Chapter 03 Problem Solving

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Published on January 29, 2008

Author: Bianca

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Chapter 3:  Chapter 3 Problem Solving Problem Solution Requirements:  Problem Solution Requirements Drawing List Known Parameters Label Unknowns Equations Answer with Units Example Problem :  Example Problem Given: A student is in a stationary hot-air balloon that is momentarily fixed at 1325 ft. above a piece of land. This pilot looks down 60o (from horizontal) and turns laterally 360o. Required: a) How many acres of land are contained by the cone created by her line of site? c) How high would the balloon be if, using the same procedure, an area four times greater is encompassed? Reminder to Professor :  Reminder to Professor Get meter sticks. Chapter 3:  Chapter 3 Problem Solving Exam I - Next Wednesday Remember to bring a calculator and pencil. Equations for Exam I:  Equations for Exam I Circumference of a Circle: S = 2pr = pd Area of a Circle: A= pr2 Volume of a Sphere: V = (4/3) p r3 Volume of a Cylinder: V = p r2 h Surface Area of a Sphere: A = 4pr2 Pythagorean Theorem: c2 = a2 + b2 Radius of a Circle or Sphere: r Diameter of a Circle or Sphere: d=2r Estimation #1:  Estimation #1 Team Exercise Close the books. Estimate the volume of a average-sized human in cubic meters. Approximate humans has one rectangular slab. Volume=Length×Width×Height (3 minutes) How could you improve this estimate? Design an experiment that could better estimate the volume of individuals. (1 minute) Estimation #2:  Estimation #2 Team Exercise Estimate the speed of hair growth in miles per hour. (3 minutes) Use Appendix A for unit conversions. What would be a more appropriate unit for the speed of hair growth? Design an experiment that could better estimate the speed of hair growth. (1 minute) Estimation #3:  Estimation #3 Class Exercise How many “square bales” will fit in a barn that is 14 foot high, 20 yards wide and 40 yards long? Estimation #4:  Estimation #4 Class Exercise How many (cubic) yards of concrete would it take for the foundation of your dream home? Engineering Exercise:  Engineering Exercise You are asked to build a storage tank for 22 cubic meters of gasoline. You want to use the least amount of metal to keep your construction costs low. Suppose that you use 1-centimeter thick steel sheets to create storage tanks. Engineering Exercise (con’t):  Engineering Exercise (con’t) If you had a tank in the shape of a cube, then how long would each side be? What would be the inner surface area of the tank? How much metal would you need? Engineering Exercise (con’t):  Engineering Exercise (con’t) If you had a tank in the shape of a sphere, then what would its radius be? What would be the inner surface area of the tank? How much metal would you need? Engineering Exercise:  Engineering Exercise If you had a tank in the shape of a cylinder, then what would its radius be? What would be the inner surface area of the tank? How much metal would you need? Aha! We will need to make some assumptions. TEAMWORK:  TEAMWORK Each team will now make a different assumptions and record their results on the table on the chalkboard. Who uses the least metal for the cylindrical tanks?:  Who uses the least metal for the cylindrical tanks? Team h r A Vmetal a h=0.5r b h=1r g h=1.5r d h=2r e h=2.5r w h=3r i h=3.5r t h=4r z h=4.5r Recorders: To the chalk board…:  Recorders: To the chalk board… Write down your team name. Write down your assumption about the connection between h and r. Write down the equation for the volume of a cylinder. Substitute. Solve for r. Find A. Find the volume of the metal. Vmetal Optimization? Height=2 Radius:  Optimization? Height=2 Radius How do we know that h=2r is the best?:  How do we know that h=2r is the best? We can use trial-and-error. We can prove it using calculus. Chapter 3:  Chapter 3 Problem Solving Problem Solution Requirements:  Problem Solution Requirements Drawing List Known Parameters Label Unknowns Equations Answer with Units Archimedes’ Principle:  Archimedes’ Principle The buoyant force acting on a floating body is equal to the weight of the media (air or water) that is displaced. Example Problem:  Example Problem How much of this log will extend above the water line? 40cm rwood = 0.600 g/cm3 rwater = 1.00 g/cm3 Problem 3.38:  Problem 3.38 Using Archimedes’ Principle, estimate the mass that can be lifted by a hot air balloon measured 10 meters in diameter. Given: r = 0.0012 g/cm3 for Air at 20°C, 1 atm r = 0.0010 g/cm3 for Air at 70°C, 1 atm Density:  Density Density = Mass / Volume r = m/V Archimedes’ Principle:  Archimedes’ Principle What is the density of a cube that floats in water and has 1/3 of its volume above the waterline? Archimedes’ Principle:  Archimedes’ Principle A 200 lb engineer stands on a set of scales in waist deep water. What is the average density of the engineer if the scales read 100 lbs? Aerospace Engineering Team Exercise:  Aerospace Engineering Team Exercise Estimate the minimum time that it would take to travel to Jupiter at Mach 1. The Earth is 93,000,000 miles from the Sun. Jupiter orbits the Sun at a distance that is 5.2 times that of the Earth-Sun distance. Slide29:  Problem 3.21 Example Problem:  Example Problem Drawing List Known Parameters Label Unknowns Equations Answer with Units How long will a 0.058kg tennis ball be in the air if it is thrown upward at 45.7m/s? Review For Exam I :  Review For Exam I Chapter 1 Know details about the Disciplines Review Tables and Figures Chapter 2 Interaction Rules – Section 2.1 Settling Conflicts – Section 2.2 Chapter 3 Estimation Problems Unit Conversion – Table 3.2 Review Items Example problems in the book Homework In-class exercises Homework 2 Revisited:  Homework 2 Revisited Problem 3.5 10 cm 21 cm d c2 = a2 + b2 r2 = d2 + (21cm)2 r = d + 10cm r (d + 10cm)2 = d2 + (21cm)2 d2 + (20cm)d + 100cm2 = d2 + (21cm)2 d = 17.1 cm Slide33:  The land must be divided into four equal-sized and equal-shaped pieces. Problem 3.19 Problem 3.34:  Problem 3.34 Estimate the amount of money students at your university spend on fast food each semester. Given: 12,000 students 1 semester = 16 weeks Meals cost $5 Estimate that students eat fast food 5 times each week Problem 3.37:  Problem 3.37 Estimate the time it would take for a passenger jet flying at Mac 0.8 to fly around the world. Make allowances for refueling. ~ 45 hours allowing for refueling Problem 3.25:  Problem 3.25 Estimate the number of toothpicks that can be made from a log measuring 3 ft in diameter and 20 ft long. ~ 30 million toothpicks Chapter 3 Summary:  Chapter 3 Summary Types of Problems Problem Solution Requirements Estimations Types of Problems:  Types of Problems Research Knowledge Troubleshooting Mathematics Resource Social Design Readiness Assessment Test #2 Chapter 2 Reading :  Readiness Assessment Test #2 Chapter 2 Reading What are the four main types of issues to consider when settling conflicts? What are the first names of your team members?

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