Chapter 15 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, May 16, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Fluid Pressure in a U-Tube A U-tube is filled with water, and the two arms are capped. The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube. Part A A one-inch depth of sand is poured onto the cap on each arm. After the caps have moved (if necessary) to reestablish equilibrium, is the right cap higher, lower, or the same height as the left cap? You did not open hints for this part. 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). Part D This question will be shown after you complete previous question(s). Pressure in the Ocean The pressure at 10 below the surface of the ocean is about 2.00×105 . Part A higher lower the same height m Pa Which of the following statements is true? You did not open hints for this part. ANSWER: Part B Now consider the pressure 20 below the surface of the ocean. Which of the following statements is true? You did not open hints for this part. ANSWER: Relating Pressure and Height in a Container Learning Goal: To understand the derivation of the law relating height and pressure in a container. The weight of a column of seawater 1 in cross section and 10 high is about 2.00×105 . The weight of a column of seawater 1 in cross section and 10 high plus the weight of a column of air with the same cross section extending up to the top of the atmosphere is about 2.00×105 . The weight of 1 of seawater at 10 below the surface of the ocean is about 2.00×105 . The density of seawater is about 2.00×105 times the density of air at sea level. m2 m N m2 m N m3 m N m The pressure is twice that at a depth of 10 . The pressure is the same as that at a depth of 10 . The pressure is equal to that at a depth of 10 plus the weight per 1 cross sectional area of a column of seawater 10 high. The pressure is equal to the weight per 1 cross sectional area of a column of seawater 20 high. m m m m2 m m2 m In this problem, you will derive the law relating pressure to height in a container by analyzing a particular system. A container of uniform cross-sectional area is filled with liquid of uniform density . Consider a thin horizontal layer of liquid (thickness ) at a height as measured from the bottom of the container. Let the pressure exerted upward on the bottom of the layer be and the pressure exerted downward on the top be . Assume throughout the problem that the system is in equilibrium (the container has not been recently shaken or moved, etc.). Part A What is , the magnitude of the force exerted upward on the bottom of the liquid? You did not open hints for this part. ANSWER: Part B What is , the magnitude of the force exerted downward on the top of the liquid? A  dy y p p + dp Fup Fup = Fdown You did not open hints for this part. ANSWER: Part C What is the weight of the thin layer of liquid? Express your answer in terms of quantities given in the problem introduction and , the magnitude of the acceleration due to gravity. You did not open hints for this part. ANSWER: Part D Since the liquid is in equilibrium, the net force on the thin layer of liquid is zero. Complete the force equation for the sum of the vertical forces acting on the liquid layer described in the problem introduction. Express your answer in terms of quantities given in the problem introduction and taking upward forces to be positive. You did not open hints for this part. ANSWER: Fdown = wlayer g wlayer = 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). A Submerged Ball A ball of mass and volume is lowered on a string into a fluid of density . Assume that the object would sink to the bottom if it were not supported by the string. Part A  = = i Fy,i mb V f What is the tension in the string when the ball is fully submerged but not touching the bottom, as shown in the figure? Express your answer in terms of any or all of the given quantities and , the magnitude of the acceleration due to gravity. You did not open hints for this part. ANSWER: Archimedes’ Principle Learning Goal: To understand the applications of Archimedes’ principle. Archimedes’ principle is a powerful tool for solving many problems involving equilibrium in fluids. It states the following: When a body is partially or completely submerged in a fluid (either a liquid or a gas), the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body. As a result of the upward Archimedes force (often called the buoyant force), some objects may float in a fluid, and all of them appear to weigh less. This is the familiar phenomenon of buoyancy. Quantitatively, the buoyant force can be found as , where is the force, is the density of the fluid, is the magnitude of the acceleration due to gravity, and is the volume of the displaced fluid. In this problem, you will be asked several qualitative questions that should help you develop a feel for Archimedes’ principle. An object is placed in a fluid and then released. Assume that the object either floats to the surface (settling so that the object is partly above and partly below the fluid surface) or sinks to the bottom. (Note that for Parts A through D, you should assume that the object has settled in equilibrium.) Part A Consider the following statement: The magnitude of the buoyant force is equal to the weight of fluid displaced by the object. Under what circumstances is this statement true? T g T = Fbuoyant = fluidgV Fbuoyant fluid g V You did not open hints for this part. ANSWER: Part B Consider the following statement: The magnitude of the buoyant force is equal to the weight of the amount of fluid that has the same total volume as the object. Under what circumstances is this statement true? You did not open hints for this part. ANSWER: Part C Consider the following statement: The magnitude of the buoyant force equals the weight of the object. Under what circumstances is this statement true? for every object submerged partially or completely in a fluid only for an object that floats only for an object that sinks for no object submerged in a fluid for an object that is partially submerged in a fluid only for an object that floats for an object completely submerged in a fluid for no object partially or completely submerged in a fluid You did not open hints for this part. ANSWER: Part D Consider the following statement: The magnitude of the buoyant force is less than the weight of the object. Under what circumstances is this statement true? ANSWER: Now apply what you know to some more complicated situations. Part E An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a denser liquid. What would you observe? You did not open hints for this part. ANSWER: for every object submerged partially or completely in a fluid for an object that floats only for an object that sinks for no object submerged in a fluid for every object submerged partially or completely in a fluid for an object that floats for an object that sinks for no object submerged in a fluid Part F An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a less dense liquid. What would you observe? You did not open hints for this part. ANSWER: Part G Two objects, T and B, have identical size and shape and have uniform density. They are carefully placed in a container filled with a liquid. Both objects float in equilibrium. Less of object T is submerged than of object B, which floats, fully submerged, closer to the bottom of the container. Which of the following statements is true? ANSWER: The object would sink all the way to the bottom. The object would float submerged more deeply than in the first container. The object would float submerged less deeply than in the first container. More than one of these outcomes is possible. The object would sink all the way to the bottom. The object would float submerged more deeply than in the first container. The object would float submerged less deeply than in the first container. More than one of these outcomes is possible. Object T has a greater density than object B. Object B has a greater density than object T. Both objects have the same density. ± Buoyant Force Conceptual Question A rectangular wooden block of weight floats with exactly one-half of its volume below the waterline. Part A What is the buoyant force acting on the block? You did not open hints for this part. ANSWER: Part B W The buoyant force cannot be determined. 2W W 1 W 2 The density of water is 1.00 . What is the density of the block? You did not open hints for this part. ANSWER: Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). g/cm3 2.00 between 1.00 and 2.00 1.00 between 0.50 and 1.00 0.50 The density cannot be determined. g/cm3 g/cm3 g/cm3 g/cm3 g/cm3 Flow Velocity of Blood Conceptual Question Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel. Imagine a healthy artery, with blood flow velocity of and mass per unit volume of . The kinetic energy per unit volume of blood is given by Imagine that plaque has narrowed an artery to one-fifth of its normal cross-sectional area (an 80% blockage). Part A Compared to normal blood flow velocity, , what is the velocity of blood as it passes through this blockage? You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C v0 = 0.14 m/s  = 1050 kg/m3 K0 =  . 1 2 v20 v0 80v0 20v0 5v0 v0/5 This question will be shown after you complete previous question(s). For parts D – F imagine that plaque has grown to a 90% blockage. Part D This question will be shown after you complete previous question(s). 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). ± Playing with a Water Hose Two children, Ferdinand and Isabella, are playing with a water hose on a sunny summer day. Isabella is holding the hose in her hand 1.0 meters above the ground and is trying to spray Ferdinand, who is standing 10.0 meters away. Part A Will Isabella be able to spray Ferdinand if the water is flowing out of the hose at a constant speed of 3.5 meters per second? Assume that the hose is pointed parallel to the ground and take the magnitude of the acceleration due to gravity to be 9.81 meters per second, per second. You did not open hints for this part. v0 g ANSWER: Part B This question will be shown after you complete previous question(s). Tactics Box 15.2 Finding Whether an Object Floats or Sinks Learning Goal: To practice Tactics Box 15.2 Finding whether an object floats or sinks. If you hold an object underwater and then release it, it can float to the surface, sink, or remain “hanging” in the water, depending on whether the fluid density is larger than, smaller than, or equal to the object’s average density . These conditions are summarized in this Tactics Box. Yes No f avg TACTICS BOX 15.2 Finding whether an object floats or sinks Object sinks Object floats Object has neutral buoyancy An object sinks if it weighs more than the fluid it displaces, that is, if its average density is greater than the density of the fluid: . An object floats on the surface if it weighs less than the fluid it displaces, that is, if its average density is less than the density of the fluid: . An object hangs motionless in the fluid if it weighs exactly the same as the fluid it displaces. It has neutral buoyancy if its average density equals the density of the fluid: . Part A Ice at 0.0 has a density of 917 . A 3.00 ice cube is gently released inside a small container filled with oil and is observed to be neutrally buoyant. What is the density of the oil, ? Express your answer in kilograms per meter cubed to three significant figures. ANSWER: Part B Once the ice cube melts, what happens to the liquid water that it produces? You did not open hints for this part. ANSWER: avg > f avg < f avg = f 'C kg/m3 cm3 oil oil = kg/m3 Part C What happens if some ethyl alcohol of density 790 is poured into the container after the ice cube has melted? ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. The liquid water sinks to the bottom of the container. The liquid water rises to the surface and floats on top of the oil. The liquid water is in static equilibrium at the location where the ice cube was originally placed. kg/m3 A layer of ethyl alcohol forms between the oil and the water. The layer of ethyl alcohol forms at the bottom of the container. The layer of ethyl alcohol forms on the surface.

Chapter 15 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, May 16, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Fluid Pressure in a U-Tube A U-tube is filled with water, and the two arms are capped. The tube is cylindrical, and the right arm has twice the radius of the left arm. The caps have negligible mass, are watertight, and can freely slide up and down the tube. Part A A one-inch depth of sand is poured onto the cap on each arm. After the caps have moved (if necessary) to reestablish equilibrium, is the right cap higher, lower, or the same height as the left cap? You did not open hints for this part. 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). Part D This question will be shown after you complete previous question(s). Pressure in the Ocean The pressure at 10 below the surface of the ocean is about 2.00×105 . Part A higher lower the same height m Pa Which of the following statements is true? You did not open hints for this part. ANSWER: Part B Now consider the pressure 20 below the surface of the ocean. Which of the following statements is true? You did not open hints for this part. ANSWER: Relating Pressure and Height in a Container Learning Goal: To understand the derivation of the law relating height and pressure in a container. The weight of a column of seawater 1 in cross section and 10 high is about 2.00×105 . The weight of a column of seawater 1 in cross section and 10 high plus the weight of a column of air with the same cross section extending up to the top of the atmosphere is about 2.00×105 . The weight of 1 of seawater at 10 below the surface of the ocean is about 2.00×105 . The density of seawater is about 2.00×105 times the density of air at sea level. m2 m N m2 m N m3 m N m The pressure is twice that at a depth of 10 . The pressure is the same as that at a depth of 10 . The pressure is equal to that at a depth of 10 plus the weight per 1 cross sectional area of a column of seawater 10 high. The pressure is equal to the weight per 1 cross sectional area of a column of seawater 20 high. m m m m2 m m2 m In this problem, you will derive the law relating pressure to height in a container by analyzing a particular system. A container of uniform cross-sectional area is filled with liquid of uniform density . Consider a thin horizontal layer of liquid (thickness ) at a height as measured from the bottom of the container. Let the pressure exerted upward on the bottom of the layer be and the pressure exerted downward on the top be . Assume throughout the problem that the system is in equilibrium (the container has not been recently shaken or moved, etc.). Part A What is , the magnitude of the force exerted upward on the bottom of the liquid? You did not open hints for this part. ANSWER: Part B What is , the magnitude of the force exerted downward on the top of the liquid? A  dy y p p + dp Fup Fup = Fdown You did not open hints for this part. ANSWER: Part C What is the weight of the thin layer of liquid? Express your answer in terms of quantities given in the problem introduction and , the magnitude of the acceleration due to gravity. You did not open hints for this part. ANSWER: Part D Since the liquid is in equilibrium, the net force on the thin layer of liquid is zero. Complete the force equation for the sum of the vertical forces acting on the liquid layer described in the problem introduction. Express your answer in terms of quantities given in the problem introduction and taking upward forces to be positive. You did not open hints for this part. ANSWER: Fdown = wlayer g wlayer = 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). A Submerged Ball A ball of mass and volume is lowered on a string into a fluid of density . Assume that the object would sink to the bottom if it were not supported by the string. Part A  = = i Fy,i mb V f What is the tension in the string when the ball is fully submerged but not touching the bottom, as shown in the figure? Express your answer in terms of any or all of the given quantities and , the magnitude of the acceleration due to gravity. You did not open hints for this part. ANSWER: Archimedes’ Principle Learning Goal: To understand the applications of Archimedes’ principle. Archimedes’ principle is a powerful tool for solving many problems involving equilibrium in fluids. It states the following: When a body is partially or completely submerged in a fluid (either a liquid or a gas), the fluid exerts an upward force on the body equal to the weight of the fluid displaced by the body. As a result of the upward Archimedes force (often called the buoyant force), some objects may float in a fluid, and all of them appear to weigh less. This is the familiar phenomenon of buoyancy. Quantitatively, the buoyant force can be found as , where is the force, is the density of the fluid, is the magnitude of the acceleration due to gravity, and is the volume of the displaced fluid. In this problem, you will be asked several qualitative questions that should help you develop a feel for Archimedes’ principle. An object is placed in a fluid and then released. Assume that the object either floats to the surface (settling so that the object is partly above and partly below the fluid surface) or sinks to the bottom. (Note that for Parts A through D, you should assume that the object has settled in equilibrium.) Part A Consider the following statement: The magnitude of the buoyant force is equal to the weight of fluid displaced by the object. Under what circumstances is this statement true? T g T = Fbuoyant = fluidgV Fbuoyant fluid g V You did not open hints for this part. ANSWER: Part B Consider the following statement: The magnitude of the buoyant force is equal to the weight of the amount of fluid that has the same total volume as the object. Under what circumstances is this statement true? You did not open hints for this part. ANSWER: Part C Consider the following statement: The magnitude of the buoyant force equals the weight of the object. Under what circumstances is this statement true? for every object submerged partially or completely in a fluid only for an object that floats only for an object that sinks for no object submerged in a fluid for an object that is partially submerged in a fluid only for an object that floats for an object completely submerged in a fluid for no object partially or completely submerged in a fluid You did not open hints for this part. ANSWER: Part D Consider the following statement: The magnitude of the buoyant force is less than the weight of the object. Under what circumstances is this statement true? ANSWER: Now apply what you know to some more complicated situations. Part E An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a denser liquid. What would you observe? You did not open hints for this part. ANSWER: for every object submerged partially or completely in a fluid for an object that floats only for an object that sinks for no object submerged in a fluid for every object submerged partially or completely in a fluid for an object that floats for an object that sinks for no object submerged in a fluid Part F An object is floating in equilibrium on the surface of a liquid. The object is then removed and placed in another container, filled with a less dense liquid. What would you observe? You did not open hints for this part. ANSWER: Part G Two objects, T and B, have identical size and shape and have uniform density. They are carefully placed in a container filled with a liquid. Both objects float in equilibrium. Less of object T is submerged than of object B, which floats, fully submerged, closer to the bottom of the container. Which of the following statements is true? ANSWER: The object would sink all the way to the bottom. The object would float submerged more deeply than in the first container. The object would float submerged less deeply than in the first container. More than one of these outcomes is possible. The object would sink all the way to the bottom. The object would float submerged more deeply than in the first container. The object would float submerged less deeply than in the first container. More than one of these outcomes is possible. Object T has a greater density than object B. Object B has a greater density than object T. Both objects have the same density. ± Buoyant Force Conceptual Question A rectangular wooden block of weight floats with exactly one-half of its volume below the waterline. Part A What is the buoyant force acting on the block? You did not open hints for this part. ANSWER: Part B W The buoyant force cannot be determined. 2W W 1 W 2 The density of water is 1.00 . What is the density of the block? You did not open hints for this part. ANSWER: Part C This question will be shown after you complete previous question(s). Part D This question will be shown after you complete previous question(s). Part E This question will be shown after you complete previous question(s). g/cm3 2.00 between 1.00 and 2.00 1.00 between 0.50 and 1.00 0.50 The density cannot be determined. g/cm3 g/cm3 g/cm3 g/cm3 g/cm3 Flow Velocity of Blood Conceptual Question Arteriosclerotic plaques forming on the inner walls of arteries can decrease the effective cross-sectional area of an artery. Even small changes in the effective area of an artery can lead to very large changes in the blood pressure in the artery and possibly to the collapse of the blood vessel. Imagine a healthy artery, with blood flow velocity of and mass per unit volume of . The kinetic energy per unit volume of blood is given by Imagine that plaque has narrowed an artery to one-fifth of its normal cross-sectional area (an 80% blockage). Part A Compared to normal blood flow velocity, , what is the velocity of blood as it passes through this blockage? You did not open hints for this part. ANSWER: Part B This question will be shown after you complete previous question(s). Part C v0 = 0.14 m/s  = 1050 kg/m3 K0 =  . 1 2 v20 v0 80v0 20v0 5v0 v0/5 This question will be shown after you complete previous question(s). For parts D – F imagine that plaque has grown to a 90% blockage. Part D This question will be shown after you complete previous question(s). 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). ± Playing with a Water Hose Two children, Ferdinand and Isabella, are playing with a water hose on a sunny summer day. Isabella is holding the hose in her hand 1.0 meters above the ground and is trying to spray Ferdinand, who is standing 10.0 meters away. Part A Will Isabella be able to spray Ferdinand if the water is flowing out of the hose at a constant speed of 3.5 meters per second? Assume that the hose is pointed parallel to the ground and take the magnitude of the acceleration due to gravity to be 9.81 meters per second, per second. You did not open hints for this part. v0 g ANSWER: Part B This question will be shown after you complete previous question(s). Tactics Box 15.2 Finding Whether an Object Floats or Sinks Learning Goal: To practice Tactics Box 15.2 Finding whether an object floats or sinks. If you hold an object underwater and then release it, it can float to the surface, sink, or remain “hanging” in the water, depending on whether the fluid density is larger than, smaller than, or equal to the object’s average density . These conditions are summarized in this Tactics Box. Yes No f avg TACTICS BOX 15.2 Finding whether an object floats or sinks Object sinks Object floats Object has neutral buoyancy An object sinks if it weighs more than the fluid it displaces, that is, if its average density is greater than the density of the fluid: . An object floats on the surface if it weighs less than the fluid it displaces, that is, if its average density is less than the density of the fluid: . An object hangs motionless in the fluid if it weighs exactly the same as the fluid it displaces. It has neutral buoyancy if its average density equals the density of the fluid: . Part A Ice at 0.0 has a density of 917 . A 3.00 ice cube is gently released inside a small container filled with oil and is observed to be neutrally buoyant. What is the density of the oil, ? Express your answer in kilograms per meter cubed to three significant figures. ANSWER: Part B Once the ice cube melts, what happens to the liquid water that it produces? You did not open hints for this part. ANSWER: avg > f avg < f avg = f 'C kg/m3 cm3 oil oil = kg/m3 Part C What happens if some ethyl alcohol of density 790 is poured into the container after the ice cube has melted? ANSWER: Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. The liquid water sinks to the bottom of the container. The liquid water rises to the surface and floats on top of the oil. The liquid water is in static equilibrium at the location where the ice cube was originally placed. kg/m3 A layer of ethyl alcohol forms between the oil and the water. The layer of ethyl alcohol forms at the bottom of the container. The layer of ethyl alcohol forms on the surface.

please email info@checkyourstudy.com Chapter 15 Practice Problems (Practice – no … Read More...
Correspondence #2 Assignment – Favorable Response to Direct Inquiry Due Tuesday, October 1,2015 — To be provided in class that day or emailed to Facts and Instructions You assist the operations manager at a manufacturing company, and one of your jobs is to ensure that you always have enough staff to maintain your production schedule. In the last week, you’ve heard from several of your supervisors that your newer employees, as well as some of the more experienced ones, are asking about how to request vacation time during the summer. They want to know • when they can take vacation, • how soon they need to let you know, • where they can go to use the online vacation leave forms (which are new since last summer when employees had to print forms and fill them out), and • how they can check online to see how much vacation they’ve accrued (also new since last summer when they had to contact their supervisors directly). Summer is a slow time for your company except for the first two weeks in June, the last week in July, and the first week in August. No one is allowed to take vacation during these weeks. You likely do not want a significant portion of your employees gone all at once either. Creating realistic details as needed, write a response to these employees explaining the vacation request policy and process. You may wish to review an actual handbook (UALR’s?!) detailing vacation/annual leave policies.

Correspondence #2 Assignment – Favorable Response to Direct Inquiry Due Tuesday, October 1,2015 — To be provided in class that day or emailed to Facts and Instructions You assist the operations manager at a manufacturing company, and one of your jobs is to ensure that you always have enough staff to maintain your production schedule. In the last week, you’ve heard from several of your supervisors that your newer employees, as well as some of the more experienced ones, are asking about how to request vacation time during the summer. They want to know • when they can take vacation, • how soon they need to let you know, • where they can go to use the online vacation leave forms (which are new since last summer when employees had to print forms and fill them out), and • how they can check online to see how much vacation they’ve accrued (also new since last summer when they had to contact their supervisors directly). Summer is a slow time for your company except for the first two weeks in June, the last week in July, and the first week in August. No one is allowed to take vacation during these weeks. You likely do not want a significant portion of your employees gone all at once either. Creating realistic details as needed, write a response to these employees explaining the vacation request policy and process. You may wish to review an actual handbook (UALR’s?!) detailing vacation/annual leave policies.

Annotated Bibliography Annotated Bibliography. For each of the tasks which are undertaken as part of this portfolio you will normally be expected to “read round” the subject area. It isn’t really sufficient just to read the relevant chapter in the textbook; you will also find information in periodicals, magazines, quality newspapers etc etc and certainly by searching the Internet. Just as in any other assignment in UWBS you are expected to identify your sources in a bibliography using Harvard referencing. An annotated bibliography is the same as a conventional bibliography but includes comments on what you found particularly useful in each of the texts that you cite. On this page you will present your annotated bibliography. You can either write the assignment here or upload it as a word document. Some of you may be using Endnote in preparation your dissertation, and in that case you could create a new endnote library for this assignment and then upload the bibliography from that endnote library. During the briefing sessions you will be shown how to upload a file and create a link. You can also find help if you click on the large ? on the Pebble beach opening page. Once you have finished, delete the red text.

Annotated Bibliography Annotated Bibliography. For each of the tasks which are undertaken as part of this portfolio you will normally be expected to “read round” the subject area. It isn’t really sufficient just to read the relevant chapter in the textbook; you will also find information in periodicals, magazines, quality newspapers etc etc and certainly by searching the Internet. Just as in any other assignment in UWBS you are expected to identify your sources in a bibliography using Harvard referencing. An annotated bibliography is the same as a conventional bibliography but includes comments on what you found particularly useful in each of the texts that you cite. On this page you will present your annotated bibliography. You can either write the assignment here or upload it as a word document. Some of you may be using Endnote in preparation your dissertation, and in that case you could create a new endnote library for this assignment and then upload the bibliography from that endnote library. During the briefing sessions you will be shown how to upload a file and create a link. You can also find help if you click on the large ? on the Pebble beach opening page. Once you have finished, delete the red text.

Annotated Bibliography:   Mayaavi.com, (2015). Strategy, Innovation and Entrepreneurship: : … Read More...
STUDENT GRADER Total Score I am submitting my own work, and I understand penalties will be assessed if I submit work for credit that is not my own. Print Name ID Number Sign Name Date # Points Score 1 4 2 8 3 6 4 12 5 4 6 10 7 8 8 6 9 6 Weeks late Adjusted Score Estimated Work Hours 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Overall Weight Adjusted Score: Deduct 20% from score for each week late Problem 1. Sketch circuits for the following logic equations. Y <= (A and B and C) or not ((A and not B and C and not D) or not (B or D)); X <= (A xor (B and C) xor not D) or (not (B xor C) and not (C or D)) Problem 2. Sketch circuits and write VHDL assignment statements for the following equations. F = m(1, 2, 6) F = M(0, 7) Problem 3. Write logic assignment statements for the following circuit. Problem 4: Sketch circuits and write VHDL assignment statements for the truth tables below. Problem 5: Sketch POS circuits for the 2XOR and 2XNOR functions. Problem 6: Sketch the circuit described by the netlist shown, and complete the timing diagram for the stimulus shown to document the circuit’s response to the example stimulus. Use a 100ns vertical grid in your timing diagram, and show all inputs and outputs. Problem 7: Create a truth table that corresponds to the simulation shown below. Show all input and output values in the truth table, and sketch a logic circuit that could have been used to create the waveform. Problem 8. The Seattle Mariners haven’t had a stolen base in 6 months, and the manager decided it was because the other teams were reading his signals to the base runners. He came up with a new set of signals (pulling on his EAR, lifting one LEG, patting the top of his HEAD, and BOWing) to indicate when runners should attempt to steal a base. A runner should STEAL a base if and only if the manager pulls his EAR and BOWs while patting his HEAD, or if he lifts his LEG and pats his HEAD without BOWing, or anytime he pulls his EAR without lifting his LEG. Sketch a minimal circuit that could be used to indicate when a runner should steal a base. Problem 9. A room has four doors and four light switches (one by each door). Sketch a circuit that allows the four switches to control the light – each switch should be able to turn the light on if it is currently off, and off if it is currently on. Note that it will not be possible to associate a given switch position with “light on” or “light off” – simply moving any switch should modify the light’s status.

STUDENT GRADER Total Score I am submitting my own work, and I understand penalties will be assessed if I submit work for credit that is not my own. Print Name ID Number Sign Name Date # Points Score 1 4 2 8 3 6 4 12 5 4 6 10 7 8 8 6 9 6 Weeks late Adjusted Score Estimated Work Hours 1 2 3 4 5 6 7 8 9 10 1 2 3 4 5 6 7 8 9 10 Overall Weight Adjusted Score: Deduct 20% from score for each week late Problem 1. Sketch circuits for the following logic equations. Y <= (A and B and C) or not ((A and not B and C and not D) or not (B or D)); X <= (A xor (B and C) xor not D) or (not (B xor C) and not (C or D)) Problem 2. Sketch circuits and write VHDL assignment statements for the following equations. F = m(1, 2, 6) F = M(0, 7) Problem 3. Write logic assignment statements for the following circuit. Problem 4: Sketch circuits and write VHDL assignment statements for the truth tables below. Problem 5: Sketch POS circuits for the 2XOR and 2XNOR functions. Problem 6: Sketch the circuit described by the netlist shown, and complete the timing diagram for the stimulus shown to document the circuit’s response to the example stimulus. Use a 100ns vertical grid in your timing diagram, and show all inputs and outputs. Problem 7: Create a truth table that corresponds to the simulation shown below. Show all input and output values in the truth table, and sketch a logic circuit that could have been used to create the waveform. Problem 8. The Seattle Mariners haven’t had a stolen base in 6 months, and the manager decided it was because the other teams were reading his signals to the base runners. He came up with a new set of signals (pulling on his EAR, lifting one LEG, patting the top of his HEAD, and BOWing) to indicate when runners should attempt to steal a base. A runner should STEAL a base if and only if the manager pulls his EAR and BOWs while patting his HEAD, or if he lifts his LEG and pats his HEAD without BOWing, or anytime he pulls his EAR without lifting his LEG. Sketch a minimal circuit that could be used to indicate when a runner should steal a base. Problem 9. A room has four doors and four light switches (one by each door). Sketch a circuit that allows the four switches to control the light – each switch should be able to turn the light on if it is currently off, and off if it is currently on. Note that it will not be possible to associate a given switch position with “light on” or “light off” – simply moving any switch should modify the light’s status.

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Question One: There are 4 legal reasons why an agreement would lack assignment is to list each of the four legal reasons.  Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if  ___________   

    factual example: X and Y . . . . b) An agreement would lack consideration if  ___________ 

    factual example: X and Y . . . c) An agreement would lack consideration if ___________    

    factual example: X and Y . . . d) An agreement would lack consideration if ___________    

    factual example: X and Y . . .  Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion.

Question One: There are 4 legal reasons why an agreement would lack assignment is to list each of the four legal reasons.  Provide a factual example for each of the four legal reasons. The factual example can be from the textbook, an actual case that you know about or you can make it up. a) An agreement would lack consideration if  ___________   

    factual example: X and Y . . . . b) An agreement would lack consideration if  ___________ 

    factual example: X and Y . . . c) An agreement would lack consideration if ___________    

    factual example: X and Y . . . d) An agreement would lack consideration if ___________    

    factual example: X and Y . . .  Question Two: Explain Promissory Estoppel. Be sure to include the elements required to prove promissory estoppel in your discussion.

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For the second problem of this assignment we’ll try out a fun and useful statistics software package. It’s called “R,” is professional quality, and is available for free on multiple platforms at http://www.r-project.org. Install it on your computer. Note, however, that I didn’t get everything to work right on Linux, so you might want to try Windows or Mac OS/X. We’ll now do linear regression and plotting in 3D using R and R-Commander, as follows: Here’s the really fun part with a rotating 3D graph! Install R-Commander using the menu system in R. Also install the Scatterplot3D package. Make a new dataset using the first 10 rows of Table of chip wirebond pull strength on page 13 in the book. Then ask for a 3D scatter plot of the new data, and include a multiple linear regression with the pull strength as the dependent variable. Submit a screen shot of the graph. Comment on the goodness of fit.

For the second problem of this assignment we’ll try out a fun and useful statistics software package. It’s called “R,” is professional quality, and is available for free on multiple platforms at http://www.r-project.org. Install it on your computer. Note, however, that I didn’t get everything to work right on Linux, so you might want to try Windows or Mac OS/X. We’ll now do linear regression and plotting in 3D using R and R-Commander, as follows: Here’s the really fun part with a rotating 3D graph! Install R-Commander using the menu system in R. Also install the Scatterplot3D package. Make a new dataset using the first 10 rows of Table of chip wirebond pull strength on page 13 in the book. Then ask for a 3D scatter plot of the new data, and include a multiple linear regression with the pull strength as the dependent variable. Submit a screen shot of the graph. Comment on the goodness of fit.

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Assignment 9 Due: 11:59pm on Friday, April 11, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 11.2 Part A Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Part B Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Problem 11.4  A B = 5 − 6 A i ^ j ^ = −9 − 5 B i ^ j ^ A  B  = -15  A B = −5 + 9 A i ^ j ^ = 5 + 6 B i ^ j ^ A  B  = 29 Part A What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct ± All Work and No Play Learning Goal: To be able to calculate work done by a constant force directed at different angles relative to displacement If an object undergoes displacement while being acted upon by a force (or several forces), it is said that work is being done on the object. If the object is moving in a straight line and the displacement and the force are known, the work done by the force can be calculated as , where is the work done by force on the object that undergoes displacement directed at angle relative to .  A B A = 2 + 5 ı ^  ^ B = −2 − 4 ı ^  ^  = 175  A B A = −6 + 2 ı ^  ^ B = − − 3 ı ^  ^  = 90 W =  = cos  F  s  F   s  W F  s  F  Note that depending on the value of , the work done can be positive, negative, or zero. In this problem, you will practice calculating work done on an object moving in a straight line. The first series of questions is related to the accompanying figure. Part A What can be said about the sign of the work done by the force ? ANSWER: Correct When , the cosine of is zero, and therefore the work done is zero. Part B cos  F  1 It is positive. It is negative. It is zero. There is not enough information to answer the question.  = 90  What can be said about the work done by force ? ANSWER: Correct When , is positive, and so the work done is positive. Part C The work done by force is ANSWER: Correct When , is negative, and so the work done is negative. Part D The work done by force is ANSWER: F  2 It is positive. It is negative. It is zero. 0 <  < 90 cos  F  3 positive negative zero 90 <  < 180 cos  F  4 Correct Part E The work done by force is ANSWER: Correct positive negative zero F  5 positive negative zero Part F The work done by force is ANSWER: Correct Part G The work done by force is ANSWER: Correct In the next series of questions, you will use the formula to calculate the work done by various forces on an object that moves 160 meters to the right. F  6 positive negative zero F  7 positive negative zero W =  = cos  F  s  F   s  Part H Find the work done by the 18-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part I Find the work done by the 30-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part J Find the work done by the 12-newton force. Use two significant figures in your answer. Express your answer in joules. W W = 2900 J W W = 4200 J W ANSWER: Correct Part K Find the work done by the 15-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Introduction to Potential Energy Learning Goal: Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to the kinetic energy to get the total mechanical energy. The first part of this problem contains short-answer questions that review the work-energy theorem. In the second part we introduce the concept of potential energy. But for now, please answer in terms of the work-energy theorem. Work-Energy Theorem The work-energy theorem states , where is the work done by all forces that act on the object, and and are the initial and final kinetic energies, respectively. Part A The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the particle if the force has a component parallel to the motion. W = -1900 J W W = -1800 J Kf = Ki + Wall Wall Ki Kf Choose the best answer to fill in the blanks above: ANSWER: Correct It is important that the force have a component acting in the direction of motion. For example, if a ball is attached to a string and whirled in uniform circular motion, the string does apply a force to the ball, but since the string's force is always perpendicular to the motion it does no work and cannot change the kinetic energy of the ball. Part B To calculate the change in energy, you must know the force as a function of _______. The work done by the force causes the energy change. Choose the best answer to fill in the blank above: ANSWER: Correct Part C To illustrate the work-energy concept, consider the case of a stone falling from to under the influence of gravity. Using the work-energy concept, we say that work is done by the gravitational _____, resulting in an increase of the ______ energy of the stone. Choose the best answer to fill in the blanks above: distance / potential distance / kinetic vertical displacement / potential none of the above acceleration work distance potential energy xi xf ANSWER: Correct Potential Energy You should read about potential energy in your text before answering the following questions. Potential energy is a concept that builds on the work-energy theorem, enlarging the concept of energy in the most physically useful way. The key aspect that allows for potential energy is the existence of conservative forces, forces for which the work done on an object does not depend on the path of the object, only the initial and final positions of the object. The gravitational force is conservative; the frictional force is not. The change in potential energy is the negative of the work done by conservative forces. Hence considering the initial and final potential energies is equivalent to calculating the work done by the conservative forces. When potential energy is used, it replaces the work done by the associated conservative force. Then only the work due to nonconservative forces needs to be calculated. In summary, when using the concept of potential energy, only nonconservative forces contribute to the work, which now changes the total energy: , where and are the final and initial potential energies, and is the work due only to nonconservative forces. Now, we will revisit the falling stone example using the concept of potential energy. Part D Rather than ascribing the increased kinetic energy of the stone to the work of gravity, we now (when using potential energy rather than work-energy) say that the increased kinetic energy comes from the ______ of the _______ energy. Choose the best answer to fill in the blanks above: ANSWER: force / kinetic potential energy / potential force / potential potential energy / kinetic Kf + Uf = Ef = Wnc + Ei = Wnc + Ki + Ui Uf Ui Wnc Correct Part E This process happens in such a way that total mechanical energy, equal to the ______ of the kinetic and potential energies, is _______. Choose the best answer to fill in the blanks above: ANSWER: Correct Problem 11.7 Part A How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: work / potential force / kinetic change / potential sum / conserved sum / zero sum / not conserved difference / conserved F  = (− + i ^ ) N j ^ ! = r m i ^ Correct Part B How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.10 A 1.8 book is lying on a 0.80- -high table. You pick it up and place it on a bookshelf 2.27 above the floor. Part A How much work does gravity do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B W = -8.6 J F  = (− + i ^ ) N j ^ ! = r m? j ^ W = 26 J kg m m Wg = -26 J How much work does your hand do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.12 The three ropes shown in the bird's-eye view of the figure are used to drag a crate 3.3 across the floor. Part A How much work is done by each of the three forces? Express your answers using two significant figures. Enter your answers numerically separated by commas. ANSWER: WH = 26 J m W1 , W2 , W3 = 1.9,1.2,-2.1 kJ Correct Enhanced EOC: Problem 11.16 A 1.2 particle moving along the x-axis experiences the force shown in the figure. The particle's velocity is 4.6 at . You may want to review ( pages 286 - 287) . For help with math skills, you may want to review: The Definite Integral Part A What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: kg m/s x = 0m x = 2m x = 0 m x = 0 m x = 2 m x = 2 m x = 2 m Correct Part B What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Can the work be negative? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: Correct Work on a Sliding Block A block of weight sits on a frictionless inclined plane, which makes an angle with respect to the horizontal, as shown. A force of magnitude , applied parallel to the incline, pulls the block up the plane at constant speed. v = 6.2 ms x = 4m x = 0 m x = 0 m x = 4 m x = 4 m x = 4 m v = 4.6 ms w  F Part A The block moves a distance up the incline. The block does not stop after moving this distance but continues to move with constant speed. What is the total work done on the block by all forces? (Include only the work done after the block has started moving, not the work needed to start the block moving from rest.) Express your answer in terms of given quantities. Hint 1. What physical principle to use To find the total work done on the block, use the work-energy theorem: . Hint 2. Find the change in kinetic energy What is the change in the kinetic energy of the block, from the moment it starts moving until it has been pulled a distance ? Remember that the block is pulled at constant speed. Hint 1. Consider kinetic energy If the block's speed does not change, its kinetic energy cannot change. ANSWER: ANSWER: L Wtot Wtot = Kf − Ki L Kf − Ki = 0 Wtot = 0 Correct Part B What is , the work done on the block by the force of gravity as the block moves a distance up the incline? Express the work done by gravity in terms of the weight and any other quantities given in the problem introduction. Hint 1. Force diagram Hint 2. Force of gravity component What is the component of the force of gravity in the direction of the block's displacement (along the inclined plane)? Express your answer in terms of and . Hint 1. Relative direction of the force and the motion Remember that the force of gravity acts down the plane, whereas the block's displacement is directed up the plane. ANSWER: Wg L w w  ANSWER: Correct Part C What is , the work done on the block by the applied force as the block moves a distance up the incline? Express your answer in terms of and other given quantities. Hint 1. How to find the work done by a constant force Remember that the work done on an object by a particular force is the integral of the dot product of the force and the instantaneous displacement of the object, over the path followed by the object. In this case, since the force is constant and the path is a straight segment of length up the inclined plane, the dot product becomes simple multiplication. ANSWER: Correct Part D What is , the work done on the block by the normal force as the block moves a distance up the inclined plane? Express your answer in terms of given quantities. Hint 1. First step in computing the work Fg|| = −wsin() Wg = −wLsin() WF F L F L WF = FL Wnormal L The work done by the normal force is equal to the dot product of the force vector and the block's displacement vector. The normal force and the block's displacement vector are perpendicular. Therefore, what is their dot product? ANSWER: ANSWER: Correct Problem 11.20 A particle moving along the -axis has the potential energy , where is in . Part A What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. N  L = 0 Wnormal = 0 y U = 3.2y3 J y m y y = 0 m Fy = 0 N y y = 1 m ANSWER: Correct Part C What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.28 A cable with 25.0 of tension pulls straight up on a 1.08 block that is initially at rest. Part A What is the block's speed after being lifted 2.40 ? Solve this problem using work and energy. Express your answer with the appropriate units. ANSWER: Correct Fy = -9.6 N y y = 2 m Fy = -38 N N kg m vf = 8.00 ms Problem 11.29 Part A How much work does an elevator motor do to lift a 1500 elevator a height of 110 ? Express your answer with the appropriate units. ANSWER: Correct Part B How much power must the motor supply to do this in 50 at constant speed? Express your answer with the appropriate units. ANSWER: Correct Problem 11.32 How many energy is consumed by a 1.20 hair dryer used for 10.0 and a 11.0 night light left on for 16.0 ? Part A Hair dryer: Express your answer with the appropriate units. kg m Wext = 1.62×106 J s = 3.23×104 P W kW min W hr ANSWER: Correct Part B Night light: Express your answer with the appropriate units. ANSWER: Correct Problem 11.42 A 2500 elevator accelerates upward at 1.20 for 10.0 , starting from rest. Part A How much work does gravity do on the elevator? Express your answer with the appropriate units. ANSWER: Correct W = 7.20×105 J = 6.34×105 W J kg m/s2 m −2.45×105 J Part B How much work does the tension in the elevator cable do on the elevator? Express your answer with the appropriate units. ANSWER: Correct Part C Use the work-kinetic energy theorem to find the kinetic energy of the elevator as it reaches 10.0 . Express your answer with the appropriate units. ANSWER: Correct Part D What is the speed of the elevator as it reaches 10.0 ? Express your answer with the appropriate units. ANSWER: Correct 2.75×105 J m 3.00×104 J m 4.90 ms Problem 11.47 A horizontal spring with spring constant 130 is compressed 17 and used to launch a 2.4 box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Part A Use work and energy to find how far the box slides across the rough surface before stopping. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.49 Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 and the coefficient of rolling friction is 0.45. Part A Use work and energy to find the length of a ramp that will stop a 15,000 truck that enters the ramp at 30 . Express your answer to two significant figures and include the appropriate units. ANSWER: Correct N/m cm kg l = 53 cm kg m/s l = 83 m Problem 11.51 Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor. Part A Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is . Express your answer in terms of the variables , , , , and free fall acceleration . ANSWER: Part B Find an expression for the speed of the block if the table is frictionless. Express your answer in terms of the variables , , , and free fall acceleration . ANSWER: μk M m h μk g v = M m h g Problem 11.57 The spring shown in the figure is compressed 60 and used to launch a 100 physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the incline is 0.12 . Part A What is the student's speed just after losing contact with the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units. ANSWER: v = cm kg 30 v = 17 ms Correct Score Summary: Your score on this assignment is 93.6%. You received 112.37 out of a possible total of 120 points. !s = 41 m

Assignment 9 Due: 11:59pm on Friday, April 11, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Problem 11.2 Part A Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Part B Evaluate the dot product if and . Express your answer using two significant figures. ANSWER: Correct Problem 11.4  A B = 5 − 6 A i ^ j ^ = −9 − 5 B i ^ j ^ A  B  = -15  A B = −5 + 9 A i ^ j ^ = 5 + 6 B i ^ j ^ A  B  = 29 Part A What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct Part B What is the angle between vectors and if and ? Express your answer as an integer and include the appropriate units. ANSWER: Correct ± All Work and No Play Learning Goal: To be able to calculate work done by a constant force directed at different angles relative to displacement If an object undergoes displacement while being acted upon by a force (or several forces), it is said that work is being done on the object. If the object is moving in a straight line and the displacement and the force are known, the work done by the force can be calculated as , where is the work done by force on the object that undergoes displacement directed at angle relative to .  A B A = 2 + 5 ı ^  ^ B = −2 − 4 ı ^  ^  = 175  A B A = −6 + 2 ı ^  ^ B = − − 3 ı ^  ^  = 90 W =  = cos  F  s  F   s  W F  s  F  Note that depending on the value of , the work done can be positive, negative, or zero. In this problem, you will practice calculating work done on an object moving in a straight line. The first series of questions is related to the accompanying figure. Part A What can be said about the sign of the work done by the force ? ANSWER: Correct When , the cosine of is zero, and therefore the work done is zero. Part B cos  F  1 It is positive. It is negative. It is zero. There is not enough information to answer the question.  = 90  What can be said about the work done by force ? ANSWER: Correct When , is positive, and so the work done is positive. Part C The work done by force is ANSWER: Correct When , is negative, and so the work done is negative. Part D The work done by force is ANSWER: F  2 It is positive. It is negative. It is zero. 0 <  < 90 cos  F  3 positive negative zero 90 <  < 180 cos  F  4 Correct Part E The work done by force is ANSWER: Correct positive negative zero F  5 positive negative zero Part F The work done by force is ANSWER: Correct Part G The work done by force is ANSWER: Correct In the next series of questions, you will use the formula to calculate the work done by various forces on an object that moves 160 meters to the right. F  6 positive negative zero F  7 positive negative zero W =  = cos  F  s  F   s  Part H Find the work done by the 18-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part I Find the work done by the 30-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Part J Find the work done by the 12-newton force. Use two significant figures in your answer. Express your answer in joules. W W = 2900 J W W = 4200 J W ANSWER: Correct Part K Find the work done by the 15-newton force. Use two significant figures in your answer. Express your answer in joules. ANSWER: Correct Introduction to Potential Energy Learning Goal: Understand that conservative forces can be removed from the work integral by incorporating them into a new form of energy called potential energy that must be added to the kinetic energy to get the total mechanical energy. The first part of this problem contains short-answer questions that review the work-energy theorem. In the second part we introduce the concept of potential energy. But for now, please answer in terms of the work-energy theorem. Work-Energy Theorem The work-energy theorem states , where is the work done by all forces that act on the object, and and are the initial and final kinetic energies, respectively. Part A The work-energy theorem states that a force acting on a particle as it moves over a ______ changes the ______ energy of the particle if the force has a component parallel to the motion. W = -1900 J W W = -1800 J Kf = Ki + Wall Wall Ki Kf Choose the best answer to fill in the blanks above: ANSWER: Correct It is important that the force have a component acting in the direction of motion. For example, if a ball is attached to a string and whirled in uniform circular motion, the string does apply a force to the ball, but since the string's force is always perpendicular to the motion it does no work and cannot change the kinetic energy of the ball. Part B To calculate the change in energy, you must know the force as a function of _______. The work done by the force causes the energy change. Choose the best answer to fill in the blank above: ANSWER: Correct Part C To illustrate the work-energy concept, consider the case of a stone falling from to under the influence of gravity. Using the work-energy concept, we say that work is done by the gravitational _____, resulting in an increase of the ______ energy of the stone. Choose the best answer to fill in the blanks above: distance / potential distance / kinetic vertical displacement / potential none of the above acceleration work distance potential energy xi xf ANSWER: Correct Potential Energy You should read about potential energy in your text before answering the following questions. Potential energy is a concept that builds on the work-energy theorem, enlarging the concept of energy in the most physically useful way. The key aspect that allows for potential energy is the existence of conservative forces, forces for which the work done on an object does not depend on the path of the object, only the initial and final positions of the object. The gravitational force is conservative; the frictional force is not. The change in potential energy is the negative of the work done by conservative forces. Hence considering the initial and final potential energies is equivalent to calculating the work done by the conservative forces. When potential energy is used, it replaces the work done by the associated conservative force. Then only the work due to nonconservative forces needs to be calculated. In summary, when using the concept of potential energy, only nonconservative forces contribute to the work, which now changes the total energy: , where and are the final and initial potential energies, and is the work due only to nonconservative forces. Now, we will revisit the falling stone example using the concept of potential energy. Part D Rather than ascribing the increased kinetic energy of the stone to the work of gravity, we now (when using potential energy rather than work-energy) say that the increased kinetic energy comes from the ______ of the _______ energy. Choose the best answer to fill in the blanks above: ANSWER: force / kinetic potential energy / potential force / potential potential energy / kinetic Kf + Uf = Ef = Wnc + Ei = Wnc + Ki + Ui Uf Ui Wnc Correct Part E This process happens in such a way that total mechanical energy, equal to the ______ of the kinetic and potential energies, is _______. Choose the best answer to fill in the blanks above: ANSWER: Correct Problem 11.7 Part A How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: work / potential force / kinetic change / potential sum / conserved sum / zero sum / not conserved difference / conserved F  = (− + i ^ ) N j ^ ! = r m i ^ Correct Part B How much work is done by the force 2.2 6.6 on a particle that moves through displacement 3.9 Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.10 A 1.8 book is lying on a 0.80- -high table. You pick it up and place it on a bookshelf 2.27 above the floor. Part A How much work does gravity do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B W = -8.6 J F  = (− + i ^ ) N j ^ ! = r m? j ^ W = 26 J kg m m Wg = -26 J How much work does your hand do on the book? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.12 The three ropes shown in the bird's-eye view of the figure are used to drag a crate 3.3 across the floor. Part A How much work is done by each of the three forces? Express your answers using two significant figures. Enter your answers numerically separated by commas. ANSWER: WH = 26 J m W1 , W2 , W3 = 1.9,1.2,-2.1 kJ Correct Enhanced EOC: Problem 11.16 A 1.2 particle moving along the x-axis experiences the force shown in the figure. The particle's velocity is 4.6 at . You may want to review ( pages 286 - 287) . For help with math skills, you may want to review: The Definite Integral Part A What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: kg m/s x = 0m x = 2m x = 0 m x = 0 m x = 2 m x = 2 m x = 2 m Correct Part B What is its velocity at ? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem What is the work–kinetic energy theorem? What is the kinetic energy at ? How is the work done in going from to related to force shown in the graph? Can the work be negative? Using the work–kinetic energy theorem, what is the kinetic energy at ? What is the velocity at ? ANSWER: Correct Work on a Sliding Block A block of weight sits on a frictionless inclined plane, which makes an angle with respect to the horizontal, as shown. A force of magnitude , applied parallel to the incline, pulls the block up the plane at constant speed. v = 6.2 ms x = 4m x = 0 m x = 0 m x = 4 m x = 4 m x = 4 m v = 4.6 ms w  F Part A The block moves a distance up the incline. The block does not stop after moving this distance but continues to move with constant speed. What is the total work done on the block by all forces? (Include only the work done after the block has started moving, not the work needed to start the block moving from rest.) Express your answer in terms of given quantities. Hint 1. What physical principle to use To find the total work done on the block, use the work-energy theorem: . Hint 2. Find the change in kinetic energy What is the change in the kinetic energy of the block, from the moment it starts moving until it has been pulled a distance ? Remember that the block is pulled at constant speed. Hint 1. Consider kinetic energy If the block's speed does not change, its kinetic energy cannot change. ANSWER: ANSWER: L Wtot Wtot = Kf − Ki L Kf − Ki = 0 Wtot = 0 Correct Part B What is , the work done on the block by the force of gravity as the block moves a distance up the incline? Express the work done by gravity in terms of the weight and any other quantities given in the problem introduction. Hint 1. Force diagram Hint 2. Force of gravity component What is the component of the force of gravity in the direction of the block's displacement (along the inclined plane)? Express your answer in terms of and . Hint 1. Relative direction of the force and the motion Remember that the force of gravity acts down the plane, whereas the block's displacement is directed up the plane. ANSWER: Wg L w w  ANSWER: Correct Part C What is , the work done on the block by the applied force as the block moves a distance up the incline? Express your answer in terms of and other given quantities. Hint 1. How to find the work done by a constant force Remember that the work done on an object by a particular force is the integral of the dot product of the force and the instantaneous displacement of the object, over the path followed by the object. In this case, since the force is constant and the path is a straight segment of length up the inclined plane, the dot product becomes simple multiplication. ANSWER: Correct Part D What is , the work done on the block by the normal force as the block moves a distance up the inclined plane? Express your answer in terms of given quantities. Hint 1. First step in computing the work Fg|| = −wsin() Wg = −wLsin() WF F L F L WF = FL Wnormal L The work done by the normal force is equal to the dot product of the force vector and the block's displacement vector. The normal force and the block's displacement vector are perpendicular. Therefore, what is their dot product? ANSWER: ANSWER: Correct Problem 11.20 A particle moving along the -axis has the potential energy , where is in . Part A What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. N  L = 0 Wnormal = 0 y U = 3.2y3 J y m y y = 0 m Fy = 0 N y y = 1 m ANSWER: Correct Part C What is the -component of the force on the particle at ? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.28 A cable with 25.0 of tension pulls straight up on a 1.08 block that is initially at rest. Part A What is the block's speed after being lifted 2.40 ? Solve this problem using work and energy. Express your answer with the appropriate units. ANSWER: Correct Fy = -9.6 N y y = 2 m Fy = -38 N N kg m vf = 8.00 ms Problem 11.29 Part A How much work does an elevator motor do to lift a 1500 elevator a height of 110 ? Express your answer with the appropriate units. ANSWER: Correct Part B How much power must the motor supply to do this in 50 at constant speed? Express your answer with the appropriate units. ANSWER: Correct Problem 11.32 How many energy is consumed by a 1.20 hair dryer used for 10.0 and a 11.0 night light left on for 16.0 ? Part A Hair dryer: Express your answer with the appropriate units. kg m Wext = 1.62×106 J s = 3.23×104 P W kW min W hr ANSWER: Correct Part B Night light: Express your answer with the appropriate units. ANSWER: Correct Problem 11.42 A 2500 elevator accelerates upward at 1.20 for 10.0 , starting from rest. Part A How much work does gravity do on the elevator? Express your answer with the appropriate units. ANSWER: Correct W = 7.20×105 J = 6.34×105 W J kg m/s2 m −2.45×105 J Part B How much work does the tension in the elevator cable do on the elevator? Express your answer with the appropriate units. ANSWER: Correct Part C Use the work-kinetic energy theorem to find the kinetic energy of the elevator as it reaches 10.0 . Express your answer with the appropriate units. ANSWER: Correct Part D What is the speed of the elevator as it reaches 10.0 ? Express your answer with the appropriate units. ANSWER: Correct 2.75×105 J m 3.00×104 J m 4.90 ms Problem 11.47 A horizontal spring with spring constant 130 is compressed 17 and used to launch a 2.4 box across a frictionless, horizontal surface. After the box travels some distance, the surface becomes rough. The coefficient of kinetic friction of the box on the surface is 0.15. Part A Use work and energy to find how far the box slides across the rough surface before stopping. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 11.49 Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward slope and a large coefficient of rolling friction as the truck tires sink into the gravel brings the truck safely to a halt. Suppose a gravel ramp slopes upward at 6.0 and the coefficient of rolling friction is 0.45. Part A Use work and energy to find the length of a ramp that will stop a 15,000 truck that enters the ramp at 30 . Express your answer to two significant figures and include the appropriate units. ANSWER: Correct N/m cm kg l = 53 cm kg m/s l = 83 m Problem 11.51 Use work and energy to find an expression for the speed of the block in the following figure just before it hits the floor. Part A Find an expression for the speed of the block if the coefficient of kinetic friction for the block on the table is . Express your answer in terms of the variables , , , , and free fall acceleration . ANSWER: Part B Find an expression for the speed of the block if the table is frictionless. Express your answer in terms of the variables , , , and free fall acceleration . ANSWER: μk M m h μk g v = M m h g Problem 11.57 The spring shown in the figure is compressed 60 and used to launch a 100 physics student. The track is frictionless until it starts up the incline. The student's coefficient of kinetic friction on the incline is 0.12 . Part A What is the student's speed just after losing contact with the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B How far up the incline does the student go? Express your answer to two significant figures and include the appropriate units. ANSWER: v = cm kg 30 v = 17 ms Correct Score Summary: Your score on this assignment is 93.6%. You received 112.37 out of a possible total of 120 points. !s = 41 m

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