move the compass along a semicircular path below the bar magnet until you’ve put it on the opposite side of the bar magnet. Describe what happens to the compass needle. 4. What do you suppose the compass needles drawn all over the screen tell you? 5. Use page 10 in your book to look up what it looks like when scientists use a drawing to represent a magnetic field. Describe the field around a bar magnet here. 6. Put the compass to the left or right of the magnet. Click “flip polarity” and notice what happens to the compass. Using the compass needle as your observation tool, describe the effect that flipping the poles of the magnet has on the magnetic field. 7. Click on the electromagnet tab along the top of the simulation window. Place the compass on the left side of the coil so that the compass center lies along the axis of the coil. <--like this 8. Move the compass along a semicircular path above the coil until you’ve put it on the opposite side of the coil. Then do the same below the coil. Notice what happens to the compass needle. Compare this answer to the answer you got to Number 2 and 3. 9. Compare the shape of the magnetic field of a bar magnet to the magnetic field of an electromagnet. 10. Use the voltage slider to change the direction of the current and investigate the shape of the magnetic field the coil using the compass after you’ve let the compass stabilize. Summarize, the effect that the direction of current has on the shape of the magnetic field around an electrified coil of wires. 11. What happens to the current in the coil when you set the voltage of the battery to zero? 12. What happens to the magnetic field around the coil when you set the voltage of the battery to zero? Part II – Investigating relationships- No Answers are written on this document after this point. All three data tables, graphs and conclusion statements go on the Google Spreadsheet that you can download from Ms. Pogge’s website. Experimental Question #1: How does distance affect the strength of the magnetic field around an electromagnet? 1. Using the Electromagnet simulation, click on “Show Field Meter.” 2. Set the battery voltage to 10V where the positive is on the right of the battery (slide the switch all the way to the right). 3. Magnetic field strength (symbol B on the top line of the meter) is measured in gauss (G). You’ll only need to record the value on the top line of the Field Meter. 4. Position zero will be right on top of the coil. Negative number positions will be to the left and positive number positions to the right of the coil. 5. Move the field meter one compass needle to the right and record the value of B at position 1. 6. This data table below will be used to help you fill in the first spreadsheet you downloaded from Ms. Pogge’s website. You will end up with 3 data tables, 3 graphs and 3 conclusion statements in your document, one for each mini-experiment you are doing. a. NOTE: Be sure to take all of your values along the horizontal axis of the coil. You’ll know you’re on the axis because the B-y measurement of the magnetic field is zero along the axis. Compass position (no units) Magnetic Field Strength ( )<--Fill in units! -5 (5 needles to the left of coil) Don’t fill in the table here...do it on the Google Spreadsheet you downloaded -4 -3 -2 -1 0 (middle of coil) 1 2 3 4 5 (5 needles to right of coil) 7. In your Google Spreadsheet: Graph the compass position on the horizontal (x) axis and magnetic field magnitude on the vertical (y) axis. 8. Make sure to label the axes and title the graph. Share this spreadsheet with your teacher. 9. Analyze your graph to discover how the two variables are related, and report the relationship between magnetic field strength and position using 1-3 complete sentences. Experimental Question #2: How does the number of coils affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the number of coils. Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet. Experimental Question #3: How does the amount of current affect the strength of the magnetic field around an electromagnet? Design an experiment to test how field strength varies with the Current. (Recall that voltage is directly proportional to current….Ohm’s Law.) Enter your data, graph your results and write your conclusion statement on the Google Spreadsheet.

Two wires each carry a current I=I=5 Amp to the left. The charge q is positive , has velocity v to the left , is directly between the two wires. 1) the net force on q zero, 2) If I is incresed to 10 amp, net force on q is down , 3) If wire 2 is moved higher up on the page, the net force on q is down. 4) If the current wire 1is reversed so that now I is to the right the net force on q is down , 5) If I and I are both incresed to 10 amp, the net force on q is zero.

Two wires each carry a current I=I=5 Amp to the left. The charge q is positive , has velocity v to the left , is directly between the two wires. 1) the net force on q zero, 2) If I is incresed to 10 amp, net force on q is down , 3) If wire 2 is moved higher up on the page, the net force on q is down. 4) If the current wire 1is reversed so that now I is to the right the net force on q is down , 5) If I and I are both incresed to 10 amp, the net force on q is zero.

8. Describe the general purposes of giving a presentation that were discussed in class. What determines which approach to use? 9. What things should you look for when assessing the facility in terms of the environment to the actual presentation? 10. You have been called upon to present “Working well with others” to 4 different audiences. Identify the changes you would need to make to prepare it for each of these groups: 1) a group of managers, 2) a group of technicians 3) a group of community members, and 4) a group of high school students. 11. Analyze your strengths and weaknesses as a presenter. Describe for me those things you feel comfortable with and those things that you feel you need to improve upon.

8. Describe the general purposes of giving a presentation that were discussed in class. What determines which approach to use? 9. What things should you look for when assessing the facility in terms of the environment to the actual presentation? 10. You have been called upon to present “Working well with others” to 4 different audiences. Identify the changes you would need to make to prepare it for each of these groups: 1) a group of managers, 2) a group of technicians 3) a group of community members, and 4) a group of high school students. 11. Analyze your strengths and weaknesses as a presenter. Describe for me those things you feel comfortable with and those things that you feel you need to improve upon.

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