Engineering/Science and Public Policy Paper NOTE: This assignment is an individual Assignment. You could discuss with peers but your submission must reflect your opinions and be completed on your own words. As an engineer/scientist, public policies will directly impact virtually every issue of your professional life: design and construction, public safety, environmental quality, materials application – just to name a few. Appreciating the importance of this process will be a key factor to your success as an engineer/scientist. The purpose of this activity is to provide you with a better understanding of: • Public policy processes that impact engineers/scientist as they practice their profession • State and federal agencies and other legal authorities with jurisdiction over engineering/science matters • The role of engineers/scientist in creating technical solutions that benefit citizens and the environment. Assignment For one of the following four contemporary issues, do the following: a) Identify federal and state agencies / legal authority b) Discuss the engineering/scientific response c) Research codes & standards that are applicable or organizations that should oversee them d) Expand on the societal impact: cost vs. benefit Contemporary Issues for Assignment 1. Policy on Federal Reserve Bank’s Prime Interest Rate and Its Impact on Global Economy 2. Policy on Oil Price vs. Shale Gas/Oil and Its Impact on U.S. and Global Economy 3. Policy on Privacy/Security of Cloud Computing Systems and Its Impact 4. Policy on Biodiesel and Trends: Past, Present, and Future Guidelines a) The document should be in single space format. b) The minimum length is 500 words and the maximum length is 1000 words. c) List of references should be included in a separate page. Appropriate citations must appear in the body of the main document.

Engineering/Science and Public Policy Paper NOTE: This assignment is an individual Assignment. You could discuss with peers but your submission must reflect your opinions and be completed on your own words. As an engineer/scientist, public policies will directly impact virtually every issue of your professional life: design and construction, public safety, environmental quality, materials application – just to name a few. Appreciating the importance of this process will be a key factor to your success as an engineer/scientist. The purpose of this activity is to provide you with a better understanding of: • Public policy processes that impact engineers/scientist as they practice their profession • State and federal agencies and other legal authorities with jurisdiction over engineering/science matters • The role of engineers/scientist in creating technical solutions that benefit citizens and the environment. Assignment For one of the following four contemporary issues, do the following: a) Identify federal and state agencies / legal authority b) Discuss the engineering/scientific response c) Research codes & standards that are applicable or organizations that should oversee them d) Expand on the societal impact: cost vs. benefit Contemporary Issues for Assignment 1. Policy on Federal Reserve Bank’s Prime Interest Rate and Its Impact on Global Economy 2. Policy on Oil Price vs. Shale Gas/Oil and Its Impact on U.S. and Global Economy 3. Policy on Privacy/Security of Cloud Computing Systems and Its Impact 4. Policy on Biodiesel and Trends: Past, Present, and Future Guidelines a) The document should be in single space format. b) The minimum length is 500 words and the maximum length is 1000 words. c) List of references should be included in a separate page. Appropriate citations must appear in the body of the main document.

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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.

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Chapter 10 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A One-Dimensional Inelastic Collision Block 1, of mass = 3.70 , moves along a frictionless air track with speed = 15.0 . It collides with block 2, of mass = 19.0 , which was initially at rest. The blocks stick together after the collision. Part A Find the magnitude of the total initial momentum of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: m1 kg v1 m/s m2 kg pi

Chapter 10 Practice Problems (Practice – no credit) Due: 11:59pm on Friday, April 18, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy A One-Dimensional Inelastic Collision Block 1, of mass = 3.70 , moves along a frictionless air track with speed = 15.0 . It collides with block 2, of mass = 19.0 , which was initially at rest. The blocks stick together after the collision. Part A Find the magnitude of the total initial momentum of the two-block system. Express your answer numerically. You did not open hints for this part. ANSWER: m1 kg v1 m/s m2 kg pi

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Name___________________________________ Period_____ Investigation: Making Waves PART I: Objectives: • Learn vocabulary describing waves • Calculate the speed of a wave • Understand how amplitude affects the speed of a wave • Understand how frequency and wavelength affect the speed of a wave Open this web site: http://phet.colorado.edu/new/simulations/sims.php?sim=Wave_on_a_String You can click on Run Now! to run the simulation online, or Run Offline to save it to your desktop. It might run faster this way. Start by Wiggling the Wrench. Spend about 5 minutes experimenting with the Tension, Manual/Pulse/Oscillate, Fixed/Loose/No end, and changing the Amplitude, Frequency and Damping. Click on Show Rulers and Timer. Practice moving the rulers around and starting/resetting the timer. Click on the Pause/Play and Step buttons to see how they work. Use these settings: Pulse, Amplitude=50, Pulse Width=35, Damping=0, Tension at High and No End. NOTE that the amplitude is just a relative scale (not centimeters). Send a single pulse down the string. This is called a TRANSVERSE PULSE. Watch the motion of the green dots.  1. As the pulse goes by from left to right, in what direction does the string move? ________________________________________________________________________________________________________________________________________________  2. A definition of TRANSVERSE is “lying across”. Why is TRANSVERSE a good name for the wave you just observed? ________________________________________________________________________________________________________________________________________________ Make another pulse, and then PAUSE the wave. Use the vertical ruler to measure the amplitude of the wave in centimeters. This is the distance from the dotted orange line to the crest of the wave. Record the amplitude in Table 1 in the first row. Now, measure the time for a pulse to travel 100 cm. To do this: • Reset the clock to 0:00 and reset the generator • Click Pause/Play—it should say PAUSED on the screen • Click Pulse • Click Pause/Play again to start a timed pulse. Pause again just as the crest (peak) of the pulse touches the window 100 cm away. Record the time for a pulse to travel 100 cm in Table 1. Run 3 time trials, and record in the table. Calculate the average time. Now, measure the amplitude and timing of pulses for two other amplitudes (one smaller than 50, one larger than 50). Do three trials at each amplitude and calculate the average times. Calculate the average wave speed for each of the three amplitudes. See below for a sample calculation. Table 1 Your measured amplitude, cm Time for pulse to travel 100 cm, seconds Average time, seconds Speed=length of string / average time Example of speed calculation: Speed = string length/ average time Speed = 100 cm/2 seconds = 50 cm/second  3. How does the amplitude of a wave affect the speed of a wave? ________________________________________________________________________ Use these settings: Oscillate, Fixed end. Try amplitude=20, frequency=51, damping=0. The result is called a periodic wave. 4. Describe the appearance of the wave you created. ________________________________________________________________________________________________________________________________________________________________________________________________________________________ You should see waves that do not move along the string. You will also see points where the string does not move at all. These waves are called STANDING WAVES. The points where the wave doesn’t move are called NODES. Pause the simulation.  5. Draw the standing wave in the box below, labeling the AMPLITUDE, WAVELENGTH and NODES of a standing wave. Use these settings: Amplitude=20, Frequency=50, Damping=0, Oscillate, No End. Reset the clock. You can also measure the wave frequency. To do this, you should pair up with another student if possible. Watch the piston go up and down to make the wave. One up and down motion represents one wave. Use the clock to measure the time required for 10 complete cycles or waves. You will also need to PAUSE the wave to measure the wavelength of the wave in centimeters (cm). The frequency of the wave is calculated in the following way: Frequency = 10 waves/# seconds for 10 cycles For example, 10 waves/5 seconds = 2 cycles per second, or 2 Hertz. Make several waves by changing the wave frequency—use numbers over 30 on the scale. For each wave, measure the wavelength using the ruler. Now, calculate the frequency. See the example in the first row of Table 2. Record the wavelength and frequency of three waves with different wavelengths. Wavelength (cm) Frequency (cycles/second or Hertz) Speed (cm/s) = Wavelength x frequency 33 cm 10 waves/5.45 sec = 1.8 Hertz 33 cm x 1.8 Hertz = 59.4 cm/second Based on the equation used to calculate the speed of a wave, answer questions 6 and 7.  6. If you increase the wavelength of a wave, how does the speed change? ________________________________________________________________________________________________________________________________________________  7. If you increase the frequency of a wave, how does the speed change? ________________________________________________________________________________________________________________________________________________ Part II: Objectives: • Interpret a 2D top view picture of a wave • Identify areas of constructive and destructive interference in 2D • Predict the behavior of water, sound, or light when you have two sources o What will happen in constructive areas o What will happen in destructive areas 1) Open the “Wave Interference” simulation from the PhET website (in Sound & Waves) 2) On the water simulation, what does the crest (peak) of the wave look like in the top view? What does the trough look like? 3) When you add two drips, what changes about the waves’ patterns? 4) What does the wave look like in the area that the two waves constructively interfere? Describe both the top view and what the side view would look like. a. TOP: b. SIDE: 5) What does the wave look like in the area that the two waves destructively interfere? Describe both the top view and what the side view would look like. a. TOP: b. SIDE: 6) Switch to the sound simulation. a. What do you think will happen when you put two speakers next to each other? b. Why do you think this will happen? c. Try it (putting two speakers together) and tell me what happened. 7) Now switch to the light simulation. a. What do you think will happen when you put two light sources next to each other? b. Why do you think this will happen? c. Try it (putting two light sources together) and tell me what happened. d. What happens when you use one light source and two slits? 8) What is similar about all three of these simulations (i.e. water, sound & light)? 9) How do I know that these things are waves and not particles? (Think about what would happen in the two slit experiment if they were particles).

Name___________________________________ Period_____ Investigation: Making Waves PART I: Objectives: • Learn vocabulary describing waves • Calculate the speed of a wave • Understand how amplitude affects the speed of a wave • Understand how frequency and wavelength affect the speed of a wave Open this web site: http://phet.colorado.edu/new/simulations/sims.php?sim=Wave_on_a_String You can click on Run Now! to run the simulation online, or Run Offline to save it to your desktop. It might run faster this way. Start by Wiggling the Wrench. Spend about 5 minutes experimenting with the Tension, Manual/Pulse/Oscillate, Fixed/Loose/No end, and changing the Amplitude, Frequency and Damping. Click on Show Rulers and Timer. Practice moving the rulers around and starting/resetting the timer. Click on the Pause/Play and Step buttons to see how they work. Use these settings: Pulse, Amplitude=50, Pulse Width=35, Damping=0, Tension at High and No End. NOTE that the amplitude is just a relative scale (not centimeters). Send a single pulse down the string. This is called a TRANSVERSE PULSE. Watch the motion of the green dots.  1. As the pulse goes by from left to right, in what direction does the string move? ________________________________________________________________________________________________________________________________________________  2. A definition of TRANSVERSE is “lying across”. Why is TRANSVERSE a good name for the wave you just observed? ________________________________________________________________________________________________________________________________________________ Make another pulse, and then PAUSE the wave. Use the vertical ruler to measure the amplitude of the wave in centimeters. This is the distance from the dotted orange line to the crest of the wave. Record the amplitude in Table 1 in the first row. Now, measure the time for a pulse to travel 100 cm. To do this: • Reset the clock to 0:00 and reset the generator • Click Pause/Play—it should say PAUSED on the screen • Click Pulse • Click Pause/Play again to start a timed pulse. Pause again just as the crest (peak) of the pulse touches the window 100 cm away. Record the time for a pulse to travel 100 cm in Table 1. Run 3 time trials, and record in the table. Calculate the average time. Now, measure the amplitude and timing of pulses for two other amplitudes (one smaller than 50, one larger than 50). Do three trials at each amplitude and calculate the average times. Calculate the average wave speed for each of the three amplitudes. See below for a sample calculation. Table 1 Your measured amplitude, cm Time for pulse to travel 100 cm, seconds Average time, seconds Speed=length of string / average time Example of speed calculation: Speed = string length/ average time Speed = 100 cm/2 seconds = 50 cm/second  3. How does the amplitude of a wave affect the speed of a wave? ________________________________________________________________________ Use these settings: Oscillate, Fixed end. Try amplitude=20, frequency=51, damping=0. The result is called a periodic wave. 4. Describe the appearance of the wave you created. ________________________________________________________________________________________________________________________________________________________________________________________________________________________ You should see waves that do not move along the string. You will also see points where the string does not move at all. These waves are called STANDING WAVES. The points where the wave doesn’t move are called NODES. Pause the simulation.  5. Draw the standing wave in the box below, labeling the AMPLITUDE, WAVELENGTH and NODES of a standing wave. Use these settings: Amplitude=20, Frequency=50, Damping=0, Oscillate, No End. Reset the clock. You can also measure the wave frequency. To do this, you should pair up with another student if possible. Watch the piston go up and down to make the wave. One up and down motion represents one wave. Use the clock to measure the time required for 10 complete cycles or waves. You will also need to PAUSE the wave to measure the wavelength of the wave in centimeters (cm). The frequency of the wave is calculated in the following way: Frequency = 10 waves/# seconds for 10 cycles For example, 10 waves/5 seconds = 2 cycles per second, or 2 Hertz. Make several waves by changing the wave frequency—use numbers over 30 on the scale. For each wave, measure the wavelength using the ruler. Now, calculate the frequency. See the example in the first row of Table 2. Record the wavelength and frequency of three waves with different wavelengths. Wavelength (cm) Frequency (cycles/second or Hertz) Speed (cm/s) = Wavelength x frequency 33 cm 10 waves/5.45 sec = 1.8 Hertz 33 cm x 1.8 Hertz = 59.4 cm/second Based on the equation used to calculate the speed of a wave, answer questions 6 and 7.  6. If you increase the wavelength of a wave, how does the speed change? ________________________________________________________________________________________________________________________________________________  7. If you increase the frequency of a wave, how does the speed change? ________________________________________________________________________________________________________________________________________________ Part II: Objectives: • Interpret a 2D top view picture of a wave • Identify areas of constructive and destructive interference in 2D • Predict the behavior of water, sound, or light when you have two sources o What will happen in constructive areas o What will happen in destructive areas 1) Open the “Wave Interference” simulation from the PhET website (in Sound & Waves) 2) On the water simulation, what does the crest (peak) of the wave look like in the top view? What does the trough look like? 3) When you add two drips, what changes about the waves’ patterns? 4) What does the wave look like in the area that the two waves constructively interfere? Describe both the top view and what the side view would look like. a. TOP: b. SIDE: 5) What does the wave look like in the area that the two waves destructively interfere? Describe both the top view and what the side view would look like. a. TOP: b. SIDE: 6) Switch to the sound simulation. a. What do you think will happen when you put two speakers next to each other? b. Why do you think this will happen? c. Try it (putting two speakers together) and tell me what happened. 7) Now switch to the light simulation. a. What do you think will happen when you put two light sources next to each other? b. Why do you think this will happen? c. Try it (putting two light sources together) and tell me what happened. d. What happens when you use one light source and two slits? 8) What is similar about all three of these simulations (i.e. water, sound & light)? 9) How do I know that these things are waves and not particles? (Think about what would happen in the two slit experiment if they were particles).

. Imagine yourself teaching a carefully planned lesson. Do the activities you imagine doing with your students correlate to your own strengths? Why or why not?

. Imagine yourself teaching a carefully planned lesson. Do the activities you imagine doing with your students correlate to your own strengths? Why or why not?

In some instances the educator plans and teaches mini-lessons using … Read More...
1 ACTIVITY PURPOSE The purpose of this activity is to give you practice preparing a four-week work schedule. PROCESS Follow the steps listed below to prepare a schedule. 1. Read the Information Sheet: Scheduling Employees. 2. The pay week for this medical record service runs Sunday – Saturday. The pay period is two pay weeks. Each full-time employee cannot work more than 40 hours per pay week, or 80 hours per pay period. Each part-time employee works 20 hours per pay week – 40 hours per pay period. 3. The first Friday of the four – week period is a holiday. 4. The medical record service has 24 hour coverage, seven days a week. All full-time employees work a five day pay week, eight hours per day, with rotating weekend coverage. Part-time employees work four hours Monday – Friday, except for their rotation weekend. On those days they work an eight hour shift. Remember to adjust their time accordingly. 5. The Assistant Director and all supervisors, except the Tumor Registry Supervisor, should be scheduled for rotating weekend coverage. 2 6. All employees, except the Tumor Registry employees, should be scheduled on a rotating basis for weekend coverage. 7. For weekend and holiday coverage, there needs to be at least two clerks and one transcriptionist on days and evenings, one clerk and one transcriptionist at night. 8. The Department Director has scheduled a two – week vacation for the first two full weeks of the four – week schedule. 9. Employees who work holidays must take the holiday time within the pay period in which the holiday occurs. 10.Use the following marks on the schedule: X – work eight hours V – vacation H – holiday D – day off 4 – hours for part-time employees 3 PERSONNEL OF HUFFMAN MEMORIAL MEDICAL RECORD DEPARTMENT DAYS (7:00 A.M. – 3:30 P.M.) Director Diane Lucas Assistant Director JoAnn DeWitt Coding 1 Supervisor – Nina Long 3 Coding/PAS Clerks – Cheryl Newman Pam Rogers Janet Bennett Transcription 1 Supervisor – 6 Transcribers – Jessica DuBois Eileen Andrews Iris Williams Diane Henderson Vivian Thomas Lois Fisher Emma Daily Filing/Retrieval 1 Supervisor – 4 Clerks – 1 Part-time Clerk – Bill James Darlene Cook Janice Stivers Larry Patterson Don Williamson Susan Evanston Tumor Registry 1 Supervisor – 1 Clerk – 1 Part-time Clerk – Mabel Smith Pauline Erskine Suzanne Chapman EVENING (3:00 P.M. – 11:00 P.M.) Transcription 1 Part-time – Beth Richman Filing/Retrieval 1 Supervisor – 2 Clerks – 1 Part-time Clerk – Daniel Johnson Harry Skinner Matthew Scott Anne Madison NIGHTS (11:00 P.M. – 7:00 A.M.) Transcription 3 Transcribers – Louise Wilson Jane Matters Nancy Lipman Filing/Retrieval 2 Clerks – Lily Jamison Helen Benson 4 INFORMATION SHEET SCHEDULING EMPLOYEES In addition to the planning, organizing and controlling of a medical record service, managers must accurately plan the work pattern for employees. This plan must insure that all duties are adequately covered, all shifts have sufficient numbers of people to perform duties, and employees are given appropriate days off. Scheduling encompasses both short term and long term plans. Short term scheduling involves planning work on a daily and/or weekly basis. Long term scheduling generally covers a four – to six – week time period, as well as yearly planning for holidays. In larger health care facilities with the medical record service providing 24 hour service, seven days a week, advanced planning is a requisite to a smooth operation. In smaller facilities with shorter hours of service, the schedule is less complex. The number of employees needed for weekend work for those facilities open on weekends is totally dependent upon the weekend workload. A volume of seventy (70) to ninety (90) discharges per day generally requires two (2) medical record clerks to process those discharges, as well as to perform the other daily responsibilities of the medical record service. It is also advisable to schedule a supervisor during the weekend in the event that any problems arise which a clerk might not be able to handle (i.e. medico-legal questions, irate patients or physicians). If you work in a department that has an active work 5 measurement program, valuable scheduling information can be obtained from the data reported. In planning for holidays, it is important to remember to: 1. obtain employee preferences for which holidays they might choose to work; 2. keep track of who has worked which holidays; 3. if a holiday occurs on a Friday or a Monday and the employee must work on the holiday, try to give them a Friday or Monday off to compensate. It is important for you to be fair in terms of assigning employees weekend work and scheduling Holidays. Everyone should share the responsibility equally. If you have all supervisors work one weekend per month, then that schedule should be followed. If you have clerks working every other weekend, then that pattern should be followed consistently. When preparing a schedule it is best to put in all the “givens” first. For example, if you have vacations scheduled for the four weeks you’re preparing, then those should be marked in first. Also included in this category would be employees who do not work weekends (i.e. personnel in the Tumor Registry). Once all work times have been scheduled, you must be certain that an employee receives two (2) days off for every seven (7) days. If an employee works more than forty (40) hours in one (1) week, the facility must pat time-an-a-half for all hours over forty. Some facilities are experimenting with a variety of scheduling techniques: flex time and the four-day work week. Both techniques have been 6 heavily debated. The final questions regarding these nontraditional alternatives end up being: 1. Are your employees willing to try it? 2. Are you ready to handle the extra planning these alternatives may warrant? 3. Do you have the necessary resources, including equipment, to accommodate a nontraditional scheduling alternative? 4. Will administrator of the facility support your proposal? Once you have established answers to those questions you are ready to embark on a new technique of scheduling. Scheduling employees can be one of the most challenging tasks that a manager faces. Whether you elect to try one of the nontraditional alternatives or use the five-day work week, the manager must: 1. be fair; 2. apply all guidelines to every employee consistently 3. utilize all available data to arrive at appropriate numbers for weekend and holiday staffing requirements; and 4. maximize the utilization of equipment and resources.

1 ACTIVITY PURPOSE The purpose of this activity is to give you practice preparing a four-week work schedule. PROCESS Follow the steps listed below to prepare a schedule. 1. Read the Information Sheet: Scheduling Employees. 2. The pay week for this medical record service runs Sunday – Saturday. The pay period is two pay weeks. Each full-time employee cannot work more than 40 hours per pay week, or 80 hours per pay period. Each part-time employee works 20 hours per pay week – 40 hours per pay period. 3. The first Friday of the four – week period is a holiday. 4. The medical record service has 24 hour coverage, seven days a week. All full-time employees work a five day pay week, eight hours per day, with rotating weekend coverage. Part-time employees work four hours Monday – Friday, except for their rotation weekend. On those days they work an eight hour shift. Remember to adjust their time accordingly. 5. The Assistant Director and all supervisors, except the Tumor Registry Supervisor, should be scheduled for rotating weekend coverage. 2 6. All employees, except the Tumor Registry employees, should be scheduled on a rotating basis for weekend coverage. 7. For weekend and holiday coverage, there needs to be at least two clerks and one transcriptionist on days and evenings, one clerk and one transcriptionist at night. 8. The Department Director has scheduled a two – week vacation for the first two full weeks of the four – week schedule. 9. Employees who work holidays must take the holiday time within the pay period in which the holiday occurs. 10.Use the following marks on the schedule: X – work eight hours V – vacation H – holiday D – day off 4 – hours for part-time employees 3 PERSONNEL OF HUFFMAN MEMORIAL MEDICAL RECORD DEPARTMENT DAYS (7:00 A.M. – 3:30 P.M.) Director Diane Lucas Assistant Director JoAnn DeWitt Coding 1 Supervisor – Nina Long 3 Coding/PAS Clerks – Cheryl Newman Pam Rogers Janet Bennett Transcription 1 Supervisor – 6 Transcribers – Jessica DuBois Eileen Andrews Iris Williams Diane Henderson Vivian Thomas Lois Fisher Emma Daily Filing/Retrieval 1 Supervisor – 4 Clerks – 1 Part-time Clerk – Bill James Darlene Cook Janice Stivers Larry Patterson Don Williamson Susan Evanston Tumor Registry 1 Supervisor – 1 Clerk – 1 Part-time Clerk – Mabel Smith Pauline Erskine Suzanne Chapman EVENING (3:00 P.M. – 11:00 P.M.) Transcription 1 Part-time – Beth Richman Filing/Retrieval 1 Supervisor – 2 Clerks – 1 Part-time Clerk – Daniel Johnson Harry Skinner Matthew Scott Anne Madison NIGHTS (11:00 P.M. – 7:00 A.M.) Transcription 3 Transcribers – Louise Wilson Jane Matters Nancy Lipman Filing/Retrieval 2 Clerks – Lily Jamison Helen Benson 4 INFORMATION SHEET SCHEDULING EMPLOYEES In addition to the planning, organizing and controlling of a medical record service, managers must accurately plan the work pattern for employees. This plan must insure that all duties are adequately covered, all shifts have sufficient numbers of people to perform duties, and employees are given appropriate days off. Scheduling encompasses both short term and long term plans. Short term scheduling involves planning work on a daily and/or weekly basis. Long term scheduling generally covers a four – to six – week time period, as well as yearly planning for holidays. In larger health care facilities with the medical record service providing 24 hour service, seven days a week, advanced planning is a requisite to a smooth operation. In smaller facilities with shorter hours of service, the schedule is less complex. The number of employees needed for weekend work for those facilities open on weekends is totally dependent upon the weekend workload. A volume of seventy (70) to ninety (90) discharges per day generally requires two (2) medical record clerks to process those discharges, as well as to perform the other daily responsibilities of the medical record service. It is also advisable to schedule a supervisor during the weekend in the event that any problems arise which a clerk might not be able to handle (i.e. medico-legal questions, irate patients or physicians). If you work in a department that has an active work 5 measurement program, valuable scheduling information can be obtained from the data reported. In planning for holidays, it is important to remember to: 1. obtain employee preferences for which holidays they might choose to work; 2. keep track of who has worked which holidays; 3. if a holiday occurs on a Friday or a Monday and the employee must work on the holiday, try to give them a Friday or Monday off to compensate. It is important for you to be fair in terms of assigning employees weekend work and scheduling Holidays. Everyone should share the responsibility equally. If you have all supervisors work one weekend per month, then that schedule should be followed. If you have clerks working every other weekend, then that pattern should be followed consistently. When preparing a schedule it is best to put in all the “givens” first. For example, if you have vacations scheduled for the four weeks you’re preparing, then those should be marked in first. Also included in this category would be employees who do not work weekends (i.e. personnel in the Tumor Registry). Once all work times have been scheduled, you must be certain that an employee receives two (2) days off for every seven (7) days. If an employee works more than forty (40) hours in one (1) week, the facility must pat time-an-a-half for all hours over forty. Some facilities are experimenting with a variety of scheduling techniques: flex time and the four-day work week. Both techniques have been 6 heavily debated. The final questions regarding these nontraditional alternatives end up being: 1. Are your employees willing to try it? 2. Are you ready to handle the extra planning these alternatives may warrant? 3. Do you have the necessary resources, including equipment, to accommodate a nontraditional scheduling alternative? 4. Will administrator of the facility support your proposal? Once you have established answers to those questions you are ready to embark on a new technique of scheduling. Scheduling employees can be one of the most challenging tasks that a manager faces. Whether you elect to try one of the nontraditional alternatives or use the five-day work week, the manager must: 1. be fair; 2. apply all guidelines to every employee consistently 3. utilize all available data to arrive at appropriate numbers for weekend and holiday staffing requirements; and 4. maximize the utilization of equipment and resources.

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

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