Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x ANSWER: Answer Requested Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. |Ax| = 5 m Ay A positive negative Bx By B Express your answers, separated by a comma, in meters to one significant figure. ANSWER: Correct Vector Components–Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and the coordinate axes, often designated . Bx, By = -2,-5 m, m F  Fx Fy  Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER:  Fx Fy F  Fx, Fy = Fcos, Fsin Correct In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies. Part B When you resolve a vector into components, the components must have the form or . The signs depend on which quadrant the vector lies in, and there will be one component with and the other with . In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you must figure out which angle is and then properly reorient the definitional triangle. As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle between and the y axis. Which of the various ways of orienting the definitional triangle must be used to resolve into components in the tilted coordinate system shown? (In the figures, the hypotenuse is orange, the side adjacent to is red, and the side opposite is yellow.) F  /2 cos() sin() F  sin(180 + ) = −sin() cos(90 + ) = −sin() sin() cos() sin(180 + ) + cos(270 − ) = 0 sin() cos()  /2 F  |F| cos() |F| sin() sin() cos()  N  N N  Indicate the number of the figure with the correct orientation. Hint 1. Recommended procedure for resolving a vector into components First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and write in the signs. Hint 2. Finding the trigonometric functions Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the   cos() side opposite has length . The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector whose magnitude is the hypotenuse; red + yellow = orange. ANSWER: Correct Part C Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: ANSWER: sin() 1 2 3 4 Correct Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates . Consider the following conditions: A. , B. , C. , D. , Which of these lettered conditions are true in which the numbered quadrants shown in ? Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and D in the fourth, enter “3, 2, 1, 4” as your response. ANSWER: Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle.     x > 0 y > 0 x > 0 y < 0 x < 0 y > 0 x < 0 y < 0 Correct Part E Now find the components and of in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Answer Requested ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Nx Ny N N  Nx, Ny = −Nsin(),Ncos() T  T  Part A Find the components of the vector with length = 1.00 and angle =10.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. What is the x component? Look at the figure shown. points in the positive x direction, so is positive. Also, the magnitude is just the length . ANSWER: Correct Part B Find the components of the vector with length = 1.00 and angle =15.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. A a  A x Ax |Ax| OL = OMcos( ) A  = 0.985,0.174 B b   Hint 1. What is the x component? The x component is still of the same form, that is, . ANSWER: Correct The components of still have the same form, that is, , despite 's placement with respect to the y axis on the drawing. Part C Find the components of the vector with length = 1.00 and angle 35.0 as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. Method 1: Find the angle that makes with the positive x axis Angle = 0.611 differs from the other two angles because it is the angle between the vector and the y axis, unlike the others, which are with respect to the x axis. What is the angle that makes with the positive x axis? Express your answer numerically in degrees. ANSWER: Hint 2. Method 2: Use vector addition Look at the figure shown. Lcos() B = 0.966,0.259 B (Lcos(), Lsin()) B C c  =  C  C 125 1. . 2. . 3. , the x component of is negative, since points in the negative x direction. Use this information to find . Similarly, find . ANSWER: Answer Requested ± Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: Correct C = C + x C y |C | = length(QR) = c sin() x Cx C C x Cx Cy C  = -0.574,0.819 A = (1, 0,−3) B = (−2, 5, 1) C = (3, 1, 1) A − B  = 3,-5,-4 Part B ANSWER: Correct Part C ANSWER: Correct Part D ANSWER: Correct B − C  = -5,4,0 −A + B − C  = -6,4,3 3A − 2C  = -3,-2,-11 Part E ANSWER: Correct Part F ANSWER: Correct Video Tutor: Balls Take High and Low Tracks First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A −2A + 3B − C  = -11,14,8 2A − 3(B − C) = 17,-12,-6 Consider the video demonstration that you just watched. Which of the following changes could potentially allow the ball on the straight inclined (yellow) track to win? Ignore air resistance. Select all that apply. Hint 1. How to approach the problem Answers A and B involve changing the steepness of part or all of the track. Answers C and D involve changing the mass of the balls. So, first you should decide which of those factors, if either, can change how fast the ball gets to the end of the track. ANSWER: Correct If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt? Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. A. Increase the tilt of the yellow track. B. Make the downhill and uphill inclines on the red track less steep, while keeping the total distance traveled by the ball the same. C. Increase the mass of the ball on the yellow track. D. Decrease the mass of the ball on the red track.

Chapter 3 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 12, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Tactics Box 3.1 Determining the Components of a Vector Learning Goal: To practice Tactics Box 3.1 Determining the Components of a Vector. When a vector is decomposed into component vectors and parallel to the coordinate axes, we can describe each component vector with a single number (a scalar) called the component. This tactics box describes how to determine the x component and y component of vector , denoted and . TACTICS BOX 3.1 Determining the components of a vector The absolute value of the x component is the magnitude of the 1. component vector . 2. The sign of is positive if points in the positive x direction; it is negative if points in the negative x direction. 3. The y component is determined similarly. Part A What is the magnitude of the component vector shown in the figure? Express your answer in meters to one significant figure. A A x A y A Ax Ay |Ax| Ax A x Ax A x A x Ay A x ANSWER: Answer Requested Part B What is the sign of the y component of vector shown in the figure? ANSWER: Correct Part C Now, combine the information given in the tactics box above to find the x and y components, and , of vector shown in the figure. |Ax| = 5 m Ay A positive negative Bx By B Express your answers, separated by a comma, in meters to one significant figure. ANSWER: Correct Vector Components–Review Learning Goal: To introduce you to vectors and the use of sine and cosine for a triangle when resolving components. Vectors are an important part of the language of science, mathematics, and engineering. They are used to discuss multivariable calculus, electrical circuits with oscillating currents, stress and strain in structures and materials, and flows of atmospheres and fluids, and they have many other applications. Resolving a vector into components is a precursor to computing things with or about a vector quantity. Because position, velocity, acceleration, force, momentum, and angular momentum are all vector quantities, resolving vectors into components is the most important skill required in a mechanics course. The figure shows the components of , and , along the x and y axes of the coordinate system, respectively. The components of a vector depend on the coordinate system’s orientation, the key being the angle between the vector and the coordinate axes, often designated . Bx, By = -2,-5 m, m F  Fx Fy  Part A The figure shows the standard way of measuring the angle. is measured to the vector from the x axis, and counterclockwise is positive. Express and in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER:  Fx Fy F  Fx, Fy = Fcos, Fsin Correct In principle, you can determine the components of any vector with these expressions. If lies in one of the other quadrants of the plane, will be an angle larger than 90 degrees (or in radians) and and will have the appropriate signs and values. Unfortunately this way of representing , though mathematically correct, leads to equations that must be simplified using trig identities such as and . These must be used to reduce all trig functions present in your equations to either or . Unless you perform this followup step flawlessly, you will fail to recoginze that , and your equations will not simplify so that you can progress further toward a solution. Therefore, it is best to express all components in terms of either or , with between 0 and 90 degrees (or 0 and in radians), and determine the signs of the trig functions by knowing in which quadrant the vector lies. Part B When you resolve a vector into components, the components must have the form or . The signs depend on which quadrant the vector lies in, and there will be one component with and the other with . In real problems the optimal coordinate system is often rotated so that the x axis is not horizontal. Furthermore, most vectors will not lie in the first quadrant. To assign the sine and cosine correctly for vectors at arbitrary angles, you must figure out which angle is and then properly reorient the definitional triangle. As an example, consider the vector shown in the diagram labeled “tilted axes,” where you know the angle between and the y axis. Which of the various ways of orienting the definitional triangle must be used to resolve into components in the tilted coordinate system shown? (In the figures, the hypotenuse is orange, the side adjacent to is red, and the side opposite is yellow.) F  /2 cos() sin() F  sin(180 + ) = −sin() cos(90 + ) = −sin() sin() cos() sin(180 + ) + cos(270 − ) = 0 sin() cos()  /2 F  |F| cos() |F| sin() sin() cos()  N  N N  Indicate the number of the figure with the correct orientation. Hint 1. Recommended procedure for resolving a vector into components First figure out the sines and cosines of , then figure out the signs from the quadrant the vector is in and write in the signs. Hint 2. Finding the trigonometric functions Sine and cosine are defined according to the following convention, with the key lengths shown in green: The hypotenuse has unit length, the side adjacent to has length , and the   cos() side opposite has length . The colors are chosen to remind you that the vector sum of the two orthogonal sides is the vector whose magnitude is the hypotenuse; red + yellow = orange. ANSWER: Correct Part C Choose the correct procedure for determining the components of a vector in a given coordinate system from this list: ANSWER: sin() 1 2 3 4 Correct Part D The space around a coordinate system is conventionally divided into four numbered quadrants depending on the signs of the x and y coordinates . Consider the following conditions: A. , B. , C. , D. , Which of these lettered conditions are true in which the numbered quadrants shown in ? Write the answer in the following way: If A were true in the third quadrant, B in the second, C in the first, and D in the fourth, enter “3, 2, 1, 4” as your response. ANSWER: Align the adjacent side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and an adjacent side along a coordinate direction with as the included angle. Align the opposite side of a right triangle with the vector and the hypotenuse along a coordinate direction with as the included angle. Align the hypotenuse of a right triangle with the vector and the opposite side along a coordinate direction with as the included angle.     x > 0 y > 0 x > 0 y < 0 x < 0 y > 0 x < 0 y < 0 Correct Part E Now find the components and of in the tilted coordinate system of Part B. Express your answer in terms of the length of the vector and the angle , with the components separated by a comma. ANSWER: Answer Requested ± Resolving Vector Components with Trigonometry Often a vector is specified by a magnitude and a direction; for example, a rope with tension exerts a force of magnitude in a direction 35 north of east. This is a good way to think of vectors; however, to calculate results with vectors, it is best to select a coordinate system and manipulate the components of the vectors in that coordinate system. Nx Ny N N  Nx, Ny = −Nsin(),Ncos() T  T  Part A Find the components of the vector with length = 1.00 and angle =10.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. What is the x component? Look at the figure shown. points in the positive x direction, so is positive. Also, the magnitude is just the length . ANSWER: Correct Part B Find the components of the vector with length = 1.00 and angle =15.0 with respect to the x axis as shown. Enter the x component followed by the y component, separated by a comma. A a  A x Ax |Ax| OL = OMcos( ) A  = 0.985,0.174 B b   Hint 1. What is the x component? The x component is still of the same form, that is, . ANSWER: Correct The components of still have the same form, that is, , despite 's placement with respect to the y axis on the drawing. Part C Find the components of the vector with length = 1.00 and angle 35.0 as shown. Enter the x component followed by the y component, separated by a comma. Hint 1. Method 1: Find the angle that makes with the positive x axis Angle = 0.611 differs from the other two angles because it is the angle between the vector and the y axis, unlike the others, which are with respect to the x axis. What is the angle that makes with the positive x axis? Express your answer numerically in degrees. ANSWER: Hint 2. Method 2: Use vector addition Look at the figure shown. Lcos() B = 0.966,0.259 B (Lcos(), Lsin()) B C c  =  C  C 125 1. . 2. . 3. , the x component of is negative, since points in the negative x direction. Use this information to find . Similarly, find . ANSWER: Answer Requested ± Vector Addition and Subtraction In general it is best to conceptualize vectors as arrows in space, and then to make calculations with them using their components. (You must first specify a coordinate system in order to find the components of each arrow.) This problem gives you some practice with the components. Let vectors , , and . Calculate the following, and express your answers as ordered triplets of values separated by commas. Part A ANSWER: Correct C = C + x C y |C | = length(QR) = c sin() x Cx C C x Cx Cy C  = -0.574,0.819 A = (1, 0,−3) B = (−2, 5, 1) C = (3, 1, 1) A − B  = 3,-5,-4 Part B ANSWER: Correct Part C ANSWER: Correct Part D ANSWER: Correct B − C  = -5,4,0 −A + B − C  = -6,4,3 3A − 2C  = -3,-2,-11 Part E ANSWER: Correct Part F ANSWER: Correct Video Tutor: Balls Take High and Low Tracks First, launch the video below. You will be asked to use your knowledge of physics to predict the outcome of an experiment. Then, close the video window and answer the questions at right. You can watch the video again at any point. Part A −2A + 3B − C  = -11,14,8 2A − 3(B − C) = 17,-12,-6 Consider the video demonstration that you just watched. Which of the following changes could potentially allow the ball on the straight inclined (yellow) track to win? Ignore air resistance. Select all that apply. Hint 1. How to approach the problem Answers A and B involve changing the steepness of part or all of the track. Answers C and D involve changing the mass of the balls. So, first you should decide which of those factors, if either, can change how fast the ball gets to the end of the track. ANSWER: Correct If the yellow track were tilted steeply enough, its ball could win. How might you go about calculating the necessary change in tilt? Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. A. Increase the tilt of the yellow track. B. Make the downhill and uphill inclines on the red track less steep, while keeping the total distance traveled by the ball the same. C. Increase the mass of the ball on the yellow track. D. Decrease the mass of the ball on the red track.

please email info@checkyourstudy.com
Chapter 1 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Curved Motion Diagram The motion diagram shown in the figure represents a pendulum released from rest at an angle of 45 from the vertical. The dots in the motion diagram represent the positions of the pendulum bob at eleven moments separated by equal time intervals. The green arrows represent the average velocity between adjacent dots. Also given is a “compass rose” in which directions are labeled with the letters of the alphabet.  Part A What is the direction of the acceleration of the object at moment 5? Enter the letter of the arrow with this direction from the compass rose in the figure. Type Z if the acceleration vector has zero length. You did not open hints for this part. ANSWER: Incorrect; Try Again Part B What is the direction of the acceleration of the object at moments 0 and 10? Enter the letters corresponding to the arrows with these directions from the compass rose in the figure, separated by commas. Type Z if the acceleration vector has zero length. You did not open hints for this part. ANSWER: Incorrect; Try Again PSS 1.1 Motion Diagrams Learning Goal: To practice Problem-Solving Strategy 1.1 for motion diagram problems. A car is traveling with constant velocity along a highway. The driver notices he is late for work, so he stomps down on the gas pedal and the car begins to speed up. The car has just achieved double its directions at time step 0, time step 10 = initial velocity when the driver spots a police officer behind him and applies the brakes. The car then slows down, coming to rest at a stoplight ahead. Draw a complete motion diagram for this situation. PROBLEM-SOLVING STRATEGY 1.1 Motion diagrams MODEL: Represent the moving object as a particle. Make simplifying assumptions when interpreting the problem statement. VISUALIZE: A complete motion diagram consists of: The position of the object in each frame of the film, shown as a dot. Use five or six dots to make the motion clear but without overcrowding the picture. More complex motions may need more dots. The average velocity vectors, found by connecting each dot in the motion diagram to the next with a vector arrow. There is one velocity vector linking each set of two position dots. Label the row of velocity vectors . The average acceleration vectors, found using Tactics Box 1.3. There is one acceleration vector linking each set of two velocity vectors. Each acceleration vector is drawn at the dot between the two velocity vectors it links. Use to indicate a point at which the acceleration is zero. Label the row of acceleration vectors . Model It is appropriate to use the particle model for the car. You should also make some simplifying assumptions. v 0 a Part A The car’s motion can be divided into three different stages: its motion before the driver realizes he’s late, its motion after the driver hits the gas (but before he sees the police car), and its motion after the driver sees the police car. Which of the following simplifying assumptions is it reasonable to make in this problem? During each of the three different stages of its motion, the car is moving with constant A. acceleration. B. During each of the three different stages of its motion, the car is moving with constant velocity. C. The highway is straight (i.e., there are no curves). D. The highway is level (i.e., there are no hills or valleys). Enter all the correct answers in alphabetical order without commas. For example, if statements C and D are correct, enter CD. ANSWER: Correct In addition to the assumptions listed above, in the rest of this problem assume that the car is moving in a straight line to the right. Visualize Part B In the three diagrams shown to the left, the position of the car at five subsequent instants of time is represented by black dots, and the car’s average velocity is represented by green arrows. Which of these diagrams best describes the position and the velocity of the car before the driver notices he is late? ANSWER: Correct Part C Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver hits the gas, but before he notices the police officer? ANSWER: Correct A B C A B C Part D Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver notices the police officer? ANSWER: Correct Part E Which of the diagrams shown below most accurately depicts the average acceleration vectors of the car during the events described in the problem introduction? ANSWER: A B C Correct You can now draw a complete motion diagram for the situation described in this problem. Your diagram should look like this: Measurements in SI Units Familiarity with SI units will aid your study of physics and all other sciences. Part A What is the approximate height of the average adult in centimeters? Hint 1. Converting between feet and centimeters The distance from your elbow to your fingertips is typically about 50 . A B C cm ANSWER: Correct If you’re not familiar with metric units of length, you can use your body to develop intuition for them. The average height of an adult is 5 6.4 . The distance from elbow to fingertips on the average adult is about 50 . Ten (1 ) is about the width of this adult’s little finger and 10 is about the width of the average hand. Part B Approximately what is the mass of the average adult in kilograms? Hint 1. Converting between pounds and kilograms Something that weighs 1 has a mass of about . ANSWER: Correct Something that weighs 1 has a mass of about . This is a useful conversion to keep in mind! ± A Trip to Europe 100 200 300 cm cm cm feet inches cm mm cm cm pound 1 kg 2 80 500 1200 kg kg kg pound (1/2) kg Learning Goal: To understand how to use dimensional analysis to solve problems. Dimensional analysis is a useful tool for solving problems that involve unit conversions. Since unit conversion is not limited to physics problems but is part of our everyday life, correct use of conversion factors is essential to working through problems of practical importance. For example, dimensional analysis could be used in problems involving currency exchange. Say you want to calculate how many euros you get if you exchange 3600 ( ), given the exchange rate , that is, 1 to 1.20 . Begin by writing down the starting value, 3600 . This can also be written as a fraction: . Next, convert dollars to euros. This conversion involves multiplying by a simple conversion factor derived from the exchange rate: . Note that the “dollar” unit, , should appear on the bottom of this conversion factor, since appears on the top of the starting value. Finally, since dollars are divided by dollars, the units can be canceled and the final result is . Currency exchange is only one example of many practical situations where dimensional analysis may help you to work through problems. Remember that dimensional analysis involves multiplying a given value by a conversion factor, resulting in a value in the new units. The conversion factor can be the ratio of any two quantities, as long as the ratio is equal to one. You and your friends are organizing a trip to Europe. Your plan is to rent a car and drive through the major European capitals. By consulting a map you estimate that you will cover a total distance of 5000 . Consider the euro-dollar exchange rate given in the introduction and use dimensional analysis to work through these simple problems. Part A You select a rental package that includes a car with an average consumption of 6.00 of fuel per 100 . Considering that in Europe the average fuel cost is 1.063 , how much (in US dollars) will you spend in fuel on your trip? Express your answer numerically in US dollars to three significant figures. You did not open hints for this part. ANSWER: US dollars USD 1 EUR = 1.20 USD euro US dollars USD 3600 USD 1 1.00 EUR 1.20 USD USD USD ( )( ) = 3000 EUR 3600 USD 1 1.00 EUR 1.20 USD km liters km euros/liter Part B How many gallons of fuel would the rental car consume per mile? Express your answer numerically in gallons per mile to three significant figures. You did not open hints for this part. ANSWER: Part C This question will be shown after you complete previous question(s). Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. Cost of fuel = USD gallons/mile

Chapter 1 Practice Problems (Practice – no credit) Due: 11:59pm on Wednesday, February 5, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Curved Motion Diagram The motion diagram shown in the figure represents a pendulum released from rest at an angle of 45 from the vertical. The dots in the motion diagram represent the positions of the pendulum bob at eleven moments separated by equal time intervals. The green arrows represent the average velocity between adjacent dots. Also given is a “compass rose” in which directions are labeled with the letters of the alphabet.  Part A What is the direction of the acceleration of the object at moment 5? Enter the letter of the arrow with this direction from the compass rose in the figure. Type Z if the acceleration vector has zero length. You did not open hints for this part. ANSWER: Incorrect; Try Again Part B What is the direction of the acceleration of the object at moments 0 and 10? Enter the letters corresponding to the arrows with these directions from the compass rose in the figure, separated by commas. Type Z if the acceleration vector has zero length. You did not open hints for this part. ANSWER: Incorrect; Try Again PSS 1.1 Motion Diagrams Learning Goal: To practice Problem-Solving Strategy 1.1 for motion diagram problems. A car is traveling with constant velocity along a highway. The driver notices he is late for work, so he stomps down on the gas pedal and the car begins to speed up. The car has just achieved double its directions at time step 0, time step 10 = initial velocity when the driver spots a police officer behind him and applies the brakes. The car then slows down, coming to rest at a stoplight ahead. Draw a complete motion diagram for this situation. PROBLEM-SOLVING STRATEGY 1.1 Motion diagrams MODEL: Represent the moving object as a particle. Make simplifying assumptions when interpreting the problem statement. VISUALIZE: A complete motion diagram consists of: The position of the object in each frame of the film, shown as a dot. Use five or six dots to make the motion clear but without overcrowding the picture. More complex motions may need more dots. The average velocity vectors, found by connecting each dot in the motion diagram to the next with a vector arrow. There is one velocity vector linking each set of two position dots. Label the row of velocity vectors . The average acceleration vectors, found using Tactics Box 1.3. There is one acceleration vector linking each set of two velocity vectors. Each acceleration vector is drawn at the dot between the two velocity vectors it links. Use to indicate a point at which the acceleration is zero. Label the row of acceleration vectors . Model It is appropriate to use the particle model for the car. You should also make some simplifying assumptions. v 0 a Part A The car’s motion can be divided into three different stages: its motion before the driver realizes he’s late, its motion after the driver hits the gas (but before he sees the police car), and its motion after the driver sees the police car. Which of the following simplifying assumptions is it reasonable to make in this problem? During each of the three different stages of its motion, the car is moving with constant A. acceleration. B. During each of the three different stages of its motion, the car is moving with constant velocity. C. The highway is straight (i.e., there are no curves). D. The highway is level (i.e., there are no hills or valleys). Enter all the correct answers in alphabetical order without commas. For example, if statements C and D are correct, enter CD. ANSWER: Correct In addition to the assumptions listed above, in the rest of this problem assume that the car is moving in a straight line to the right. Visualize Part B In the three diagrams shown to the left, the position of the car at five subsequent instants of time is represented by black dots, and the car’s average velocity is represented by green arrows. Which of these diagrams best describes the position and the velocity of the car before the driver notices he is late? ANSWER: Correct Part C Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver hits the gas, but before he notices the police officer? ANSWER: Correct A B C A B C Part D Which of the diagrams shown to the left best describes the position and the velocity of the car after the driver notices the police officer? ANSWER: Correct Part E Which of the diagrams shown below most accurately depicts the average acceleration vectors of the car during the events described in the problem introduction? ANSWER: A B C Correct You can now draw a complete motion diagram for the situation described in this problem. Your diagram should look like this: Measurements in SI Units Familiarity with SI units will aid your study of physics and all other sciences. Part A What is the approximate height of the average adult in centimeters? Hint 1. Converting between feet and centimeters The distance from your elbow to your fingertips is typically about 50 . A B C cm ANSWER: Correct If you’re not familiar with metric units of length, you can use your body to develop intuition for them. The average height of an adult is 5 6.4 . The distance from elbow to fingertips on the average adult is about 50 . Ten (1 ) is about the width of this adult’s little finger and 10 is about the width of the average hand. Part B Approximately what is the mass of the average adult in kilograms? Hint 1. Converting between pounds and kilograms Something that weighs 1 has a mass of about . ANSWER: Correct Something that weighs 1 has a mass of about . This is a useful conversion to keep in mind! ± A Trip to Europe 100 200 300 cm cm cm feet inches cm mm cm cm pound 1 kg 2 80 500 1200 kg kg kg pound (1/2) kg Learning Goal: To understand how to use dimensional analysis to solve problems. Dimensional analysis is a useful tool for solving problems that involve unit conversions. Since unit conversion is not limited to physics problems but is part of our everyday life, correct use of conversion factors is essential to working through problems of practical importance. For example, dimensional analysis could be used in problems involving currency exchange. Say you want to calculate how many euros you get if you exchange 3600 ( ), given the exchange rate , that is, 1 to 1.20 . Begin by writing down the starting value, 3600 . This can also be written as a fraction: . Next, convert dollars to euros. This conversion involves multiplying by a simple conversion factor derived from the exchange rate: . Note that the “dollar” unit, , should appear on the bottom of this conversion factor, since appears on the top of the starting value. Finally, since dollars are divided by dollars, the units can be canceled and the final result is . Currency exchange is only one example of many practical situations where dimensional analysis may help you to work through problems. Remember that dimensional analysis involves multiplying a given value by a conversion factor, resulting in a value in the new units. The conversion factor can be the ratio of any two quantities, as long as the ratio is equal to one. You and your friends are organizing a trip to Europe. Your plan is to rent a car and drive through the major European capitals. By consulting a map you estimate that you will cover a total distance of 5000 . Consider the euro-dollar exchange rate given in the introduction and use dimensional analysis to work through these simple problems. Part A You select a rental package that includes a car with an average consumption of 6.00 of fuel per 100 . Considering that in Europe the average fuel cost is 1.063 , how much (in US dollars) will you spend in fuel on your trip? Express your answer numerically in US dollars to three significant figures. You did not open hints for this part. ANSWER: US dollars USD 1 EUR = 1.20 USD euro US dollars USD 3600 USD 1 1.00 EUR 1.20 USD USD USD ( )( ) = 3000 EUR 3600 USD 1 1.00 EUR 1.20 USD km liters km euros/liter Part B How many gallons of fuel would the rental car consume per mile? Express your answer numerically in gallons per mile to three significant figures. You did not open hints for this part. ANSWER: Part C This question will be shown after you complete previous question(s). Score Summary: Your score on this assignment is 0%. You received 0 out of a possible total of 0 points. Cost of fuel = USD gallons/mile

please email info@checkyourstudy.com
Chapter 5 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 Tactics Box 5.1 Drawing Force Vectors Learning Goal: To practice Tactics Box 5.1 Drawing Force Vectors. To visualize how forces are exerted on objects, we can use simple diagrams such as vectors. This Tactics Box illustrates the process of drawing a force vector by using the particle model, in which objects are treated as points. TACTICS BOX 5.1 Drawing force vectors Represent the object 1. as a particle. 2. Place the tail of the force vector on the particle. 3. Draw the force vector as an arrow pointing in the proper direction and with a length proportional to the size of the force. 4. Give the vector an appropriate label. The resulting diagram for a force exerted on an object is shown in the drawing. Note that the object is represented as a black dot. Part A A book lies on a table. A pushing force parallel to the table top and directed to the right is exerted on the book. Follow the steps above to draw the force vector . Use the black dot as the particle representing the book. F  F push F push

Chapter 5 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 Tactics Box 5.1 Drawing Force Vectors Learning Goal: To practice Tactics Box 5.1 Drawing Force Vectors. To visualize how forces are exerted on objects, we can use simple diagrams such as vectors. This Tactics Box illustrates the process of drawing a force vector by using the particle model, in which objects are treated as points. TACTICS BOX 5.1 Drawing force vectors Represent the object 1. as a particle. 2. Place the tail of the force vector on the particle. 3. Draw the force vector as an arrow pointing in the proper direction and with a length proportional to the size of the force. 4. Give the vector an appropriate label. The resulting diagram for a force exerted on an object is shown in the drawing. Note that the object is represented as a black dot. Part A A book lies on a table. A pushing force parallel to the table top and directed to the right is exerted on the book. Follow the steps above to draw the force vector . Use the black dot as the particle representing the book. F  F push F push

please email info@checkyourstudy.com
Part I. (20%) Multiple Choice Questions (only one answer) 1. What is the SS7 A-link? a. Signaling Link between SSP and STP b. Signaling Link between STP and STP c. Signaling Link between SCP and SCP d. Signaling Link between SSP and SSP 2. How is a TDM trunk identified on the SS7 network? It is identified by _____. a. IP Address b. ISDN B channel c. UDP port number d. Circuit Identificaiton Code (CIC) 3. What is the layer-3 protocol for ISUP? a. IP b. Q.931 c. MTP3 d. TCAP 4. Which of the following signaling is required to support Local Number Portability (LNP)? a. SIP b. Q.931 c. SS7 d. MGCP 5. Which of the following signlaing is NOT supported on the local telephone switch? a. ISDN/Q.931 b. SIP c. SS7 d. Station Signaling 6. Which of the following protocol is used by Advanced Intelligent Network (AIN) for remote database query? One of the AIN features is 1-800/1-900 calls. a. TCAP b. ISUP c. MGCP d. SIP 7. Which of the following is an NNI signaling? a. ISDN/Q.931 b. SIP c. MGCP d. SS7 8. Which of the following message is used by Access Media Gateway (MG) to inform Media Gateway Controller (MGC) that a phone is off-hook? a. NTFY b. RQNT c. CRCX d. MDCX 9. Which of the following device supports codec (such as G.711)? a. Media Gateway Contoller b. Media Gateway (Access Gateway) c. Analog Phone d. Signaling Transfer Point (STP) 10. In MGCP, a connection is _______________ ? a. The same as a TCP connection b. The same as a phone call. c. An end-point and its associated RTP session. d. A TDM channel identified by CIC Part II Questions (10%). 1. Provide two reasons for separating Media Gateway Controller (MGC) and Media Gateway. Media gateways are often controlled by a separate Media Gateway Controller which provides the call control and signaling functionality. 2. Identify the signaling between the network devices. (enter N/A if not applicable) 1 Media Gateway Controller Media Gateway Controller 2 Media Gateway Controller Media Gateway 3 Media Gateway Controller Class-5 (local) Switch 4 Media Gateway Controller SIP Proxy 5 Media Gateway Media Gateway Part III (20%) Call Flow Diagram and protocol stacks Media Gateway Controller (MGC) also has the function of SS7 Signaling Gateway. 1. Show the call flow diagram from Phone-22 (SIP) to Phone-33 (SIP). 2. Show the call flow diagram from Phone-41 (analog) to Phone-42(analog) over the VoIP Carrier Network. Note: each signaling message is an arrow with its own label. Do not use one arrow and one label to represent multiple messages.

Part I. (20%) Multiple Choice Questions (only one answer) 1. What is the SS7 A-link? a. Signaling Link between SSP and STP b. Signaling Link between STP and STP c. Signaling Link between SCP and SCP d. Signaling Link between SSP and SSP 2. How is a TDM trunk identified on the SS7 network? It is identified by _____. a. IP Address b. ISDN B channel c. UDP port number d. Circuit Identificaiton Code (CIC) 3. What is the layer-3 protocol for ISUP? a. IP b. Q.931 c. MTP3 d. TCAP 4. Which of the following signaling is required to support Local Number Portability (LNP)? a. SIP b. Q.931 c. SS7 d. MGCP 5. Which of the following signlaing is NOT supported on the local telephone switch? a. ISDN/Q.931 b. SIP c. SS7 d. Station Signaling 6. Which of the following protocol is used by Advanced Intelligent Network (AIN) for remote database query? One of the AIN features is 1-800/1-900 calls. a. TCAP b. ISUP c. MGCP d. SIP 7. Which of the following is an NNI signaling? a. ISDN/Q.931 b. SIP c. MGCP d. SS7 8. Which of the following message is used by Access Media Gateway (MG) to inform Media Gateway Controller (MGC) that a phone is off-hook? a. NTFY b. RQNT c. CRCX d. MDCX 9. Which of the following device supports codec (such as G.711)? a. Media Gateway Contoller b. Media Gateway (Access Gateway) c. Analog Phone d. Signaling Transfer Point (STP) 10. In MGCP, a connection is _______________ ? a. The same as a TCP connection b. The same as a phone call. c. An end-point and its associated RTP session. d. A TDM channel identified by CIC Part II Questions (10%). 1. Provide two reasons for separating Media Gateway Controller (MGC) and Media Gateway. Media gateways are often controlled by a separate Media Gateway Controller which provides the call control and signaling functionality. 2. Identify the signaling between the network devices. (enter N/A if not applicable) 1 Media Gateway Controller Media Gateway Controller 2 Media Gateway Controller Media Gateway 3 Media Gateway Controller Class-5 (local) Switch 4 Media Gateway Controller SIP Proxy 5 Media Gateway Media Gateway Part III (20%) Call Flow Diagram and protocol stacks Media Gateway Controller (MGC) also has the function of SS7 Signaling Gateway. 1. Show the call flow diagram from Phone-22 (SIP) to Phone-33 (SIP). 2. Show the call flow diagram from Phone-41 (analog) to Phone-42(analog) over the VoIP Carrier Network. Note: each signaling message is an arrow with its own label. Do not use one arrow and one label to represent multiple messages.

      Part I. Multiple choice (20 points)   … Read More...
Doppler Shift 73 Because of the Doppler Effect, light emitted by an object can appear to change wavelength due to its motion toward or away from an observer. When the observer and the source of light are moving toward each other, the light is shifted to shorter wavelengths (blueshifted). When the observer and the source of light are moving away from each other, the light is shifted to longer wavelengths (redshifted). Part I: Motion of Source Star is not . rnovrng r ABCD 1) Consider the situations shown (A—D). a) In which situation will the observer receive light that is shifted to shorter wavelengths? b) Will this light be blueshifted or redshifted for this case? c) What direction is the star moving relative to the observer for this case? 2) Consider the situations shown (A—D). a) In which situation will the observer receive light that is shifted to longer wavelengths? b) Will this light be blueshifted or redshifted for this case? c) What direction is the star moving relative to the observer for this case? . 74 Doppler Shift 3) In which of the srtuations shown (A—D) will theobserver receive light that Is not Doppler Shifted at all? Explain your reasoning. – 4) Imagine our solar system Is moving In the Milky Way toward a group of three stars. Star A is a blue star that is slightly closer to us than the other two. Star B is a red star that is farthest away from us. Star C is a yellow star that is halfway between Stars A end B. a) Which of these three stars, if any, will give off light that appears to be blueshifted? Explain your reasoning. . / b) Which of these three stars, if any, will give off light that appears to be redshifted? Explain your reasoning. c) Which of these three stars, if any, will give off light that appears to have no shift? Explain your reasoning. — 5) You overhear two students discussing the topic of Doppler Shift. Student 1: Since Betelgeuse is a red star, it must be going away from us, and since Rigel is a blue star it must be coming toward us. Student 2: 1 disagree, the color of the star does not tell you if it is moving. You have to look at the shift in wavelength of the lines in the star’s absorption spectrum to determine whether it’s moving toward or away from you. Do you agree or disagree with either or both of the students? Explain your reasoning. 5 Part II: Shift in Absorption Spectra When we study an astronomical object like a star or galaxy, we examine the spectrum of light it gives off. Since the lines of a spectrum occur at specific wavelengths we can determine that an object is moving when we see that the lines have been shifted to either longer or shorter wavelengths. For the absorption line spectra shown on the next page, short-wavelength light (the blue end of the spectrum) is shown on the left-hand side and long-wavelength light (the red end of the spectrum) is shown on the right-hand side. Doppler Shift 75 For the three absorption line spectra shown below (A, B, and C), one of the spectra corresponds to a star that is not moving relative to you, one of the spectra is from a star that is moving toward you, and one of the spectra is from a star that is moving away from you. A B Blue J___ ..‘ C 6) Which of the three spectra above corresponds with the star moving toward you? Explain your reasoning. If two sources of llght are moving relative to an observer, the light from the star that is moving faster will appear to undergo a greater Doppler Consider the four spectra at the right. The spectrum labeled F is an absorption line spectrum from a star that is at rest. Again, note that short-wavelength (blue) light is shown on the left-hand side of each spectrum and long-wavelength (red) light is shown on the right-hand side of each spectrum. 7) Which of the three spectra corresponds with the star moving away from you? Explain your reasoning. Part 111: Size of Shift and Speed Blue Red . – 76 Doppler Shift 8) Which of the four spectra would be from the star that is moving the fastest? Would this star be moving toward or away from the observer? 9) Of the stars that are moving, which spectra would be from the star that is moving the slowest? Describe the motion of this star, – (fJ 1O)An Important line In the absorption spectrum of stars occurs at a wavelength of 656 nm for stars at rest. Irna me that you observe five stars (H—L) from Earth and discover that this Important absorption line Is measured at the wavelength shown in the table below for each of the five stars, Star Wavelength of Absorption Line H 649nm I 660 nm J 656nrn K 658nrn L 647nm a) Which of the stars are gMng off light that appears blueshifted? Explain your reasoning. b) Which of the stars are gMng off light that appears redshifted? Explain your reasoning. d) Which star is moving the fastest? Is it moving toward or away from the observer? Explain your reasoning. , . . c) Which star is giving off light that appears shifted by the greatest amount? Is this light shifted to longer or shorter wavelengths? Explain your reasoning. a) Which planets will receive a radio signal that Is redshifted? Explain your reasoning. b) Which planets wfll receive a radio signal that is shifted to shorter wavelengths? Explain your reasoning. a a . ii) The figure at right shows a spaceprobe and five planets. The motion of the spaceprobe is indicated by the arrow. The spaceprobe is continuously broadcasting a radio signal in all directions. 4 C E not to scale c) Will all the planets receive radio signals from the spaceprobe that are Doppler shifted? Explain your reasoning. d) How will the size of the Doppler Shift in the radio signals detected at Planets A and B compare? Explain your reasoning. Cats r , ‘, e) How Will the slz of 1h Dupler Shift in the radio signals deteed °lane E and B compare? Explain your reasoning. ‘

Doppler Shift 73 Because of the Doppler Effect, light emitted by an object can appear to change wavelength due to its motion toward or away from an observer. When the observer and the source of light are moving toward each other, the light is shifted to shorter wavelengths (blueshifted). When the observer and the source of light are moving away from each other, the light is shifted to longer wavelengths (redshifted). Part I: Motion of Source Star is not . rnovrng r ABCD 1) Consider the situations shown (A—D). a) In which situation will the observer receive light that is shifted to shorter wavelengths? b) Will this light be blueshifted or redshifted for this case? c) What direction is the star moving relative to the observer for this case? 2) Consider the situations shown (A—D). a) In which situation will the observer receive light that is shifted to longer wavelengths? b) Will this light be blueshifted or redshifted for this case? c) What direction is the star moving relative to the observer for this case? . 74 Doppler Shift 3) In which of the srtuations shown (A—D) will theobserver receive light that Is not Doppler Shifted at all? Explain your reasoning. – 4) Imagine our solar system Is moving In the Milky Way toward a group of three stars. Star A is a blue star that is slightly closer to us than the other two. Star B is a red star that is farthest away from us. Star C is a yellow star that is halfway between Stars A end B. a) Which of these three stars, if any, will give off light that appears to be blueshifted? Explain your reasoning. . / b) Which of these three stars, if any, will give off light that appears to be redshifted? Explain your reasoning. c) Which of these three stars, if any, will give off light that appears to have no shift? Explain your reasoning. — 5) You overhear two students discussing the topic of Doppler Shift. Student 1: Since Betelgeuse is a red star, it must be going away from us, and since Rigel is a blue star it must be coming toward us. Student 2: 1 disagree, the color of the star does not tell you if it is moving. You have to look at the shift in wavelength of the lines in the star’s absorption spectrum to determine whether it’s moving toward or away from you. Do you agree or disagree with either or both of the students? Explain your reasoning. 5 Part II: Shift in Absorption Spectra When we study an astronomical object like a star or galaxy, we examine the spectrum of light it gives off. Since the lines of a spectrum occur at specific wavelengths we can determine that an object is moving when we see that the lines have been shifted to either longer or shorter wavelengths. For the absorption line spectra shown on the next page, short-wavelength light (the blue end of the spectrum) is shown on the left-hand side and long-wavelength light (the red end of the spectrum) is shown on the right-hand side. Doppler Shift 75 For the three absorption line spectra shown below (A, B, and C), one of the spectra corresponds to a star that is not moving relative to you, one of the spectra is from a star that is moving toward you, and one of the spectra is from a star that is moving away from you. A B Blue J___ ..‘ C 6) Which of the three spectra above corresponds with the star moving toward you? Explain your reasoning. If two sources of llght are moving relative to an observer, the light from the star that is moving faster will appear to undergo a greater Doppler Consider the four spectra at the right. The spectrum labeled F is an absorption line spectrum from a star that is at rest. Again, note that short-wavelength (blue) light is shown on the left-hand side of each spectrum and long-wavelength (red) light is shown on the right-hand side of each spectrum. 7) Which of the three spectra corresponds with the star moving away from you? Explain your reasoning. Part 111: Size of Shift and Speed Blue Red . – 76 Doppler Shift 8) Which of the four spectra would be from the star that is moving the fastest? Would this star be moving toward or away from the observer? 9) Of the stars that are moving, which spectra would be from the star that is moving the slowest? Describe the motion of this star, – (fJ 1O)An Important line In the absorption spectrum of stars occurs at a wavelength of 656 nm for stars at rest. Irna me that you observe five stars (H—L) from Earth and discover that this Important absorption line Is measured at the wavelength shown in the table below for each of the five stars, Star Wavelength of Absorption Line H 649nm I 660 nm J 656nrn K 658nrn L 647nm a) Which of the stars are gMng off light that appears blueshifted? Explain your reasoning. b) Which of the stars are gMng off light that appears redshifted? Explain your reasoning. d) Which star is moving the fastest? Is it moving toward or away from the observer? Explain your reasoning. , . . c) Which star is giving off light that appears shifted by the greatest amount? Is this light shifted to longer or shorter wavelengths? Explain your reasoning. a) Which planets will receive a radio signal that Is redshifted? Explain your reasoning. b) Which planets wfll receive a radio signal that is shifted to shorter wavelengths? Explain your reasoning. a a . ii) The figure at right shows a spaceprobe and five planets. The motion of the spaceprobe is indicated by the arrow. The spaceprobe is continuously broadcasting a radio signal in all directions. 4 C E not to scale c) Will all the planets receive radio signals from the spaceprobe that are Doppler shifted? Explain your reasoning. d) How will the size of the Doppler Shift in the radio signals detected at Planets A and B compare? Explain your reasoning. Cats r , ‘, e) How Will the slz of 1h Dupler Shift in the radio signals deteed °lane E and B compare? Explain your reasoning. ‘

  ANSWERS Part 1 1 C is the answer because … Read More...
Operational amplifiers are often used to amplify a sensor output. This problem will walk you through the design of a simple temperature measuring device based on a platinum wire sensor. Goal: Build a circuit that will provide a calibrated output between .32V and 2.12V for temperatures sensed between 0°C and 100°C. (The final circuit can be seen at the end of this homework but we will work out each stage in turn.) The platinum wire sensor has a resistance of 100Ω at 0°C and 138.5Ω at 100°C, or a change of 0.385Ω/°C. (The arrow through the resistor in the circuit indicates it is a variable resistor.) A 0.5mA source is used to excite the platinum wire resistor to obtain a voltage. The first stage of our circuit will be to buffer the output of the sensor so we do not load the sensor circuit by drawing off any of the .5mA current to the op amp. A. (10 points) What is V1 when the temperature is 0°C, 1°C, 20°C and 100°C? (Use at least four decimal points.) B. (10 points)The output voltage of the resistor changes by I*ΔRT where I =0.5mA and ΔRT = 0.385Ω/°C. It is too small, so we need amplify this so the V2 output in the second stage of this circuit will be 5mV per degree using a non-inverting amplifier. So we want 5mV = (I*ΔRT * gain) per degree centigrade. What is the required gain for this circuit? Choose values of R1 and R2 between 1k and 100kΩ to achieve this. Choose Rin to be 1K-10kΩ. C. (10 points) What is V2 for a temperature of 0°C and for 1°C. What is the difference between the two voltages? (Hint: The difference should be exactly 5mV! The resistance of the platinum wire will be 100.385Ω @ 1°C.) D. (10 extra credit points) We would like for the output voltage, V2, to be 0V when the temperature is 0°C. This can be done by adding a third stage with an offset voltage in the circuit below. Find Voffset so that VC = 0V when the temperature is 0°C. Let R3 =R4 = R5 and pick appropriate values of the resistors between 1k and 10kΩ. (Hint: V2= the voltage when the temperature is 0°C you found in part C. Find Voffset so that Vc =0V. Superposition may a good technique to use here. You can analyze the circuit when V2=0 and the offset is activated and then you can analyze the circuit when V2 = the value from part C and the offset voltage is zero.) What is Voffset? What values did you chose for the resistors? What is VC when the temperature is is 0°C, 1°C, 20°C and 100°C? E. The voltage VC should now be 0V when the temperature is 0°C and increase by 10mV for every degree centigrade. We need to multiply this by 1.8, the factor to convert a degree Centigrade to a degree Fahrenheit. The output of this stage, V4, should range from 0V to 1.80V and then we will add an offset to change the VF output range to 0.32V to 2.12V in the last stage. The following circuit can be used. Note that this circuit uses inverting amplifiers instead of non-inverting amplifiers. (10 extra credit points) Find the correct resistor values for R7, R8 so that V4 will range between 0V to -1.80V when the temperature is sensed between 0°C and 100°C. (10 extra credit points) Find Voffset2 and then determine VF at 0°C, 1°C, 20°C and 100°C so the VF will range from 0.32V to 2.12V. (Hint: When VC = 0V at 0°C, the V4 output of this stage will also be 0V. Determine the offset voltage so VF = 0.32V. Choose R9 = R10 = R11 = 1kΩ, so at 0°C, VF = 0.32V = VR10 with the current going from the output back through R10 to zero volts, then down through R11 and the Voffset2 source. Since VR10=VR11=0.32V, determine Voffset2. When the temperature is 100°C the output should be 2.12V.)

Operational amplifiers are often used to amplify a sensor output. This problem will walk you through the design of a simple temperature measuring device based on a platinum wire sensor. Goal: Build a circuit that will provide a calibrated output between .32V and 2.12V for temperatures sensed between 0°C and 100°C. (The final circuit can be seen at the end of this homework but we will work out each stage in turn.) The platinum wire sensor has a resistance of 100Ω at 0°C and 138.5Ω at 100°C, or a change of 0.385Ω/°C. (The arrow through the resistor in the circuit indicates it is a variable resistor.) A 0.5mA source is used to excite the platinum wire resistor to obtain a voltage. The first stage of our circuit will be to buffer the output of the sensor so we do not load the sensor circuit by drawing off any of the .5mA current to the op amp. A. (10 points) What is V1 when the temperature is 0°C, 1°C, 20°C and 100°C? (Use at least four decimal points.) B. (10 points)The output voltage of the resistor changes by I*ΔRT where I =0.5mA and ΔRT = 0.385Ω/°C. It is too small, so we need amplify this so the V2 output in the second stage of this circuit will be 5mV per degree using a non-inverting amplifier. So we want 5mV = (I*ΔRT * gain) per degree centigrade. What is the required gain for this circuit? Choose values of R1 and R2 between 1k and 100kΩ to achieve this. Choose Rin to be 1K-10kΩ. C. (10 points) What is V2 for a temperature of 0°C and for 1°C. What is the difference between the two voltages? (Hint: The difference should be exactly 5mV! The resistance of the platinum wire will be 100.385Ω @ 1°C.) D. (10 extra credit points) We would like for the output voltage, V2, to be 0V when the temperature is 0°C. This can be done by adding a third stage with an offset voltage in the circuit below. Find Voffset so that VC = 0V when the temperature is 0°C. Let R3 =R4 = R5 and pick appropriate values of the resistors between 1k and 10kΩ. (Hint: V2= the voltage when the temperature is 0°C you found in part C. Find Voffset so that Vc =0V. Superposition may a good technique to use here. You can analyze the circuit when V2=0 and the offset is activated and then you can analyze the circuit when V2 = the value from part C and the offset voltage is zero.) What is Voffset? What values did you chose for the resistors? What is VC when the temperature is is 0°C, 1°C, 20°C and 100°C? E. The voltage VC should now be 0V when the temperature is 0°C and increase by 10mV for every degree centigrade. We need to multiply this by 1.8, the factor to convert a degree Centigrade to a degree Fahrenheit. The output of this stage, V4, should range from 0V to 1.80V and then we will add an offset to change the VF output range to 0.32V to 2.12V in the last stage. The following circuit can be used. Note that this circuit uses inverting amplifiers instead of non-inverting amplifiers. (10 extra credit points) Find the correct resistor values for R7, R8 so that V4 will range between 0V to -1.80V when the temperature is sensed between 0°C and 100°C. (10 extra credit points) Find Voffset2 and then determine VF at 0°C, 1°C, 20°C and 100°C so the VF will range from 0.32V to 2.12V. (Hint: When VC = 0V at 0°C, the V4 output of this stage will also be 0V. Determine the offset voltage so VF = 0.32V. Choose R9 = R10 = R11 = 1kΩ, so at 0°C, VF = 0.32V = VR10 with the current going from the output back through R10 to zero volts, then down through R11 and the Voffset2 source. Since VR10=VR11=0.32V, determine Voffset2. When the temperature is 100°C the output should be 2.12V.)

A) At 0 deg C —> R =100 Ohm, I … Read More...
Count the atoms on both sides of the arrow to demonstrate that these equations are balanced. a. 2 C3H8(g) + 7 O2(g) →6CO(g) + 8HO(l) b. 2 C8H18(g) + 25O2(g) → 16 C02(g) + 18 H2O(l)

Count the atoms on both sides of the arrow to demonstrate that these equations are balanced. a. 2 C3H8(g) + 7 O2(g) →6CO(g) + 8HO(l) b. 2 C8H18(g) + 25O2(g) → 16 C02(g) + 18 H2O(l)

Both sides have 16 carbon , 36 hydrogen and 50 … Read More...
Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 Assignment 4 – Noise and Correlation 1. If a signal is measured as 2.5 V and the noise is 28 mV (28 × 10−3 V), what is the SNR in dB? 2. A single sinusoidal signal is found with some noise. If the RMS value of the noise is 0.5 V and the SNR is 10 dB, what is the RMS amplitude of the sinusoid? 3. The file signal_noise.mat contains a variable x that consists of a 1.0-V peak sinusoidal signal buried in noise. What is the SNR for this signal and noise? Assume that the noise RMS is much greater than the signal RMS. Note: “signal_noise.mat” and other files used in these assignments can be downloaded from the content area of Brightspace, within the “Data Files for Exercises” folder. These files can be opened in Matlab by copying into the active folder and double-clicking on the file or using the Matlab load command using the format: load(‘signal_noise.mat’). To discover the variables within the files use the Matlab who command. 4. An 8-bit ADC converter that has an input range of ±5 V is used to convert a signal that ranges between ±2 V. What is the SNR of the input if the input noise equals the quantization noise of the converter? Hint: Refer to Equation below to find the quantization noise: 5. The file filter1.mat contains the spectrum of a fourth-order lowpass filter as variable x in dB. The file also contains the corresponding frequencies of x in variable freq. Plot the spectrum of this filter both as dB versus log frequency and as linear amplitude versus linear frequency. The frequency axis should range between 10 and 400 Hz in both plots. Hint: Use Equation below to convert: Biomedical Signal and Image Processing (4800_420_001) Assigned on September 12th, 2017 6. Generate one cycle of the square wave similar to the one shown below in a 500-point MATLAB array. Determine the RMS value of this waveform. [Hint: When you take the square of the data array, be sure to use a period before the up arrow so that MATLAB does the squaring point-by-point (i.e., x.^2).]. 7. A resistor produces 10 μV noise (i.e., 10 × 10−6 V noise) when the room temperature is 310 K and the bandwidth is 1 kHz (i.e., 1000 Hz). What current noise would be produced by this resistor? 8. A 3-ma current flows through both a diode (i.e., a semiconductor) and a 20,000-Ω (i.e., 20-kΩ) resistor. What is the net current noise, in? Assume a bandwidth of 1 kHz (i.e., 1 × 103 Hz). Which of the two components is responsible for producing the most noise? 9. Determine if the two signals, x and y, in file correl1.mat are correlated by checking the angle between them. 10. Modify the approach used in Practice Problem 3 to find the angle between short signals: Do not attempt to plot these vectors as it would require a 6-dimensional plot!

Whatsapp +919911743277  
Name ____________________________________ Motion in 2D Simulation Go to http://phet.colorado.edu/simulations/sims.php?sim=Motion_in_2D and click on Run Now. 1) Once the simulation opens, click on ‘Show Both’ for Velocity and Acceleration at the top of the page. Now click and drag the red ball around the screen. Make 3 observations about the blue and green arrows (also called vectors) as you drag the ball around. 2) Which color vector (arrow) represents velocity and which one represents acceleration? How can you tell? 3) Try dragging the ball around and around in a circular path. What do you notice about the lengths and directions of the blue and green vectors? Describe their behavior in detail below. 4) Now move the ball at a slow constant speed across the screen. What do you notice now about the vectors? Explain why this happens. 5) What happens to the vectors when you jerk the ball rapidly back and forth across the screen? Explain why this happens. 6) Now click on ‘Circular’ on the bottom. Describe the motion of the ball and the behavior of the two vectors. Is there a force on the ball? How can you tell? Be detailed in your explanations. 7) Click on ‘Simple Harmonic’ on the bottom. Based on the behavior of the ball and the vectors, write a definition of Simple Harmonic Motion.

Name ____________________________________ Motion in 2D Simulation Go to http://phet.colorado.edu/simulations/sims.php?sim=Motion_in_2D and click on Run Now. 1) Once the simulation opens, click on ‘Show Both’ for Velocity and Acceleration at the top of the page. Now click and drag the red ball around the screen. Make 3 observations about the blue and green arrows (also called vectors) as you drag the ball around. 2) Which color vector (arrow) represents velocity and which one represents acceleration? How can you tell? 3) Try dragging the ball around and around in a circular path. What do you notice about the lengths and directions of the blue and green vectors? Describe their behavior in detail below. 4) Now move the ball at a slow constant speed across the screen. What do you notice now about the vectors? Explain why this happens. 5) What happens to the vectors when you jerk the ball rapidly back and forth across the screen? Explain why this happens. 6) Now click on ‘Circular’ on the bottom. Describe the motion of the ball and the behavior of the two vectors. Is there a force on the ball? How can you tell? Be detailed in your explanations. 7) Click on ‘Simple Harmonic’ on the bottom. Based on the behavior of the ball and the vectors, write a definition of Simple Harmonic Motion.

Name ____________________________________                                      Motion in 2D Simulation   Go to http://phet.colorado.edu/simulations/sims.php?sim=Motion_in_2D … Read More...