After reading the supplement article on Business Analytics linked to the week 1 schedule, write an essay on how business analytics impacts you today, or its potential role in your chosen career path. Do research for your paper, or interview someone who works in your area. The goals of this paper are two-fold: (1) focus on high quality writing, using the COBE Writing Styles Guide for writing help and citations. (2) consider the importance of BI from a personal/work/career perspective.

After reading the supplement article on Business Analytics linked to the week 1 schedule, write an essay on how business analytics impacts you today, or its potential role in your chosen career path. Do research for your paper, or interview someone who works in your area. The goals of this paper are two-fold: (1) focus on high quality writing, using the COBE Writing Styles Guide for writing help and citations. (2) consider the importance of BI from a personal/work/career perspective.

  Business analytics importance and its potential     Introduction … Read More...
one page summary for osh (Occupational safety and health (OSH) also commonly referred to as occupational health and safety (OHS) or workplace health and safety (WHS) is an area concerned with the safety, health and welfare of people engaged in work or employment.) . The questions are 1. What happened? 2. Why it happened? 3. What could be done so it does not happen again?

one page summary for osh (Occupational safety and health (OSH) also commonly referred to as occupational health and safety (OHS) or workplace health and safety (WHS) is an area concerned with the safety, health and welfare of people engaged in work or employment.) . The questions are 1. What happened? 2. Why it happened? 3. What could be done so it does not happen again?

one page summary for osh (Occupational safety and health (OSH) … Read More...
1. The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.2 seconds and a standard deviation of 0.1 seconds. 1‐1. (2 points) What is the probability that a reaction requires more than 0.5 seconds? 1‐2. (2 points) What is the probability that a reaction requires between 0.4 and 0.5 seconds? 1‐3. (2 points) What is the reaction time that is exceeded 95% of the time? 2. Spherical Uniform Distribution (Google! You do not have to explain why): 2‐1. (2 points) How can we pick a set of random points uniformly distributed on the unit circle x12 + x 2=1? 2‐2. (2 points) How can we pick a set of random points uniformly distributed on the 4‐dimensional unit 2 2 2 2 2 sphere x1 + x2 + x3 + x4 + x5 =1? 3. The random variable X has a binomial distribution with n = 19 and p = 0.4. Determine the following probabilities. (You may use computer. But, you have to show the formula.) 3‐1. (2 points) P(X ≤ 12) 3‐2. (2 points) P(X ≥ 18) 3‐3. (2 points) P(13 ≤ X < 15) 4. (2 points) Show the mean and the variance of the triangular distribution with lower limit a, upper limit b and mode c, where a < b and a ≤ c ≤ b. (You must show why.) 5. (2 points) An electronic office product contains 5000 electronic components. Assume that the probability that each component operates without failure during the useful life of the product is 0.999, and assume that the components fail independently. Approximate the probability that 10 or more of the original 5000 components fail during the useful life of the product. 6. Consider the following system made up of functional components in parallel and series. C2 0.80 C1 0.90 C4 0.95 C3 0.85 6‐1. (2 points) What is the probability that the system operates? 6‐2. (2 points) What is the probability that the system fails due to the components in series? Assume parallel components do not fail. 6‐3. (2 points) What is the probability that the system fails due to the components in parallel? Assume series components do not fail. 6‐4. (2 points) Compute and compare the probabilities that the system fails when the probability that component C1 functions is improved to a value of 0.95 and when the probability that component C2 functions is improved to a value of 0.85. Which improvement increases the system reliability more? 7. (2 points) Suppose that the joint distribution of X and Y has probability density function f(x, y) = 0.25xy for 0 < x < 2 and 0 < y < 2. Compute V(2X + 3Y). (Show all your work.)

1. The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.2 seconds and a standard deviation of 0.1 seconds. 1‐1. (2 points) What is the probability that a reaction requires more than 0.5 seconds? 1‐2. (2 points) What is the probability that a reaction requires between 0.4 and 0.5 seconds? 1‐3. (2 points) What is the reaction time that is exceeded 95% of the time? 2. Spherical Uniform Distribution (Google! You do not have to explain why): 2‐1. (2 points) How can we pick a set of random points uniformly distributed on the unit circle x12 + x 2=1? 2‐2. (2 points) How can we pick a set of random points uniformly distributed on the 4‐dimensional unit 2 2 2 2 2 sphere x1 + x2 + x3 + x4 + x5 =1? 3. The random variable X has a binomial distribution with n = 19 and p = 0.4. Determine the following probabilities. (You may use computer. But, you have to show the formula.) 3‐1. (2 points) P(X ≤ 12) 3‐2. (2 points) P(X ≥ 18) 3‐3. (2 points) P(13 ≤ X < 15) 4. (2 points) Show the mean and the variance of the triangular distribution with lower limit a, upper limit b and mode c, where a < b and a ≤ c ≤ b. (You must show why.) 5. (2 points) An electronic office product contains 5000 electronic components. Assume that the probability that each component operates without failure during the useful life of the product is 0.999, and assume that the components fail independently. Approximate the probability that 10 or more of the original 5000 components fail during the useful life of the product. 6. Consider the following system made up of functional components in parallel and series. C2 0.80 C1 0.90 C4 0.95 C3 0.85 6‐1. (2 points) What is the probability that the system operates? 6‐2. (2 points) What is the probability that the system fails due to the components in series? Assume parallel components do not fail. 6‐3. (2 points) What is the probability that the system fails due to the components in parallel? Assume series components do not fail. 6‐4. (2 points) Compute and compare the probabilities that the system fails when the probability that component C1 functions is improved to a value of 0.95 and when the probability that component C2 functions is improved to a value of 0.85. Which improvement increases the system reliability more? 7. (2 points) Suppose that the joint distribution of X and Y has probability density function f(x, y) = 0.25xy for 0 < x < 2 and 0 < y < 2. Compute V(2X + 3Y). (Show all your work.)

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Homework 4 – Construction and Water Management 80 points total Refer to Lecture 6a – Construction Part I, 6b – Construction Part II, and Chapter 6 in your textbook. 1. What is the difference between an owner, a design professional, and a constructor? (6 points) 2. Briefly explain the process of ‘Design-bid-build’ construction. How is it different than a ‘design-build’ type of project? (6 points) 3. Describe, in at least one sentence, the main function of the following construction equipment (2 points each): a. Crane b. Skidsteer c. Excavator d. Backhoe e. Grader f. Pile driver 4. What are 5 major components of a construction staging plan? (5 points) 5. What are 5 administrative controls used for environmental management on a construction site? (For example: protecting native plants) (5 points) 6. Explain the major differences between scaffolding, falsework, and formwork. (6 points) Refer to Lecture 7a, slides 11, 12, & 13 and pages 165-166 in your textbook for background information on using the Rational Method for flowrate calculations. 7. The Bush library park is planted with native grasses and is 15 acres in size. Assume the drainage system was designed to handle a 1-hour storm of 100-year-storm magnitude. The intensity data for different storm events for Dallas County can be found in this document, on page 6: http://iswm.nctcog.org/Documents/archives/site_development_manual/Appendices.pdf a. What is the expected flowrate for the native park area, calculated using the Rational Method? The runoff coefficient for the park can be approximated as 0.10. (6 points) b. What would be the design flowrate if they had paved over the area to create a large parking lot, instead of the park? Assume the runoff coefficient of concrete to be 0.92. (6 points) 8. Refer to page 94 in your textbook. What are four common urban stormwater pollutants and their possible sources? What are the possible impacts from each pollutant to receiving waters? (12 points) Refer to slides 6, 7, and 8 of Lecture 7b, and your in-class assignment for the following question. 9. What is the horizontal pressure force from water stored behind a dam wall if the dam is filled to capacity at 425ft? How high up from the bottom of the dam does the force act? (10 points) Read the following article and answer the question below: http://news.nationalgeographic.com/news/2006/06/060609-gorges-dam_2.html 10. What are three negative environmental, social, or political impacts in China from the Three Gorges Dam? What are three positive impacts? (6 points)

Homework 4 – Construction and Water Management 80 points total Refer to Lecture 6a – Construction Part I, 6b – Construction Part II, and Chapter 6 in your textbook. 1. What is the difference between an owner, a design professional, and a constructor? (6 points) 2. Briefly explain the process of ‘Design-bid-build’ construction. How is it different than a ‘design-build’ type of project? (6 points) 3. Describe, in at least one sentence, the main function of the following construction equipment (2 points each): a. Crane b. Skidsteer c. Excavator d. Backhoe e. Grader f. Pile driver 4. What are 5 major components of a construction staging plan? (5 points) 5. What are 5 administrative controls used for environmental management on a construction site? (For example: protecting native plants) (5 points) 6. Explain the major differences between scaffolding, falsework, and formwork. (6 points) Refer to Lecture 7a, slides 11, 12, & 13 and pages 165-166 in your textbook for background information on using the Rational Method for flowrate calculations. 7. The Bush library park is planted with native grasses and is 15 acres in size. Assume the drainage system was designed to handle a 1-hour storm of 100-year-storm magnitude. The intensity data for different storm events for Dallas County can be found in this document, on page 6: http://iswm.nctcog.org/Documents/archives/site_development_manual/Appendices.pdf a. What is the expected flowrate for the native park area, calculated using the Rational Method? The runoff coefficient for the park can be approximated as 0.10. (6 points) b. What would be the design flowrate if they had paved over the area to create a large parking lot, instead of the park? Assume the runoff coefficient of concrete to be 0.92. (6 points) 8. Refer to page 94 in your textbook. What are four common urban stormwater pollutants and their possible sources? What are the possible impacts from each pollutant to receiving waters? (12 points) Refer to slides 6, 7, and 8 of Lecture 7b, and your in-class assignment for the following question. 9. What is the horizontal pressure force from water stored behind a dam wall if the dam is filled to capacity at 425ft? How high up from the bottom of the dam does the force act? (10 points) Read the following article and answer the question below: http://news.nationalgeographic.com/news/2006/06/060609-gorges-dam_2.html 10. What are three negative environmental, social, or political impacts in China from the Three Gorges Dam? What are three positive impacts? (6 points)

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Assignment 8 Due: 11:59pm on Friday, April 4, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 10.3 Part A If a particle’s speed increases by a factor of 5, by what factor does its kinetic energy change? ANSWER: Correct Conceptual Question 10.11 A spring is compressed 1.5 . Part A How far must you compress a spring with twice the spring constant to store the same amount of energy? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct = 25 K2 K1 cm x = 1.1 cm Problem 10.2 The lowest point in Death Valley is below sea level. The summit of nearby Mt. Whitney has an elevation of 4420 . Part A What is the change in potential energy of an energetic 80 hiker who makes it from the floor of Death Valley to the top of Mt.Whitney? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 10.3 Part A At what speed does a 1800 compact car have the same kinetic energy as a 1.80×104 truck going 21.0 ? Express your answer with the appropriate units. ANSWER: Correct Problem 10.5 A boy reaches out of a window and tosses a ball straight up with a speed of 13 . The ball is 21 above the ground as he releases it. 85m m kg U = 3.5×106 J kg kg km/hr vc = 66.4 km hr m/s m Part A Use energy to find the ball’s maximum height above the ground. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Use energy to find the ball’s speed as it passes the window on its way down. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C Use energy to find the speed of impact on the ground. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Hmax = 30 m v = 13 ms v = 24 ms Problem 10.8 A 59.0 skateboarder wants to just make it to the upper edge of a “quarter pipe,” a track that is one-quarter of a circle with a radius of 2.30 . Part A What speed does he need at the bottom? Express your answer with the appropriate units. ANSWER: Correct Problem 10.12 A 1500 car traveling at 12 suddenly runs out of gas while approaching the valley shown in the figure. The alert driver immediately puts the car in neutral so that it will roll. Part A kg m 6.71 ms kg m/s What will be the car’s speed as it coasts into the gas station on the other side of the valley? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Ups and Downs Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational field of the earth. In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy. In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The energy transformations that take place involve the object’s kinetic energy and its gravitational potential energy . The law of conservation of energy for such cases implies that the sum of the object’s kinetic energy and potential energy does not change with time. This idea can be expressed by the equation , where “i” denotes the “initial” moment and “f” denotes the “final” moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem. First, let us consider an object launched vertically upward with an initial speed . Neglect air resistance. Part A As the projectile goes upward, what energy changes take place? ANSWER: v = 6.8 ms K = (1/2)mv2 U = mgh Ki + Ui = Kf + Uf v Correct Part B At the top point of the flight, what can be said about the projectile’s kinetic and potential energy? ANSWER: Correct Strictly speaking, it is not the ball that possesses potential energy; rather, it is the system “Earth-ball.” Although we will often talk about “the gravitational potential energy of an elevated object,” it is useful to keep in mind that the energy, in fact, is associated with the interactions between the earth and the elevated object. Part C The potential energy of the object at the moment of launch __________. ANSWER: Both kinetic and potential energy decrease. Both kinetic and potential energy increase. Kinetic energy decreases; potential energy increases. Kinetic energy increases; potential energy decreases. Both kinetic and potential energy are at their maximum values. Both kinetic and potential energy are at their minimum values. Kinetic energy is at a maximum; potential energy is at a minimum. Kinetic energy is at a minimum; potential energy is at a maximum. Correct Usually, the zero level is chosen so as to make the relevant calculations simpler. In this case, it makes good sense to assume that at the ground level–but this is not, by any means, the only choice! Part D Using conservation of energy, find the maximum height to which the object will rise. Express your answer in terms of and the magnitude of the acceleration of gravity . ANSWER: Correct You may remember this result from kinematics. It is comforting to know that our new approach yields the same answer. Part E At what height above the ground does the projectile have a speed of ? Express your answer in terms of and the magnitude of the acceleration of gravity . ANSWER: is negative is positive is zero depends on the choice of the “zero level” of potential energy U = 0 hmax v g hmax = v2 2g h 0.5v v g h = 3 v2 8g Correct Part F What is the speed of the object at the height of ? Express your answer in terms of and . Use three significant figures in the numeric coefficient. Hint 1. How to approach the problem You are being asked for the speed at half of the maximum height. You know that at the initial height ( ), the speed is . All of the energy is kinetic energy, and so, the total energy is . At the maximum height, all of the energy is potential energy. Since the gravitational potential energy is proportional to , half of the initial kinetic energy must have been converted to potential energy when the projectile is at . Thus, the kinetic energy must be half of its original value (i.e., when ). You need to determine the speed, as a multiple of , that corresponds to such a kinetic energy. ANSWER: Correct Let us now consider objects launched at an angle. For such situations, using conservation of energy leads to a quicker solution than can be produced by kinematics. Part G A ball is launched as a projectile with initial speed at an angle above the horizontal. Using conservation of energy, find the maximum height of the ball’s flight. Express your answer in terms of , , and . Hint 1. Find the final kinetic energy Find the final kinetic energy of the ball. Here, the best choice of “final” moment is the point at which the ball reaches its maximum height, since this is the point we are interested in. u (1/2)hmax v g h = 0 v (1/2)mv2 h (1/2)hmax (1/4)mv2 h = (1/2)hmax v u = 0.707v v hmax v g Kf Express your answer in terms of , , and . Hint 1. Find the speed at the maximum height The speed of the ball at the maximum height is __________. ANSWER: ANSWER: ANSWER: Correct Part H A ball is launched with initial speed from ground level up a frictionless slope. The slope makes an angle with the horizontal. Using conservation of energy, find the maximum vertical height to which the ball will climb. Express your answer in terms of , , and . You may or may not use all of these quantities. v m 0 v v cos v sin v tan Kf = 0.5m(vcos( ))2 hmax = (vsin( ))2 2g v hmax v g ANSWER: Correct Interestingly, the answer does not depend on . The difference between this situation and the projectile case is that the ball moving up a slope has no kinetic energy at the top of its trajectory whereas the projectile launched at an angle does. Part I A ball is launched with initial speed from the ground level up a frictionless hill. The hill becomes steeper as the ball slides up; however, the ball remains in contact with the hill at all times. Using conservation of energy, find the maximum vertical height to which the ball will climb. Express your answer in terms of and . ANSWER: Correct The profile of the hill does not matter; the equation would have the same terms regardless of the steepness of the hill. Problem 10.14 A 12- -long spring is attached to the ceiling. When a 2.2 mass is hung from it, the spring stretches to a length of 17 . Part A What is the spring constant ? Express your answer to two significant figures and include the appropriate units. hmax = v2 2g v hmax v g hmax = v2 2g Ki + Ui = Kf + Uf cm kg cm k ANSWER: Correct Part B How long is the spring when a 3.0 mass is suspended from it? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 10.17 A 6.2 mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in . You may want to review ( pages 255 – 257) . For help with math skills, you may want to review: Solving Algebraic Equations = 430 k Nm kg y = 19 cm kg Part A What does the spring scale read just before the mass touches the lower spring? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces acting on the mass before it touches the scale. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? ANSWER: Correct Part B The scale reads 22 when the lower spring has been compressed by 2.7 . What is the value of the spring constant for the lower spring? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces acting on the mass. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? Use these to determine the force on the mass by the spring, taking note of the directions from your picture. How is the spring constant related to the force by the spring and the compression of the spring? Check your units. ANSWER: F = 61 N N cm k = 1400 k Nm Correct Part C At what compression length will the scale read zero? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces on the mass. When the scale reads zero, what is the force on the mass due to the scale? What is the gravitational force on the mass? What is the force on the mass by the spring? How is the compression length related to the force by the spring and the spring constant? Check your units. ANSWER: Correct Problem 10.18 Part A How far must you stretch a spring with = 800 to store 180 of energy? Express your answer to two significant figures and include the appropriate units. ANSWER: y = 4.2 cm k N/m J Correct Problem 10.22 A 15 runaway grocery cart runs into a spring with spring constant 230 and compresses it by 57 . Part A What was the speed of the cart just before it hit the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Spring Gun A spring-loaded toy gun is used to shoot a ball straight up in the air. The ball reaches a maximum height , measured from the equilibrium position of the spring. s = 0.67 m kg N/m cm v = 2.2 ms H Part A The same ball is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the ball go this time? Neglect friction. Assume that the spring is ideal and that the distance by which the spring is compressed is negligible compared to . Hint 1. Potential energy of the spring The potential energy of a spring is proportional to the square of the distance the spring is compressed. The spring was compressed half the distance, so the mass, when launched, has one quarter of the energy as in the first trial. Hint 2. Potential energy of the ball At the highest point in the ball’s trajectory, all of the spring’s potential energy has been converted into gravitational potential energy of the ball. ANSWER: Correct A Bullet Is Fired into a Wooden Block A bullet of mass is fired horizontally with speed at a wooden block of mass resting on a frictionless table. The bullet hits the block and becomes completely embedded within it. After the bullet has come to rest within the block, the block, with the bullet in it, is traveling at speed . H height = H 4 mb vi mw vf Part A Which of the following best describes this collision? Hint 1. Types of collisions An inelastic collision is a collision in which kinetic energy is not conserved. In a partially inelastic collision, kinetic energy is lost, but the objects colliding do not stick together. From this information, you can infer what completely inelastic and elastic collisions are. ANSWER: Correct Part B Which of the following quantities, if any, are conserved during this collision? Hint 1. When is kinetic energy conserved? Kinetic energy is conserved only in perfectly elastic collisions. ANSWER: perfectly elastic partially inelastic perfectly inelastic Correct Part C What is the speed of the block/bullet system after the collision? Express your answer in terms of , , and . Hint 1. Find the momentum after the collision What is the total momentum of the block/bullet system after the collision? Express your answer in terms of and other given quantities. ANSWER: Hint 2. Use conservation of momentum The momentum of the block/bullet system is conserved. Therefore, the momentum before the collision is the same as the momentum after the collision. Find a second expression for , this time expressed as the total momentum of the system before the collision. Express your answer in terms of and other given quantities. ANSWER: kinetic energy only momentum only kinetic energy and momentum neither momentum nor kinetic energy vi mw mb ptotal vf ptotal = (mw + mb)vf ptotal vi ptotal = mbvi ANSWER: Correct Problem 10.31 Ball 1, with a mass of 150 and traveling at 15.0 , collides head on with ball 2, which has a mass of 340 and is initially at rest. Part A What are the final velocities of each ball if the collision is perfectly elastic? Express your answer with the appropriate units. ANSWER: Correct Part B Express your answer with the appropriate units. ANSWER: Correct Part C vf = mb vi mb+mw g m/s g (vfx) = -5.82 1 ms (vfx) = 9.18 2 ms What are the final velocities of each ball if the collision is perfectly inelastic? Express your answer with the appropriate units. ANSWER: Correct Part D Express your answer with the appropriate units. ANSWER: Correct Enhanced EOC: Problem 10.43 A package of mass is released from rest at a warehouse loading dock and slides down the = 2.2 – high, frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass , from the bottom of the chute. You may want to review ( pages 265 – 269) . For help with math skills, you may want to review: Solving Algebraic Equations (vfx) = 4.59 1 ms (vfx) = 4.59 2 ms m h m 2m Part A Suppose the packages stick together. What is their common speed after the collision? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem There are two parts to this problem: the block sliding down the frictionless incline and the collision. What conservation laws are valid in each part? In terms of , what are the kinetic and potential energies of the block at the top of the incline? What is the potential energy of the same block at the bottom just before the collision? What are the kinetic energy and velocity of block just before the collision? What is conserved during the collision? What is the total momentum of the two blocks before the collision? What is the momentum of the two blocks stuck together after the collision? What is the velocity of the two blocks after the collision? ANSWER: Correct Part B Suppose the collision between the packages is perfectly elastic. To what height does the package of mass rebound? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem There are three parts to this problem: the block sliding down the incline, the collision, and mass going back up the incline. What conservation laws are valid in each part? m m v = 2.2 ms m m What is an elastic collision? For an elastic collision, how are the initial and final velocities related when one of the masses is initially at rest? Using the velocity of just before the collision from Part A, what is the velocity of just after the collision in this case? What are the kinetic and potential energies of mass just after the collision? What is the kinetic energy of mass at its maximum rebound height? Using conservation of energy, what is the potential energy of mass at its maximum height? What is the maximum height? ANSWER: Correct Problem 10.35 A cannon tilted up at a 35.0 angle fires a cannon ball at 79.0 from atop a 21.0 -high fortress wall. Part A What is the ball’s impact speed on the ground below? Express your answer with the appropriate units. ANSWER: Correct Problem 10.45 A 1000 safe is 2.5 above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 48 . m m m m m h = 24 cm $ m/s m vf = 81.6 ms kg m cm Part A What is the spring constant of the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 10.49 A 100 block on a frictionless table is firmly attached to one end of a spring with = 21 . The other end of the spring is anchored to the wall. A 30 ball is thrown horizontally toward the block with a speed of 6.0 . Part A If the collision is perfectly elastic, what is the ball’s speed immediately after the collision? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the maximum compression of the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: = 2.5×105 k Nm g k N/m g m/s v = 3.2 ms Correct Part C Repeat part A for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D Repeat part B for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 99.4%. You received 120.28 out of a possible total of 121 points. x = 0.19 m v = 1.4 ms x = 0.11 m

Assignment 8 Due: 11:59pm on Friday, April 4, 2014 You will receive no credit for items you complete after the assignment is due. Grading Policy Conceptual Question 10.3 Part A If a particle’s speed increases by a factor of 5, by what factor does its kinetic energy change? ANSWER: Correct Conceptual Question 10.11 A spring is compressed 1.5 . Part A How far must you compress a spring with twice the spring constant to store the same amount of energy? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct = 25 K2 K1 cm x = 1.1 cm Problem 10.2 The lowest point in Death Valley is below sea level. The summit of nearby Mt. Whitney has an elevation of 4420 . Part A What is the change in potential energy of an energetic 80 hiker who makes it from the floor of Death Valley to the top of Mt.Whitney? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 10.3 Part A At what speed does a 1800 compact car have the same kinetic energy as a 1.80×104 truck going 21.0 ? Express your answer with the appropriate units. ANSWER: Correct Problem 10.5 A boy reaches out of a window and tosses a ball straight up with a speed of 13 . The ball is 21 above the ground as he releases it. 85m m kg U = 3.5×106 J kg kg km/hr vc = 66.4 km hr m/s m Part A Use energy to find the ball’s maximum height above the ground. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B Use energy to find the ball’s speed as it passes the window on its way down. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part C Use energy to find the speed of impact on the ground. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Hmax = 30 m v = 13 ms v = 24 ms Problem 10.8 A 59.0 skateboarder wants to just make it to the upper edge of a “quarter pipe,” a track that is one-quarter of a circle with a radius of 2.30 . Part A What speed does he need at the bottom? Express your answer with the appropriate units. ANSWER: Correct Problem 10.12 A 1500 car traveling at 12 suddenly runs out of gas while approaching the valley shown in the figure. The alert driver immediately puts the car in neutral so that it will roll. Part A kg m 6.71 ms kg m/s What will be the car’s speed as it coasts into the gas station on the other side of the valley? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Ups and Downs Learning Goal: To apply the law of conservation of energy to an object launched upward in the gravitational field of the earth. In the absence of nonconservative forces such as friction and air resistance, the total mechanical energy in a closed system is conserved. This is one particular case of the law of conservation of energy. In this problem, you will apply the law of conservation of energy to different objects launched from the earth. The energy transformations that take place involve the object’s kinetic energy and its gravitational potential energy . The law of conservation of energy for such cases implies that the sum of the object’s kinetic energy and potential energy does not change with time. This idea can be expressed by the equation , where “i” denotes the “initial” moment and “f” denotes the “final” moment. Since any two moments will work, the choice of the moments to consider is, technically, up to you. That choice, though, is usually suggested by the question posed in the problem. First, let us consider an object launched vertically upward with an initial speed . Neglect air resistance. Part A As the projectile goes upward, what energy changes take place? ANSWER: v = 6.8 ms K = (1/2)mv2 U = mgh Ki + Ui = Kf + Uf v Correct Part B At the top point of the flight, what can be said about the projectile’s kinetic and potential energy? ANSWER: Correct Strictly speaking, it is not the ball that possesses potential energy; rather, it is the system “Earth-ball.” Although we will often talk about “the gravitational potential energy of an elevated object,” it is useful to keep in mind that the energy, in fact, is associated with the interactions between the earth and the elevated object. Part C The potential energy of the object at the moment of launch __________. ANSWER: Both kinetic and potential energy decrease. Both kinetic and potential energy increase. Kinetic energy decreases; potential energy increases. Kinetic energy increases; potential energy decreases. Both kinetic and potential energy are at their maximum values. Both kinetic and potential energy are at their minimum values. Kinetic energy is at a maximum; potential energy is at a minimum. Kinetic energy is at a minimum; potential energy is at a maximum. Correct Usually, the zero level is chosen so as to make the relevant calculations simpler. In this case, it makes good sense to assume that at the ground level–but this is not, by any means, the only choice! Part D Using conservation of energy, find the maximum height to which the object will rise. Express your answer in terms of and the magnitude of the acceleration of gravity . ANSWER: Correct You may remember this result from kinematics. It is comforting to know that our new approach yields the same answer. Part E At what height above the ground does the projectile have a speed of ? Express your answer in terms of and the magnitude of the acceleration of gravity . ANSWER: is negative is positive is zero depends on the choice of the “zero level” of potential energy U = 0 hmax v g hmax = v2 2g h 0.5v v g h = 3 v2 8g Correct Part F What is the speed of the object at the height of ? Express your answer in terms of and . Use three significant figures in the numeric coefficient. Hint 1. How to approach the problem You are being asked for the speed at half of the maximum height. You know that at the initial height ( ), the speed is . All of the energy is kinetic energy, and so, the total energy is . At the maximum height, all of the energy is potential energy. Since the gravitational potential energy is proportional to , half of the initial kinetic energy must have been converted to potential energy when the projectile is at . Thus, the kinetic energy must be half of its original value (i.e., when ). You need to determine the speed, as a multiple of , that corresponds to such a kinetic energy. ANSWER: Correct Let us now consider objects launched at an angle. For such situations, using conservation of energy leads to a quicker solution than can be produced by kinematics. Part G A ball is launched as a projectile with initial speed at an angle above the horizontal. Using conservation of energy, find the maximum height of the ball’s flight. Express your answer in terms of , , and . Hint 1. Find the final kinetic energy Find the final kinetic energy of the ball. Here, the best choice of “final” moment is the point at which the ball reaches its maximum height, since this is the point we are interested in. u (1/2)hmax v g h = 0 v (1/2)mv2 h (1/2)hmax (1/4)mv2 h = (1/2)hmax v u = 0.707v v hmax v g Kf Express your answer in terms of , , and . Hint 1. Find the speed at the maximum height The speed of the ball at the maximum height is __________. ANSWER: ANSWER: ANSWER: Correct Part H A ball is launched with initial speed from ground level up a frictionless slope. The slope makes an angle with the horizontal. Using conservation of energy, find the maximum vertical height to which the ball will climb. Express your answer in terms of , , and . You may or may not use all of these quantities. v m 0 v v cos v sin v tan Kf = 0.5m(vcos( ))2 hmax = (vsin( ))2 2g v hmax v g ANSWER: Correct Interestingly, the answer does not depend on . The difference between this situation and the projectile case is that the ball moving up a slope has no kinetic energy at the top of its trajectory whereas the projectile launched at an angle does. Part I A ball is launched with initial speed from the ground level up a frictionless hill. The hill becomes steeper as the ball slides up; however, the ball remains in contact with the hill at all times. Using conservation of energy, find the maximum vertical height to which the ball will climb. Express your answer in terms of and . ANSWER: Correct The profile of the hill does not matter; the equation would have the same terms regardless of the steepness of the hill. Problem 10.14 A 12- -long spring is attached to the ceiling. When a 2.2 mass is hung from it, the spring stretches to a length of 17 . Part A What is the spring constant ? Express your answer to two significant figures and include the appropriate units. hmax = v2 2g v hmax v g hmax = v2 2g Ki + Ui = Kf + Uf cm kg cm k ANSWER: Correct Part B How long is the spring when a 3.0 mass is suspended from it? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Enhanced EOC: Problem 10.17 A 6.2 mass hanging from a spring scale is slowly lowered onto a vertical spring, as shown in . You may want to review ( pages 255 – 257) . For help with math skills, you may want to review: Solving Algebraic Equations = 430 k Nm kg y = 19 cm kg Part A What does the spring scale read just before the mass touches the lower spring? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces acting on the mass before it touches the scale. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? ANSWER: Correct Part B The scale reads 22 when the lower spring has been compressed by 2.7 . What is the value of the spring constant for the lower spring? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces acting on the mass. What is the net force on the mass? What is the force on the mass due to gravity? What is the force on the mass due to the scale? Use these to determine the force on the mass by the spring, taking note of the directions from your picture. How is the spring constant related to the force by the spring and the compression of the spring? Check your units. ANSWER: F = 61 N N cm k = 1400 k Nm Correct Part C At what compression length will the scale read zero? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem Draw a picture showing the forces on the mass. When the scale reads zero, what is the force on the mass due to the scale? What is the gravitational force on the mass? What is the force on the mass by the spring? How is the compression length related to the force by the spring and the spring constant? Check your units. ANSWER: Correct Problem 10.18 Part A How far must you stretch a spring with = 800 to store 180 of energy? Express your answer to two significant figures and include the appropriate units. ANSWER: y = 4.2 cm k N/m J Correct Problem 10.22 A 15 runaway grocery cart runs into a spring with spring constant 230 and compresses it by 57 . Part A What was the speed of the cart just before it hit the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Spring Gun A spring-loaded toy gun is used to shoot a ball straight up in the air. The ball reaches a maximum height , measured from the equilibrium position of the spring. s = 0.67 m kg N/m cm v = 2.2 ms H Part A The same ball is shot straight up a second time from the same gun, but this time the spring is compressed only half as far before firing. How far up does the ball go this time? Neglect friction. Assume that the spring is ideal and that the distance by which the spring is compressed is negligible compared to . Hint 1. Potential energy of the spring The potential energy of a spring is proportional to the square of the distance the spring is compressed. The spring was compressed half the distance, so the mass, when launched, has one quarter of the energy as in the first trial. Hint 2. Potential energy of the ball At the highest point in the ball’s trajectory, all of the spring’s potential energy has been converted into gravitational potential energy of the ball. ANSWER: Correct A Bullet Is Fired into a Wooden Block A bullet of mass is fired horizontally with speed at a wooden block of mass resting on a frictionless table. The bullet hits the block and becomes completely embedded within it. After the bullet has come to rest within the block, the block, with the bullet in it, is traveling at speed . H height = H 4 mb vi mw vf Part A Which of the following best describes this collision? Hint 1. Types of collisions An inelastic collision is a collision in which kinetic energy is not conserved. In a partially inelastic collision, kinetic energy is lost, but the objects colliding do not stick together. From this information, you can infer what completely inelastic and elastic collisions are. ANSWER: Correct Part B Which of the following quantities, if any, are conserved during this collision? Hint 1. When is kinetic energy conserved? Kinetic energy is conserved only in perfectly elastic collisions. ANSWER: perfectly elastic partially inelastic perfectly inelastic Correct Part C What is the speed of the block/bullet system after the collision? Express your answer in terms of , , and . Hint 1. Find the momentum after the collision What is the total momentum of the block/bullet system after the collision? Express your answer in terms of and other given quantities. ANSWER: Hint 2. Use conservation of momentum The momentum of the block/bullet system is conserved. Therefore, the momentum before the collision is the same as the momentum after the collision. Find a second expression for , this time expressed as the total momentum of the system before the collision. Express your answer in terms of and other given quantities. ANSWER: kinetic energy only momentum only kinetic energy and momentum neither momentum nor kinetic energy vi mw mb ptotal vf ptotal = (mw + mb)vf ptotal vi ptotal = mbvi ANSWER: Correct Problem 10.31 Ball 1, with a mass of 150 and traveling at 15.0 , collides head on with ball 2, which has a mass of 340 and is initially at rest. Part A What are the final velocities of each ball if the collision is perfectly elastic? Express your answer with the appropriate units. ANSWER: Correct Part B Express your answer with the appropriate units. ANSWER: Correct Part C vf = mb vi mb+mw g m/s g (vfx) = -5.82 1 ms (vfx) = 9.18 2 ms What are the final velocities of each ball if the collision is perfectly inelastic? Express your answer with the appropriate units. ANSWER: Correct Part D Express your answer with the appropriate units. ANSWER: Correct Enhanced EOC: Problem 10.43 A package of mass is released from rest at a warehouse loading dock and slides down the = 2.2 – high, frictionless chute to a waiting truck. Unfortunately, the truck driver went on a break without having removed the previous package, of mass , from the bottom of the chute. You may want to review ( pages 265 – 269) . For help with math skills, you may want to review: Solving Algebraic Equations (vfx) = 4.59 1 ms (vfx) = 4.59 2 ms m h m 2m Part A Suppose the packages stick together. What is their common speed after the collision? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem There are two parts to this problem: the block sliding down the frictionless incline and the collision. What conservation laws are valid in each part? In terms of , what are the kinetic and potential energies of the block at the top of the incline? What is the potential energy of the same block at the bottom just before the collision? What are the kinetic energy and velocity of block just before the collision? What is conserved during the collision? What is the total momentum of the two blocks before the collision? What is the momentum of the two blocks stuck together after the collision? What is the velocity of the two blocks after the collision? ANSWER: Correct Part B Suppose the collision between the packages is perfectly elastic. To what height does the package of mass rebound? Express your answer to two significant figures and include the appropriate units. Hint 1. How to approach the problem There are three parts to this problem: the block sliding down the incline, the collision, and mass going back up the incline. What conservation laws are valid in each part? m m v = 2.2 ms m m What is an elastic collision? For an elastic collision, how are the initial and final velocities related when one of the masses is initially at rest? Using the velocity of just before the collision from Part A, what is the velocity of just after the collision in this case? What are the kinetic and potential energies of mass just after the collision? What is the kinetic energy of mass at its maximum rebound height? Using conservation of energy, what is the potential energy of mass at its maximum height? What is the maximum height? ANSWER: Correct Problem 10.35 A cannon tilted up at a 35.0 angle fires a cannon ball at 79.0 from atop a 21.0 -high fortress wall. Part A What is the ball’s impact speed on the ground below? Express your answer with the appropriate units. ANSWER: Correct Problem 10.45 A 1000 safe is 2.5 above a heavy-duty spring when the rope holding the safe breaks. The safe hits the spring and compresses it 48 . m m m m m h = 24 cm $ m/s m vf = 81.6 ms kg m cm Part A What is the spring constant of the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Problem 10.49 A 100 block on a frictionless table is firmly attached to one end of a spring with = 21 . The other end of the spring is anchored to the wall. A 30 ball is thrown horizontally toward the block with a speed of 6.0 . Part A If the collision is perfectly elastic, what is the ball’s speed immediately after the collision? Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part B What is the maximum compression of the spring? Express your answer to two significant figures and include the appropriate units. ANSWER: = 2.5×105 k Nm g k N/m g m/s v = 3.2 ms Correct Part C Repeat part A for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Part D Repeat part B for the case of a perfectly inelastic collision. Express your answer to two significant figures and include the appropriate units. ANSWER: Correct Score Summary: Your score on this assignment is 99.4%. You received 120.28 out of a possible total of 121 points. x = 0.19 m v = 1.4 ms x = 0.11 m

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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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ENGR 3300: Fluid Mechanics, Fall 2015 Assignment 3 Due: Friday, Oct. 2, 2015 Topics: Chapter 3 & 4 Solutions must be neatly written and must include the following steps (if applicable) to receive full credit. 1. Given: List all known parameters in the problem. 2. Find: List what parameters the problem is asking you to find. 3. Solution: List all equations needed to solve the problem, and show all your work. Draw any necessary sketches or free body diagrams. Circle or box your final answer, and make sure to include appropriate units in your final answer. Grading: 15 total points (10 points for completeness + 5 points for one randomly chosen problem graded for correctness) 1. Water flows at a steady rate up a vertical pipe and out a nozzle into open air. The pipe diameter is 1 inch and the nozzle diameter is 0.5 inches. (a) Determine the minimum pressure that would be required at section 1 (shown in the figure below) to produce a fluid velocity of 30 ft/s at the nozzle (section 2). (b) If the pipe was inverted, determine the minimum pressure that would be required at section 1 to maintain the 30 ft/s velocity at the nozzle. 2. Water flows from a large tank through a small pipe with a diameter of 5 cm. A mercury manometer is placed along the pipe. Assuming the flow is frictionless, (a) estimate the velocity of the water in the pipe and (b) determine the rate of discharge (i.e. volumetric flow rate) from the tank. 3. An engineer is designing a suit for a race car driver and wants to supply cooling air to the suit from an air inlet on the body of the race car. The air speed at the inlet location must be 65 mph when the race car is traveling at 230 mph. Under these conditions, what would be the static pressure at the proposed inlet location? 4. Air flows downward toward a horizontal flat plate. The velocity field is given by ? = (??! − ??!)(2 + cos ??) where a = 5 s-1, ω = 2π s-1, and x and y (measured in meters) are horizontal and vertically upward, respectively, and t is in seconds. (a) Obtain an algebraic equation for a streamline at t = 0. (b) Plot the streamline that passes through point (x,y) = (3,3) at this instant.

ENGR 3300: Fluid Mechanics, Fall 2015 Assignment 3 Due: Friday, Oct. 2, 2015 Topics: Chapter 3 & 4 Solutions must be neatly written and must include the following steps (if applicable) to receive full credit. 1. Given: List all known parameters in the problem. 2. Find: List what parameters the problem is asking you to find. 3. Solution: List all equations needed to solve the problem, and show all your work. Draw any necessary sketches or free body diagrams. Circle or box your final answer, and make sure to include appropriate units in your final answer. Grading: 15 total points (10 points for completeness + 5 points for one randomly chosen problem graded for correctness) 1. Water flows at a steady rate up a vertical pipe and out a nozzle into open air. The pipe diameter is 1 inch and the nozzle diameter is 0.5 inches. (a) Determine the minimum pressure that would be required at section 1 (shown in the figure below) to produce a fluid velocity of 30 ft/s at the nozzle (section 2). (b) If the pipe was inverted, determine the minimum pressure that would be required at section 1 to maintain the 30 ft/s velocity at the nozzle. 2. Water flows from a large tank through a small pipe with a diameter of 5 cm. A mercury manometer is placed along the pipe. Assuming the flow is frictionless, (a) estimate the velocity of the water in the pipe and (b) determine the rate of discharge (i.e. volumetric flow rate) from the tank. 3. An engineer is designing a suit for a race car driver and wants to supply cooling air to the suit from an air inlet on the body of the race car. The air speed at the inlet location must be 65 mph when the race car is traveling at 230 mph. Under these conditions, what would be the static pressure at the proposed inlet location? 4. Air flows downward toward a horizontal flat plate. The velocity field is given by ? = (??! − ??!)(2 + cos ??) where a = 5 s-1, ω = 2π s-1, and x and y (measured in meters) are horizontal and vertically upward, respectively, and t is in seconds. (a) Obtain an algebraic equation for a streamline at t = 0. (b) Plot the streamline that passes through point (x,y) = (3,3) at this instant.

1. The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.2 seconds and a standard deviation of 0.1 seconds. 1‐1. (2 points) What is the probability that a reaction requires more than 0.5 seconds? 1‐2. (2 points) What is the probability that a reaction requires between 0.4 and 0.5 seconds? 1‐3. (2 points) What is the reaction time that is exceeded 95% of the time? 2. Spherical Uniform Distribution (Google! You do not have to explain why): 2‐1. (2 points) How can we pick a set of random points uniformly distributed on the unit circle x12 + x 2=1? 2‐2. (2 points) How can we pick a set of random points uniformly distributed on the 4‐dimensional unit 2 2 2 2 2 sphere x1 + x2 + x3 + x4 + x5 =1? 3. The random variable X has a binomial distribution with n = 19 and p = 0.4. Determine the following probabilities. (You may use computer. But, you have to show the formula.) 3‐1. (2 points) P(X ≤ 12) 3‐2. (2 points) P(X ≥ 18) 3‐3. (2 points) P(13 ≤ X < 15) 4. (2 points) Show the mean and the variance of the triangular distribution with lower limit a, upper limit b and mode c, where a < b and a ≤ c ≤ b. (You must show why.) 5. (2 points) An electronic office product contains 5000 electronic components. Assume that the probability that each component operates without failure during the useful life of the product is 0.999, and assume that the components fail independently. Approximate the probability that 10 or more of the original 5000 components fail during the useful life of the product. 6. Consider the following system made up of functional components in parallel and series. C2 0.80 C1 0.90 C4 0.95 C3 0.85 6‐1. (2 points) What is the probability that the system operates? 6‐2. (2 points) What is the probability that the system fails due to the components in series? Assume parallel components do not fail. 6‐3. (2 points) What is the probability that the system fails due to the components in parallel? Assume series components do not fail. 6‐4. (2 points) Compute and compare the probabilities that the system fails when the probability that component C1 functions is improved to a value of 0.95 and when the probability that component C2 functions is improved to a value of 0.85. Which improvement increases the system reliability more? 7. (2 points) Suppose that the joint distribution of X and Y has probability density function f(x, y) = 0.25xy for 0 < x < 2 and 0 < y < 2. Compute V(2X + 3Y). (Show all your work.)

1. The reaction time of a driver to visual stimulus is normally distributed with a mean of 0.2 seconds and a standard deviation of 0.1 seconds. 1‐1. (2 points) What is the probability that a reaction requires more than 0.5 seconds? 1‐2. (2 points) What is the probability that a reaction requires between 0.4 and 0.5 seconds? 1‐3. (2 points) What is the reaction time that is exceeded 95% of the time? 2. Spherical Uniform Distribution (Google! You do not have to explain why): 2‐1. (2 points) How can we pick a set of random points uniformly distributed on the unit circle x12 + x 2=1? 2‐2. (2 points) How can we pick a set of random points uniformly distributed on the 4‐dimensional unit 2 2 2 2 2 sphere x1 + x2 + x3 + x4 + x5 =1? 3. The random variable X has a binomial distribution with n = 19 and p = 0.4. Determine the following probabilities. (You may use computer. But, you have to show the formula.) 3‐1. (2 points) P(X ≤ 12) 3‐2. (2 points) P(X ≥ 18) 3‐3. (2 points) P(13 ≤ X < 15) 4. (2 points) Show the mean and the variance of the triangular distribution with lower limit a, upper limit b and mode c, where a < b and a ≤ c ≤ b. (You must show why.) 5. (2 points) An electronic office product contains 5000 electronic components. Assume that the probability that each component operates without failure during the useful life of the product is 0.999, and assume that the components fail independently. Approximate the probability that 10 or more of the original 5000 components fail during the useful life of the product. 6. Consider the following system made up of functional components in parallel and series. C2 0.80 C1 0.90 C4 0.95 C3 0.85 6‐1. (2 points) What is the probability that the system operates? 6‐2. (2 points) What is the probability that the system fails due to the components in series? Assume parallel components do not fail. 6‐3. (2 points) What is the probability that the system fails due to the components in parallel? Assume series components do not fail. 6‐4. (2 points) Compute and compare the probabilities that the system fails when the probability that component C1 functions is improved to a value of 0.95 and when the probability that component C2 functions is improved to a value of 0.85. Which improvement increases the system reliability more? 7. (2 points) Suppose that the joint distribution of X and Y has probability density function f(x, y) = 0.25xy for 0 < x < 2 and 0 < y < 2. Compute V(2X + 3Y). (Show all your work.)

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