EXPERIMENT 6 FET CHARACTERISTIC CURVES ________________________________________ Bring a diskette to save your data. ________________________________________ OBJECT: The objective of this lab is to investigate the DC characteristics and operation of a field effect transistor (FET). The FET recommended to be used in this lab is 2N5486 n-channel FET. • Gathering data for the DC characteristics ________________________________________ APPARATUS: Dual DC Power Supply, Voltmeter, and 1k resistors, 2N5486 N-Channel FET. ________________________________________ THEORY: A JFET (Junction Field Effect Transistor) is a three terminal device (drain, source, and gate) similar to the BJT. The difference between them is that the JFET is a voltage controlled constant current device, whereas BJT is a current controlled current source device. Whereas for BJT the relationship between an output parameter, iC, and an input parameter, iB, is given by a constant , the relationship in JFET between an output parameter, iD, and an input parameter, vGS, is more complex. PROCEDURE: Measuring ID versus VDS (Output Characteristics) 1. Build the circuit shown below. 2. Obtain the output characteristics i.e. ID versus VDS. a. Set VGS = 0. Vary the voltage across drain (VDS) from 0 to 8 V with steps of 1 V and measure the corresponding drain current (ID). b. Repeat the procedure for different values of VGS. (0V, -0.5V, -1V, -1.5V, -2V, -2.5V, -3.0V, -3.5V, -4.0V). 3. Record the values in Table 1 and plot the graph ID vs. VGS. VGS 0 -0.5 -1.0 -1.5` -2.0 -2.5 -3.0 -3.5 -4.0 VDS ID ID ID ID ID ID ID ID ID 0 0 0.002mA 0.002mA 0.002mA 0.002mA 0.002mA 0.002mA 0.002mA 0mA 1 0 0.7 mA 0.7 mA 0.66 mA 0.6 mA 0.6 mA 0.5 0.1mA 0mA 2 0 1.5 mA 1.3 mA 1.3mA 1.2 mA 1.1 mA 0.7 0.1mA 0mA 3 0 2.1 mA 2.6 mA 1.9 mA 1.8 mA 1.5 mA 0.8 mA 0.1mA 0mA 4 0 2.7 mA 2.6 mA 2.5 mA 2.4 mA 1.7 mA 0.8 mA 0.1mA 0mA 5 0 3.4 mA 3.3 mA 3.1 mA 2.8 mA 1.8 mA 0.9 mA 0.1mA 0mA 6 0 4.1 mA 3.4 mA 3.7 mA 3.2 mA 1.9 mA 0.9 mA 0.1mA 0mA 7 0 4.7 mA 4.5 mA 4.2 mA 3.4 mA 1.9 mA 0.9 mA 0.1mA 0mA 8 0 5.3 mA 5.1 mA 6.6 mA 3.5 mA 2.0 mA 0.9 mA 0.1mA 0mA Table 1. vds=0:8; id=[0 6.2e-3 9.7e-3 11.3e-3 11.9e-3 12.2e-3 12.3e-3 12.3e-3 12.32e-3]; plot(vds,id);grid on;hold on id2=[0 5.23e-3 8.05e-3 9.15e-3 9.57e-3 9.77e-3 9.88e-3 9.9e-3 9.92e-3]; plot(vds,id2);grid on;hold on id3=[0 4.29e-3 6.41e-3 7.17e-3 7.46e-3 7.60e-3 7.67e-3 7.73e-3 7.76e-3]; plot(vds,id3);grid on;hold on ________________________________________ Measuring ID versus VGS (Transconductance Characteristics) 1. For the same circuit, obtain the transconductance characteristics. i.e. ID versus VGS. a. Set a particular value of voltage for VDS, i.e. 5V. Start with a gate voltage VGS of 0 V, and measure the corresponding drain current (ID). b. Then decrease VGS in steps of 0.5 V until VGS is -4V. c. At each step record the drain current. VDS = 5 V VGS ID 0 3.42 mA -0.5 3.36 mA -1.00 3.27 mA -1.50 3.12 mA -2.00 2.79 mA -2.50 1.84 mA -3.00 0.71 mA -3.50 0.11 mA -4.00 0 mA Table 2. 2. Plot the graph with ID versus VGS using Excel, MATLAB, or some other program. Discussion Questions—Make sure you answer the following questions in your discussion. Use all of the data obtained to answer the following questions: 1. Discuss the output and transconductance curves obtained in lab? Are they what you expected? 2. Are the output characteristics spaced evenly? Should they be? 3. What are the applications of a JFET?

EXPERIMENT 6 FET CHARACTERISTIC CURVES ________________________________________ Bring a diskette to save your data. ________________________________________ OBJECT: The objective of this lab is to investigate the DC characteristics and operation of a field effect transistor (FET). The FET recommended to be used in this lab is 2N5486 n-channel FET. • Gathering data for the DC characteristics ________________________________________ APPARATUS: Dual DC Power Supply, Voltmeter, and 1k resistors, 2N5486 N-Channel FET. ________________________________________ THEORY: A JFET (Junction Field Effect Transistor) is a three terminal device (drain, source, and gate) similar to the BJT. The difference between them is that the JFET is a voltage controlled constant current device, whereas BJT is a current controlled current source device. Whereas for BJT the relationship between an output parameter, iC, and an input parameter, iB, is given by a constant , the relationship in JFET between an output parameter, iD, and an input parameter, vGS, is more complex. PROCEDURE: Measuring ID versus VDS (Output Characteristics) 1. Build the circuit shown below. 2. Obtain the output characteristics i.e. ID versus VDS. a. Set VGS = 0. Vary the voltage across drain (VDS) from 0 to 8 V with steps of 1 V and measure the corresponding drain current (ID). b. Repeat the procedure for different values of VGS. (0V, -0.5V, -1V, -1.5V, -2V, -2.5V, -3.0V, -3.5V, -4.0V). 3. Record the values in Table 1 and plot the graph ID vs. VGS. VGS 0 -0.5 -1.0 -1.5` -2.0 -2.5 -3.0 -3.5 -4.0 VDS ID ID ID ID ID ID ID ID ID 0 0 0.002mA 0.002mA 0.002mA 0.002mA 0.002mA 0.002mA 0.002mA 0mA 1 0 0.7 mA 0.7 mA 0.66 mA 0.6 mA 0.6 mA 0.5 0.1mA 0mA 2 0 1.5 mA 1.3 mA 1.3mA 1.2 mA 1.1 mA 0.7 0.1mA 0mA 3 0 2.1 mA 2.6 mA 1.9 mA 1.8 mA 1.5 mA 0.8 mA 0.1mA 0mA 4 0 2.7 mA 2.6 mA 2.5 mA 2.4 mA 1.7 mA 0.8 mA 0.1mA 0mA 5 0 3.4 mA 3.3 mA 3.1 mA 2.8 mA 1.8 mA 0.9 mA 0.1mA 0mA 6 0 4.1 mA 3.4 mA 3.7 mA 3.2 mA 1.9 mA 0.9 mA 0.1mA 0mA 7 0 4.7 mA 4.5 mA 4.2 mA 3.4 mA 1.9 mA 0.9 mA 0.1mA 0mA 8 0 5.3 mA 5.1 mA 6.6 mA 3.5 mA 2.0 mA 0.9 mA 0.1mA 0mA Table 1. vds=0:8; id=[0 6.2e-3 9.7e-3 11.3e-3 11.9e-3 12.2e-3 12.3e-3 12.3e-3 12.32e-3]; plot(vds,id);grid on;hold on id2=[0 5.23e-3 8.05e-3 9.15e-3 9.57e-3 9.77e-3 9.88e-3 9.9e-3 9.92e-3]; plot(vds,id2);grid on;hold on id3=[0 4.29e-3 6.41e-3 7.17e-3 7.46e-3 7.60e-3 7.67e-3 7.73e-3 7.76e-3]; plot(vds,id3);grid on;hold on ________________________________________ Measuring ID versus VGS (Transconductance Characteristics) 1. For the same circuit, obtain the transconductance characteristics. i.e. ID versus VGS. a. Set a particular value of voltage for VDS, i.e. 5V. Start with a gate voltage VGS of 0 V, and measure the corresponding drain current (ID). b. Then decrease VGS in steps of 0.5 V until VGS is -4V. c. At each step record the drain current. VDS = 5 V VGS ID 0 3.42 mA -0.5 3.36 mA -1.00 3.27 mA -1.50 3.12 mA -2.00 2.79 mA -2.50 1.84 mA -3.00 0.71 mA -3.50 0.11 mA -4.00 0 mA Table 2. 2. Plot the graph with ID versus VGS using Excel, MATLAB, or some other program. Discussion Questions—Make sure you answer the following questions in your discussion. Use all of the data obtained to answer the following questions: 1. Discuss the output and transconductance curves obtained in lab? Are they what you expected? 2. Are the output characteristics spaced evenly? Should they be? 3. What are the applications of a JFET?

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Task 4 – Learning Outcome 2.1 Apply dimensional analysis to energy and mass transfer relationships a. The Reynolds number (Re) is a function of density, viscosity, and velocity of a fluid and a characteristic length (diameter of the pipe). Establish that Re = C (Vdr/m )-d by dimensional analysis and suggest appropriate methods to obtain constants C and d.

Task 4 – Learning Outcome 2.1 Apply dimensional analysis to energy and mass transfer relationships a. The Reynolds number (Re) is a function of density, viscosity, and velocity of a fluid and a characteristic length (diameter of the pipe). Establish that Re = C (Vdr/m )-d by dimensional analysis and suggest appropriate methods to obtain constants C and d.

The third task : Tutorial Topic 5 – IT and Information Systems Search business magazines and other sources of information for recent articles that discuss the use of information technology in delivering significant business benefits to an organisation. Use other sources to find additional information about the organisation. For the tutorial, prepare a brief report on your findings, and identify the application area(s) in the organisation that IT has supported. HOW TO DO THIS: 1. Identify an organisation big enough to have material published about it. 2. Write short introduction/description of the organisation 3. Identify business magazines that publish articles about IT 4. Other sources of information could be the organisations website 5. Or the company that is selling the information technology 6. Brief report – what is a report? what is the writing style of a report? Examples of information sourses: 1. http://www.infoworld.com/about 2. http://www.emeraldinsight.com/learning/management_thinking/articles/?subject=ebusiness 3. http://www.computerworlduk.com/it-business/ 4. http://www.businessweek.com/reports 5. http://www.informationweek.com/ 6. http://www.webroot.com/us/en/business/resources/articles/ or search for Business IT articles

The third task : Tutorial Topic 5 – IT and Information Systems Search business magazines and other sources of information for recent articles that discuss the use of information technology in delivering significant business benefits to an organisation. Use other sources to find additional information about the organisation. For the tutorial, prepare a brief report on your findings, and identify the application area(s) in the organisation that IT has supported. HOW TO DO THIS: 1. Identify an organisation big enough to have material published about it. 2. Write short introduction/description of the organisation 3. Identify business magazines that publish articles about IT 4. Other sources of information could be the organisations website 5. Or the company that is selling the information technology 6. Brief report – what is a report? what is the writing style of a report? Examples of information sourses: 1. http://www.infoworld.com/about 2. http://www.emeraldinsight.com/learning/management_thinking/articles/?subject=ebusiness 3. http://www.computerworlduk.com/it-business/ 4. http://www.businessweek.com/reports 5. http://www.informationweek.com/ 6. http://www.webroot.com/us/en/business/resources/articles/ or search for Business IT articles

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9. Identify and discuss the trade-offs associated with operating a supply chain that handles both forward and reverse movements as compared with separate supply chains for these movements.

9. Identify and discuss the trade-offs associated with operating a supply chain that handles both forward and reverse movements as compared with separate supply chains for these movements.

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Watch the video below, and then answer the questions below. http://www.youtube.com/watch?v=tZbDMUaqwE8 What does J.D. Bowen say is the problem with realism? A. Realism places too much emphasis on security, and thus its answers are all about conflict. B. Realism is too deterministic, ignoring the unpredictable human element in international relations. C. Realism discounts the possibility of progress and positive change. D. Realism can’t explain why a small country would fight a larger, more powerful one. E. Realism is like liberalism without a moral compass. Which of the following is NOT a characteristic of liberal thought? A. There are important issues in international relations beyond security and conflict. B. International actors have opportunities for cooperation. C. There is no real conflict of interests in international politics. D. Businesses and other non-state organizations have power. E. Interdependence is a facet of the international system. According to liberal theory, which of the following would be a potential actor in the international political system? A. states B. businesses C. aid groups D. churches E. all of these options Bowen claims that the United Nations is based on a “clearly liberal logic.” What is that logic? A. preventing conflict through the efforts of non-state actors B. preventing conflict through collective security C. preventing conflict through nuclear deterrence D. promoting freedom and democracy E. holding Germany accountable for its aggression in World War II Which of the following would most likely be a research topic for liberal theorists? A. how cultures develop identities B. how states can measure their military power by counting equipment and personnel C. how the United Nations can be more effective at preventing war D. why security is a masculine concept E. all of these options ———————————————————————————————————————

Watch the video below, and then answer the questions below. http://www.youtube.com/watch?v=tZbDMUaqwE8 What does J.D. Bowen say is the problem with realism? A. Realism places too much emphasis on security, and thus its answers are all about conflict. B. Realism is too deterministic, ignoring the unpredictable human element in international relations. C. Realism discounts the possibility of progress and positive change. D. Realism can’t explain why a small country would fight a larger, more powerful one. E. Realism is like liberalism without a moral compass. Which of the following is NOT a characteristic of liberal thought? A. There are important issues in international relations beyond security and conflict. B. International actors have opportunities for cooperation. C. There is no real conflict of interests in international politics. D. Businesses and other non-state organizations have power. E. Interdependence is a facet of the international system. According to liberal theory, which of the following would be a potential actor in the international political system? A. states B. businesses C. aid groups D. churches E. all of these options Bowen claims that the United Nations is based on a “clearly liberal logic.” What is that logic? A. preventing conflict through the efforts of non-state actors B. preventing conflict through collective security C. preventing conflict through nuclear deterrence D. promoting freedom and democracy E. holding Germany accountable for its aggression in World War II Which of the following would most likely be a research topic for liberal theorists? A. how cultures develop identities B. how states can measure their military power by counting equipment and personnel C. how the United Nations can be more effective at preventing war D. why security is a masculine concept E. all of these options ———————————————————————————————————————

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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.

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Chapter 6 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy PSS 6.1 Equilibrium Problems Learning Goal: To practice Problem-Solving Strategy 6.1 for equilibrium problems. A pair of students are lifting a heavy trunk on move-in day. Using two ropes tied to a small ring at the center of the top of the trunk, they pull the trunk straight up at a constant velocity . Each rope makes an angle with respect to the vertical. The gravitational force acting on the trunk has magnitude . Find the tension in each rope. PROBLEM-SOLVING STRATEGY 6.1 Equilibrium problems MODEL: Make simplifying assumptions. VISUALIZE: Establish a coordinate system, define symbols, and identify what the problem is asking you to find. This is the process of translating words into symbols. Identify all forces acting on the object, and show them on a free-body diagram. These elements form the pictorial representation of the problem. SOLVE: The mathematical representation is based on Newton’s first law: . The vector sum of the forces is found directly from the free-body diagram. v  FG T F  = = net i F  i 0 ASSESS: Check if your result has the correct units, is reasonable, and answers the question. Model The trunk is moving at a constant velocity. This means that you can model it as a particle in dynamic equilibrium and apply the strategy above. Furthermore, you can ignore the masses of the ropes and the ring because it is reasonable to assume that their combined weight is much less than the weight of the trunk. Visualize Part A The most convenient coordinate system for this problem is one in which the y axis is vertical and the ropes both lie in the xy plane, as shown below. Identify the forces acting on the trunk, and then draw a free-body diagram of the trunk in the diagram below. The black dot represents the trunk as it is lifted by the students. Draw the vectors starting at the black dot. The location and orientation of the vectors will be graded. The length of the vectors will not be graded. ANSWER: Part B This question will be shown after you complete previous question(s). Solve Part C This question will be shown after you complete previous question(s). Assess Part D This question will be shown after you complete previous question(s). A Gymnast on a Rope A gymnast of mass 70.0 hangs from a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume that the rope does not stretch. Use the value for the acceleration of gravity. Part A Calculate the tension in the rope if the gymnast hangs motionless on the rope. Express your answer in newtons. You did not open hints for this part. ANSWER: Part B Calculate the tension in the rope if the gymnast climbs the rope at a constant rate. Express your answer in newtons. You did not open hints for this part. kg 9.81m/s2 T T = N T ANSWER: Part C Calculate the tension in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.10 . Express your answer in newtons. You did not open hints for this part. ANSWER: Part D Calculate the tension in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.10 . Express your answer in newtons. You did not open hints for this part. ANSWER: T = N T m/s2 T = N T m/s2 T = N Applying Newton’s 2nd Law Learning Goal: To learn a systematic approach to solving Newton’s 2nd law problems using a simple example. Once you have decided to solve a problem using Newton’s 2nd law, there are steps that will lead you to a solution. One such prescription is the following: Visualize the problem and identify special cases. Isolate each body and draw the forces acting on it. Choose a coordinate system for each body. Apply Newton’s 2nd law to each body. Write equations for the constraints and other given information. Solve the resulting equations symbolically. Check that your answer has the correct dimensions and satisfies special cases. If numbers are given in the problem, plug them in and check that the answer makes sense. Think about generalizations or simplfications of the problem. As an example, we will apply this procedure to find the acceleration of a block of mass that is pulled up a frictionless plane inclined at angle with respect to the horizontal by a perfect string that passes over a perfect pulley to a block of mass that is hanging vertically. Visualize the problem and identify special cases First examine the problem by drawing a picture and visualizing the motion. Apply Newton’s 2nd law, , to each body in your mind. Don’t worry about which quantities are given. Think about the forces on each body: How are these consistent with the direction of the acceleration for that body? Can you think of any special cases that you can solve quickly now and use to test your understanding later? m2  m1 F = ma One special case in this problem is if , in which case block 1 would simply fall freely under the acceleration of gravity: . Part A Consider another special case in which the inclined plane is vertical ( ). In this case, for what value of would the acceleration of the two blocks be equal to zero? Express your answer in terms of some or all of the variables and . ANSWER: Isolate each body and draw the forces acting on it A force diagram should include only real forces that act on the body and satisfy Newton’s 3rd law. One way to check if the forces are real is to detrmine whether they are part of a Newton’s 3rd law pair, that is, whether they result from a physical interaction that also causes an opposite force on some other body, which may not be part of the problem. Do not decompose the forces into components, and do not include resultant forces that are combinations of other real forces like centripetal force or fictitious forces like the “centrifugal” force. Assign each force a symbol, but don’t start to solve the problem at this point. Part B Which of the four drawings is a correct force diagram for this problem? = 0 m2 = −g a 1 j ^  = /2 m1 m2 g m1 = ANSWER: Choose a coordinate system for each body Newton’s 2nd law, , is a vector equation. To add or subtract vectors it is often easiest to decompose each vector into components. Whereas a particular set of vector components is only valid in a particular coordinate system, the vector equality holds in any coordinate system, giving you freedom to pick a coordinate system that most simplifies the equations that result from the component equations. It’s generally best to pick a coordinate system where the acceleration of the system lies directly on one of the coordinate axes. If there is no acceleration, then pick a coordinate system with as many unknowns as possible along the coordinate axes. Vectors that lie along the axes appear in only one of the equations for each component, rather than in two equations with trigonometric prefactors. Note that it is sometimes advantageous to use different coordinate systems for each body in the problem. In this problem, you should use Cartesian coordinates and your axes should be stationary with respect to the inclined plane. Part C Given the criteria just described, what orientation of the coordinate axes would be best to use in this problem? In the answer options, “tilted” means with the x axis oriented parallel to the plane (i.e., at angle to the horizontal), and “level” means with the x axis horizontal. ANSWER: Apply Newton’s 2nd law to each body a b c d F  = ma  tilted for both block 1 and block 2 tilted for block 1 and level for block 2 level for block 1 and tilted for block 2 level for both block 1 and block 2 Part D What is , the sum of the x components of the forces acting on block 2? Take forces acting up the incline to be positive. Express your answer in terms of some or all of the variables tension , , the magnitude of the acceleration of gravity , and . You did not open hints for this part. ANSWER: Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Lifting a Bucket A 6- bucket of water is being pulled straight up by a string at a constant speed. F2x T m2 g  m2a2x =F2x = kg Part A What is the tension in the rope? ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Friction Force on a Dancer on a Drawbridge A dancer is standing on one leg on a drawbridge that is about to open. The coefficients of static and kinetic friction between the drawbridge and the dancer’s foot are and , respectively. represents the normal force exerted on the dancer by the bridge, and represents the gravitational force exerted on the dancer, as shown in the drawing . For all the questions, we can assume that the bridge is a perfectly flat surface and lacks the curvature characteristic of most bridges. about 42 about 60 about 78 0 because the bucket has no acceleration. N N N N μs μk n F  g Part A Before the drawbridge starts to open, it is perfectly level with the ground. The dancer is standing still on one leg. What is the x component of the friction force, ? Express your answer in terms of some or all of the variables , , and/or . You did not open hints for this part. ANSWER: Part B The drawbridge then starts to rise and the dancer continues to stand on one leg. The drawbridge stops just at the point where the dancer is on the verge of slipping. What is the magnitude of the frictional force now? Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer. F  f n μs μk Ff = Ff n μs μk  You did not open hints for this part. ANSWER: Part C Then, because the bridge is old and poorly designed, it falls a little bit and then jerks. This causes the person to start to slide down the bridge at a constant speed. What is the magnitude of the frictional force now? Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer. ANSWER: Part D The bridge starts to come back down again. The dancer stops sliding. However, again because of the age and design of the bridge it never makes it all the way down; rather it stops half a meter short. This half a meter corresponds to an angle degree (see the diagram, which has the angle exaggerated). What is the force of friction now? Express your answer in terms of some or all of the variables , , and . Ff = Ff n μs μk  Ff =   1 Ff  n Fg You did not open hints for this part. ANSWER: Kinetic Friction Ranking Task Below are eight crates of different mass. The crates are attached to massless ropes, as indicated in the picture, where the ropes are marked by letters. Each crate is being pulled to the right at the same constant speed. The coefficient of kinetic friction between each crate and the surface on which it slides is the same for all eight crates. Ff = Part A Rank the ropes on the basis of the force each exerts on the crate immediately to its left. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: Pushing a Block Learning Goal: To understand kinetic and static friction. A block of mass lies on a horizontal table. The coefficient of static friction between the block and the table is . The coefficient of kinetic friction is , with . Part A m μs μk μk < μs If the block is at rest (and the only forces acting on the block are the force due to gravity and the normal force from the table), what is the magnitude of the force due to friction? You did not open hints for this part. ANSWER: Part B Suppose you want to move the block, but you want to push it with the least force possible to get it moving. With what force must you be pushing the block just before the block begins to move? Express the magnitude of in terms of some or all the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. ANSWER: Part C Suppose you push horizontally with half the force needed to just make the block move. What is the magnitude of the friction force? Express your answer in terms of some or all of the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. Ffriction = F F μs μk m g F = μs μk m g ANSWER: Part D Suppose you push horizontally with precisely enough force to make the block start to move, and you continue to apply the same amount of force even after it starts moving. Find the acceleration of the block after it begins to move. Express your answer in terms of some or all of the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. Ffriction = a μs μk m g a =

Chapter 6 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, March 14, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy PSS 6.1 Equilibrium Problems Learning Goal: To practice Problem-Solving Strategy 6.1 for equilibrium problems. A pair of students are lifting a heavy trunk on move-in day. Using two ropes tied to a small ring at the center of the top of the trunk, they pull the trunk straight up at a constant velocity . Each rope makes an angle with respect to the vertical. The gravitational force acting on the trunk has magnitude . Find the tension in each rope. PROBLEM-SOLVING STRATEGY 6.1 Equilibrium problems MODEL: Make simplifying assumptions. VISUALIZE: Establish a coordinate system, define symbols, and identify what the problem is asking you to find. This is the process of translating words into symbols. Identify all forces acting on the object, and show them on a free-body diagram. These elements form the pictorial representation of the problem. SOLVE: The mathematical representation is based on Newton’s first law: . The vector sum of the forces is found directly from the free-body diagram. v  FG T F  = = net i F  i 0 ASSESS: Check if your result has the correct units, is reasonable, and answers the question. Model The trunk is moving at a constant velocity. This means that you can model it as a particle in dynamic equilibrium and apply the strategy above. Furthermore, you can ignore the masses of the ropes and the ring because it is reasonable to assume that their combined weight is much less than the weight of the trunk. Visualize Part A The most convenient coordinate system for this problem is one in which the y axis is vertical and the ropes both lie in the xy plane, as shown below. Identify the forces acting on the trunk, and then draw a free-body diagram of the trunk in the diagram below. The black dot represents the trunk as it is lifted by the students. Draw the vectors starting at the black dot. The location and orientation of the vectors will be graded. The length of the vectors will not be graded. ANSWER: Part B This question will be shown after you complete previous question(s). Solve Part C This question will be shown after you complete previous question(s). Assess Part D This question will be shown after you complete previous question(s). A Gymnast on a Rope A gymnast of mass 70.0 hangs from a vertical rope attached to the ceiling. You can ignore the weight of the rope and assume that the rope does not stretch. Use the value for the acceleration of gravity. Part A Calculate the tension in the rope if the gymnast hangs motionless on the rope. Express your answer in newtons. You did not open hints for this part. ANSWER: Part B Calculate the tension in the rope if the gymnast climbs the rope at a constant rate. Express your answer in newtons. You did not open hints for this part. kg 9.81m/s2 T T = N T ANSWER: Part C Calculate the tension in the rope if the gymnast climbs up the rope with an upward acceleration of magnitude 1.10 . Express your answer in newtons. You did not open hints for this part. ANSWER: Part D Calculate the tension in the rope if the gymnast slides down the rope with a downward acceleration of magnitude 1.10 . Express your answer in newtons. You did not open hints for this part. ANSWER: T = N T m/s2 T = N T m/s2 T = N Applying Newton’s 2nd Law Learning Goal: To learn a systematic approach to solving Newton’s 2nd law problems using a simple example. Once you have decided to solve a problem using Newton’s 2nd law, there are steps that will lead you to a solution. One such prescription is the following: Visualize the problem and identify special cases. Isolate each body and draw the forces acting on it. Choose a coordinate system for each body. Apply Newton’s 2nd law to each body. Write equations for the constraints and other given information. Solve the resulting equations symbolically. Check that your answer has the correct dimensions and satisfies special cases. If numbers are given in the problem, plug them in and check that the answer makes sense. Think about generalizations or simplfications of the problem. As an example, we will apply this procedure to find the acceleration of a block of mass that is pulled up a frictionless plane inclined at angle with respect to the horizontal by a perfect string that passes over a perfect pulley to a block of mass that is hanging vertically. Visualize the problem and identify special cases First examine the problem by drawing a picture and visualizing the motion. Apply Newton’s 2nd law, , to each body in your mind. Don’t worry about which quantities are given. Think about the forces on each body: How are these consistent with the direction of the acceleration for that body? Can you think of any special cases that you can solve quickly now and use to test your understanding later? m2  m1 F = ma One special case in this problem is if , in which case block 1 would simply fall freely under the acceleration of gravity: . Part A Consider another special case in which the inclined plane is vertical ( ). In this case, for what value of would the acceleration of the two blocks be equal to zero? Express your answer in terms of some or all of the variables and . ANSWER: Isolate each body and draw the forces acting on it A force diagram should include only real forces that act on the body and satisfy Newton’s 3rd law. One way to check if the forces are real is to detrmine whether they are part of a Newton’s 3rd law pair, that is, whether they result from a physical interaction that also causes an opposite force on some other body, which may not be part of the problem. Do not decompose the forces into components, and do not include resultant forces that are combinations of other real forces like centripetal force or fictitious forces like the “centrifugal” force. Assign each force a symbol, but don’t start to solve the problem at this point. Part B Which of the four drawings is a correct force diagram for this problem? = 0 m2 = −g a 1 j ^  = /2 m1 m2 g m1 = ANSWER: Choose a coordinate system for each body Newton’s 2nd law, , is a vector equation. To add or subtract vectors it is often easiest to decompose each vector into components. Whereas a particular set of vector components is only valid in a particular coordinate system, the vector equality holds in any coordinate system, giving you freedom to pick a coordinate system that most simplifies the equations that result from the component equations. It’s generally best to pick a coordinate system where the acceleration of the system lies directly on one of the coordinate axes. If there is no acceleration, then pick a coordinate system with as many unknowns as possible along the coordinate axes. Vectors that lie along the axes appear in only one of the equations for each component, rather than in two equations with trigonometric prefactors. Note that it is sometimes advantageous to use different coordinate systems for each body in the problem. In this problem, you should use Cartesian coordinates and your axes should be stationary with respect to the inclined plane. Part C Given the criteria just described, what orientation of the coordinate axes would be best to use in this problem? In the answer options, “tilted” means with the x axis oriented parallel to the plane (i.e., at angle to the horizontal), and “level” means with the x axis horizontal. ANSWER: Apply Newton’s 2nd law to each body a b c d F  = ma  tilted for both block 1 and block 2 tilted for block 1 and level for block 2 level for block 1 and tilted for block 2 level for both block 1 and block 2 Part D What is , the sum of the x components of the forces acting on block 2? Take forces acting up the incline to be positive. Express your answer in terms of some or all of the variables tension , , the magnitude of the acceleration of gravity , and . You did not open hints for this part. ANSWER: Part E This question will be shown after you complete previous question(s). Part F This question will be shown after you complete previous question(s). Part G This question will be shown after you complete previous question(s). Lifting a Bucket A 6- bucket of water is being pulled straight up by a string at a constant speed. F2x T m2 g  m2a2x =F2x = kg Part A What is the tension in the rope? ANSWER: Part B This question will be shown after you complete previous question(s). Part C This question will be shown after you complete previous question(s). Friction Force on a Dancer on a Drawbridge A dancer is standing on one leg on a drawbridge that is about to open. The coefficients of static and kinetic friction between the drawbridge and the dancer’s foot are and , respectively. represents the normal force exerted on the dancer by the bridge, and represents the gravitational force exerted on the dancer, as shown in the drawing . For all the questions, we can assume that the bridge is a perfectly flat surface and lacks the curvature characteristic of most bridges. about 42 about 60 about 78 0 because the bucket has no acceleration. N N N N μs μk n F  g Part A Before the drawbridge starts to open, it is perfectly level with the ground. The dancer is standing still on one leg. What is the x component of the friction force, ? Express your answer in terms of some or all of the variables , , and/or . You did not open hints for this part. ANSWER: Part B The drawbridge then starts to rise and the dancer continues to stand on one leg. The drawbridge stops just at the point where the dancer is on the verge of slipping. What is the magnitude of the frictional force now? Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer. F  f n μs μk Ff = Ff n μs μk  You did not open hints for this part. ANSWER: Part C Then, because the bridge is old and poorly designed, it falls a little bit and then jerks. This causes the person to start to slide down the bridge at a constant speed. What is the magnitude of the frictional force now? Express your answer in terms of some or all of the variables , , and/or . The angle should not appear in your answer. ANSWER: Part D The bridge starts to come back down again. The dancer stops sliding. However, again because of the age and design of the bridge it never makes it all the way down; rather it stops half a meter short. This half a meter corresponds to an angle degree (see the diagram, which has the angle exaggerated). What is the force of friction now? Express your answer in terms of some or all of the variables , , and . Ff = Ff n μs μk  Ff =   1 Ff  n Fg You did not open hints for this part. ANSWER: Kinetic Friction Ranking Task Below are eight crates of different mass. The crates are attached to massless ropes, as indicated in the picture, where the ropes are marked by letters. Each crate is being pulled to the right at the same constant speed. The coefficient of kinetic friction between each crate and the surface on which it slides is the same for all eight crates. Ff = Part A Rank the ropes on the basis of the force each exerts on the crate immediately to its left. Rank from largest to smallest. To rank items as equivalent, overlap them. You did not open hints for this part. ANSWER: Pushing a Block Learning Goal: To understand kinetic and static friction. A block of mass lies on a horizontal table. The coefficient of static friction between the block and the table is . The coefficient of kinetic friction is , with . Part A m μs μk μk < μs If the block is at rest (and the only forces acting on the block are the force due to gravity and the normal force from the table), what is the magnitude of the force due to friction? You did not open hints for this part. ANSWER: Part B Suppose you want to move the block, but you want to push it with the least force possible to get it moving. With what force must you be pushing the block just before the block begins to move? Express the magnitude of in terms of some or all the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. ANSWER: Part C Suppose you push horizontally with half the force needed to just make the block move. What is the magnitude of the friction force? Express your answer in terms of some or all of the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. Ffriction = F F μs μk m g F = μs μk m g ANSWER: Part D Suppose you push horizontally with precisely enough force to make the block start to move, and you continue to apply the same amount of force even after it starts moving. Find the acceleration of the block after it begins to move. Express your answer in terms of some or all of the variables , , and , as well as the acceleration due to gravity . You did not open hints for this part. ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. Ffriction = a μs μk m g a =

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Why did American audiences embrace the film noir, with its dark moodiness that marked a dramatic departure from the lavish spec¬tacle and optimism characteristic of Hollywood films in the 1930s? 9) In 1-2 sentences, briefly describe how an “average” director differs from an auteur director, according to François Truffaut’s 1954 essay, “A Certain Tendency in French Cinema.”

Why did American audiences embrace the film noir, with its dark moodiness that marked a dramatic departure from the lavish spec¬tacle and optimism characteristic of Hollywood films in the 1930s? 9) In 1-2 sentences, briefly describe how an “average” director differs from an auteur director, according to François Truffaut’s 1954 essay, “A Certain Tendency in French Cinema.”

He assumed that the executive was the real writer of … Read More...