Working with Measurement PDF

 38 000 000 0.0043 6500 2000  4.967 x 10^15 5120000000000 1.59 x 10^-13 Too long, don't solve. NA A NA A NP NP P P All measurements have some error. The acceptable level of accuracy depends on the consequences...

 38 000 000 0.0043 6500 2000  4.967 x 10^15 5120000000000 1.59 x 10^-13 Too long, don't solve. NA A NA A NP NP P P All measurements have some error. The acceptable level of accuracy depends on the consequences of errors, the purpose of the measurement, and cost-feasibility. For example, a small error in a swimming pool volume is insignificant, but a small error in medicine dosage can have serious consequences. The graduated cylinder is the most appropriate for precisely measuring 29 mL due to its smaller divisions and ability to estimate values to the nearest 0.2 mL. 50 238.450 50 238.5 50 200 5 x 10^4 5.024 x 10^4  1.1 Engineering Design An x-ray image of the bones in an arm CAN YOU SOLVE THE PROBLEM? In 1895, Wilhelm Conrad Röntgen was experimenting with electron beams when he noticed that a nearby screen coated with a fluorescent material glowed during his tests. He shielded the equipment with heavy black paper, but the screen still glowed. He deduced that © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Xray Computer/Shutterstock invisible radiation, which he called x-radiation, must have passed through the shield from the equipment to the nearby screen. X-radiation emissions are now called x-rays. Very soon after his initial discovery, Wilhelm noticed that x-rays interact with different materials, such as bone and muscle, in different ways. These different interactions could be used to produce images that could show the internal structure of a person or object that is normally not visible to the naked eye. Within the year after Wilhelm’s discovery, x-ray technology was being used to help diagnose medical conditions and learn more about the structure of the human body. X-ray technology has been refined based on new discoveries, and this technology is used in many applications, including security screening of luggage and industrial part inspection. INFER Describe one problem that can be solved using x-ray technology. How do you think this problem was solved before the development of x-ray technology? Evidence Notebook As you explore the lesson, gather evidence to explain how both science and engineering practices are used to develop solutions that rely on x-ray technology. Lesson 1 Engineering Design 5 EXPLORATION 1 Solving an Everyday Problem Every day you solve many problems. Most of these problems are small problems, and you consider your options and find a resolution in a very short amount of time. Sometimes, the problem has more serious consequences, so you may carefully consider options before making a decision. Kai Moves to a New School FIGURE 1: City buses often have a rack for cyclists to Kai opens the door of the refrigerator and examines transport their bicycles during a commute. the shelves, looking for something to eat. Kai’s mom enters the kitchen and begins a conversation. “Are you ready to start at your new school on Monday?” “I guess.” “Have you thought about how you’re going to get there?” “Just take the bus like I did at my old school, right?” “This school doesn’t have yellow school buses. Most people live close to the school, and there are sidewalks and public transit.” “So, I take the regular city bus?” © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Mike Dotta/Shutterstock “That’s one option. I could give you a ride, but I leave for work around 8.” “So I would have to get up early, and then sit around waiting for school to open? Never mind. Besides, I like the idea of getting around by myself here,” Kai explains. “I’m 15 now.” Kai stops looking for food and looks at the city bus schedule online. “Let’s see, classes start at 9,” Kai mumbles. “If I catch the 8:40 bus, I should get there in time. With five minutes to walk to the bus stop, I need to leave our apartment by 8:35. That means I get to sleep in compared to my last school.” Kai then looks at the school website to check the rules for taking public transit. “It looks like you can ride the bus for free if you have your school ID.” Kai continues looking at the registration forms. “Oh, I just realized that I won’t have my ID until Monday, so I won’t be able to ride the bus in the morning.” ANALYZE What problem does Kai need to solve? 6 Unit 1 Physics and Engineering  Kai Evaluates Needs and Wants FIGURE 2: Walking is a popular way for students to get to school when they live near the school. “Maybe I could walk, we’re not that far away.” Kai resumes looking for food. “That’s a good idea,” Kai’s mom agrees. “How long do you think it would take to walk to school?” Kai asks, finally grabbing an apple and some peanut butter. “We’re less than a mile from school, so I think only about 20 minutes. That’s almost as fast as the bus, and it could be a good way for you to make some new friends. I think Mr. Suarez’s kids walk, maybe you could walk with them.” “Is that the family that lives in the apartment below us? Wouldn’t it be weird for me to just join them? I mean we’ve never even spoken.” “I happened to meet the Suarez family yesterday and we’re invited down to visit tomorrow afternoon. So you’ll get a chance to meet them before Monday. Why don’t we start with that and see how it goes?” “OK.” Kai peruses maps of the area. “I was just thinking, I have some time now and the weather’s nice, maybe we can walk the route and see how long it really takes. Then I can also check out the bus stops, in case I decide to ride the bus.” “OK. Let me find some shoes.” DESIGN What factors (needs, concerns, or desires) can Kai use to help choose the best solution for the problem you identified earlier? List the factors, and then rank them in the © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Monkey Business Images/ second column by order of importance, with 1 being the most important. Factors Rank Shutterstock Lesson 1 Engineering Design 7  Kai Considers Options As they walk, Kai observes, “The bus stops are covered, so that’s nice. Maybe the city bus will be fine.” They look at the bike lanes and the bike trail that goes through the park. “If I had a bike, that would be something. That trail looks nice. I could get to school in only 10 minutes, I think.” “You never used your last bike,” Kai’s mom comments with a raised eyebrow. “I didn’t ride because we lived a lot farther from school, and all my friends rode the bus,” Kai says, “and also, it snowed for months on end. The weather is a lot nicer here.” Just then, they arrive at the school. “Look—” Kai points, ”there are bike racks. My last school didn’t have those, so it looks like more students bike here.” FIGURE 3: Many schools have bike racks for students to store their bikes during school hours. © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Kristi Blokhin/Shutterstock “I’m not sure how I feel about you biking in city traffic,” Kai’s mom cautioned. “I wouldn’t really be in traffic; there are bike lanes. And I would just ride through the park for most of the trip anyway. Not that it matters, I don’t have a bike anyway.” Kai continues thinking out loud, “If I bike, I can’t really talk to anyone. Maybe I should just walk with the neighbors, but what if I don’t like them or they don’t like me?” “Let’s just see how tomorrow goes.” They continue to walk home, observing the city and its people. PLAN List the options Kai is considering. 8 Unit 1 Physics and Engineering  Kai Simplifies the Problem Kai’s mom recalls, “Hmm... I was just thinking, your FIGURE 4: A bicycle is a cost-effective and energy- uncle mentioned the other day that now that your efficient mode of transportation. cousin is off at college, they have a spare bike. Since there are bike lanes...” “Can you ask him if I can borrow the bike?” Kai’s mom messages Kai’s uncle to ask about using the bike. As they walk home, Kai continues analyzing options. “I do want to start meeting people. But I also want to be able to get around quickly. If I bike and then decide to walk or take the bus home with someone, can we go pick up my bike later?” “No, I don’t think that’s practical,” Kai’s mom hesitates, “and I don’t like the idea of you leaving the bike at school overnight.” “True, but it would be nice to have the option to bike. I guess I could just take the bike on the bus or walk with it if I decided to walk with some of the other kids.” Later, as they arrive home Kai realizes “we don’t really have much space to keep a bike...” Kai’s mom replies, “If you really want to bike, we can find a place.” “You know, after Monday I’ll have my ID, and riding the bus will be an easier option. I just need to decide what I want to do Monday morning for now.” The phone dings with Kai’s uncle’s response. “Your uncle says he can drop off the bike for you tomorrow. What should I tell him?” © Houghton Mifflin Harcourt Publishing Company Image Credits: ©Martin Parker/Alamy ANALYZE How is Kai simplifying the problem? Collaborate In a small group, debate the methods Kai could use to get to school on the first day. Together with your group, choose the method that you would recommend to Kai, and explain your choice to the class. Evidence Notebook People often follow a process similar to Kai’s decision process to solve everyday problems. What is the benefit of using a systematic process to solve problems? Describe how a systematic problem-solving process might have led to the application of x-ray technology for medical imaging. Lesson 1 Engineering Design 9 EXPLORATION 2 The Engineering Design Process The engineering design process helps engineers consider all of the relevant information to find the best solution possible. While the process lays out specific steps, engineers may revisit steps whenever needed. As Kai was looking for a solution to the problem of getting to school, Kai followed several steps similar to those in the engineering design process. Systematically Solving Problems Engineering design begins by identifying a need or want, and then engineers work to develop a solution to meet the need or want. Engineers systematically develop and test possible solutions to find the best solution possible, given existing constraints. The engineering design process is a formalized process to help guide engineers to develop a solution for any type of problem. While the steps are ordered, they may be revisited at different times during the process when needed. FIGURE 5: This diagram is a model of the engineering design process. Though steps are usually performed in a particular order, an engineer may return to any previous step any time new information makes it necessary. Identify the want/need. DESIGNING SOLUTIONS OPTIMIZING SOLUTIONS Brainstorm solutions. Revisit the problem, if DEFINING THE PROBLEM needed, to clarify criteria. State the problem. Model solutions. Refine the prototype based Use criteria to evaluate on the results of the test. Research the problem and the solutions. solutions to similar problems. Test the prototype. Consider tradeoffs, if necessary. Specify criteria and constraints to delimit the problem. Evaluate test results with respect Develop a prototype from a model. to the criteria and constraints. Test the prototype. © Houghton Mifflin Harcourt Publishing Company Is the problem well defined? NO YES Evaluate test results with respect Given the constraints, is this to the criteria and constraints. the best possible solution? Return to any NO YES previous step Given the constraints, does the Return to any Continue to Designing Solutions solution satisfy the key criteria? previous step NO YES Implement the solution and communicate the results. Return to any previous step Continue to Optimizing Solutions 10 Unit 1 Physics and Engineering  ANALYZE The model of the engineering design process in Figure 5 shows three specific questions engineers use to evaluate their current information and decide whether to return to a previous step or move forward in the process. Are these the only points at which an engineer may evaluate their progress and choose to repeat a previous step? Explain your answer. Collaborate To iterate means to repeat. The engineering design process is iterative because steps can be repeated again and again. Each iteration requires money and time. Which steps of the engineering design process are most likely to be repeated, and why? Compare your views with a partner’s. Defining and Delimiting the Problem To fully define a problem, an engineer needs to gather as much information as possible about the problem. The engineer might look at the system around the problem, research scientific issues, and find out how other people have solved similar problems. Language Arts Connection Choose a universal human need, such as access to clean water or food. For your local community, define a problem that is preventing this need from being met. Use multiple sources to gather as much information as possible about the problem. Make a poster to raise awareness for the problem that states, as specifically as possible, the problem that could be solved using the engineering design process. Engineers delimit a problem, or set the scope for how much of the problem will be solved, by specifying criteria. Criteria (singular criterion) are desirable features of a solution. Some criteria may be chosen based on scientific knowledge or desires of the intended user. Other criteria may be set by society. For example, society values clean air, so vehicle designers set criteria to minimize air pollutants emitted from vehicles while they operate. Constraints are the limitations on a solution. Two of the most common constraints © Houghton Mifflin Harcourt Publishing Company engineers face are budget and time. Constraints prohibit certain solutions. For example, an engine cannot output more energy than it takes in. This is a constraint due to the laws of physics. When a problem is complex, engineers divide the problem into smaller, more limited problems. These smaller parts of the problem may be solved by several groups working at the same time. Because one group’s decisions may affect another group’s work, team members must communicate frequently in order to coordinate their work. DESIGN A team is designing a bicycle. How can this problem be divided into smaller, more limited problems that can be solved simultaneously? Lesson 1 Engineering Design 11  Engineering Criteria and Constraints Engineers need to be able to evaluate how well solutions satisfy criteria and constraints. For example, an engineer may begin by saying they want their solution to be affordable, but affordability varies based on the situation. This criterion would be more measurable if a target price were specified, and then solutions could be evaluated for how closely they match the target price. Criteria vary in importance, from very important to nice to have. Prioritizing criteria is important for guiding design decisions later in the process. An acceptable solution may not satisfy all of the criteria, but it should satisfy the most important criteria. Constraints may be dictated by society, the laws of physics, or something specific to the problem. A solution is unacceptable if it does not stay within the constraints. A bridge, for example, must be able to support a minimum load without collapsing. APPLY In a local wildlife reserve, a simple two-plank bridge over a low swampy area has sunk on one side and needs to be replaced. The group that maintains trails has put together their requirements, and a pair of students has offered to build new bridges. Rephrase each statement as a measurable criterion or constraint. Not too expensive Can hold two adults and a dog Resistant to weather Won’t pollute water Designing Solutions After a problem is well defined and delimited, engineers can begin brainstorming possible solutions. The goal of brainstorming is to generate many possible solutions without judgment. Solutions may be based on existing designs or may be newly imagined by the engineer. Creativity is an important aspect of the brainstorming phase. © Houghton Mifflin Harcourt Publishing Company EXPLAIN When first brainstorming solutions, engineers focus on criteria while largely ignoring constraints. Why do you think this is? Evidence Notebook During the design phase of the engineering design process, engineers make many different models of potential solutions. What is the purpose of these models? What types of models might engineers make when designing a structural beam, such as the one in the unit project? 12 Unit 1 Physics and Engineering  Evaluating Design Solutions Once engineers have several possible solutions, all of the solutions must be evaluated against the criteria and constraints. Constraints can be used to eliminate solutions— though parts of these solutions may still be considered—remaining solutions can then be judged against the criteria. Solutions that are expected to better satisfy the criteria are more desirable. Parts of different solutions may be combined to better satisfy the criteria. Engineering Tradeoffs Sometimes, a solution that performs well for one criterion may perform poorly for another criterion or not satisfy all constraints. When this happens, an engineer may need to make a tradeoff, which is when one desired feature is given up in return for another. For example, materials for a more durable bike are more expensive than other materials. In this example, the engineer needs to decide which is more important: a durable bike or a more affordable bike. The engineer needs to make a tradeoff, such as accepting a lower-durability solution in order to make the bike more affordable. Deciding on a tradeoff depends on which criterion is considered more important. Therefore criteria must be carefully prioritized when delimiting engineering problems. Most complex designs may involve making tradeoffs, but not every decision is a tradeoff. Consider the three different designs for bus stop shelters. Glass’s transparency to sunlight might be desirable on cold days but undesirable on hot, sunny days. Both the wood and metal shelters block the sunlight, but the aesthetics (how attractive something is) and durability of these materials differ. Depending on how transparency, durability, and aesthetics are valued, a different material might be seen as!a better choice. Aesthetic factors may be difficult to measure. © Houghton Mifflin Harcourt Publishing Company Image Credits: (l) ©Annie Eagle/Alamy; FIGURE 6: Three bus stop shelters made of different materials (c) ©saturno dona’/Alamy; (r) ©Urbanimages/Alamy a wood b metal c glass EVALUATE The following describe pairs of characteristics for possible solutions. The criteria are that the bus stop has a long lifetime, low initial price, is low maintenance, and that it looks nice in the neighborhood. Which of the following would be considered tradeoffs? Select all correct answers. a. shorter lifetime / lower initial price b. more attractive / lower initial price c. more maintenance / lower initial price d. more maintenance / higher initial price e. better wind resistance / more attractive Lesson 1 Engineering Design 13  Engineering Decision Matrix A decision matrix is a tool engineers use to organize and evaluate how well multiple solutions satisfy each of the criteria. By turning qualitative descriptions, such as excellent or okay, into numerical values, you can score each solution. The highest overall score should show the best choice among the designs. Each criterion is given a number, called a weight, to describe its relative importance. Greater weight means greater importance. Figure!7 shows a decision matrix for three lawnmowers. For this solution, safety is the most important criterion and aesthetics is the least important. Each design is scored from 0–5 depending on how well it meets each criterion—0 means not at all and 5 means perfect. Each score is multiplied by the criterion weight, and then the weighted scores are added to give an overall score that shows how well each design meets the criteria. FIGURE 7: A decision matrix evaluating three lawnmowers Design criteria Weight Lawnmower 1 Lawnmower 2 Lawnmower 3 Safety 5 4 1 5 Reliability 4 2 3 4 Affordability 2 1 2 1 Aesthetics 1 1 3 0 Total points 31 24 43 EVALUATE Look at the window designs in Figure 8, then complete the decision matrix. Specify two more criteria and assign each criterion a weight. Score each proposed solution and calculate the total points. Compare the designs’ scores and then circle the best choice. Decision matrix for windows in a home Design criteria Weight Sliding panes Vertical pivot Horizontal pivot Cleanable from inside Safety © Houghton Mifflin Harcourt Publishing Company Total points FIGURE 8: Window designs as proposed solutions for a problem a sliding panes b vertical pivot c horizontal pivot 14 Unit 1 Physics and Engineering  Developing and Testing Prototypes During the design phase, engineers can model solutions to examine different features. Proposed solutions must be tested because solutions may not perform as expected. A!prototype is a model of a solution that can be tested. Prototypes may or may not be made of the same materials as the final product, and they may not be full-scale. When a solution fails to satisfy the criteria and constraints, adjustments must be made, and the solution must be tested again. ANALYZE Lead is a substance which can be harmful to human health, and is often found in older buildings. A lead test kit should identify lead on wood or drywall accurately at least 95% of the time when the sample is 0.5% or more lead by weight. Which prototypes meet the criteria? Select all correct answers. a. Prototype A identifies lead correctly more than 90% of the time. b. Prototype B identifies lead correctly 80% of the time on all surfaces. c. Prototype C identifies lead correctly 95% of the time on all surfaces. d. Prototype D identifies lead correctly 98% of the time on drywall or plaster. e. Prototype E identifies lead correctly 97% of the time on drywall, plaster, or wood. Optimizing Solutions An engineer may iterate through the testing and modification steps multiple times during the design phase until an acceptable solution is found. Once an acceptable solution is developed, engineers may continue on to optimizing their solution if time and budget permit. To optimize a solution means to make it the best solution possible. An engineer might optimize one part of a design by defining it as a separate problem. When that part is put back into the overall solution, further iterations of the design process may be needed to adjust other parts of the design. With each iteration through the steps of the engineering design process, engineers learn more about the problem and its possible solutions. New information is incorporated in the next iteration; the optimized solution reflects many refinements of the initial design. For example, early x-ray images were blurry and required long exposures. When scientists learned more about the possible damaging effects of x-rays, they looked for ways to limit exposure to the radiation while improving or maintaining the detail of the images. Communicating a Solution © Houghton Mifflin Harcourt Publishing Company Communication is an important part of the design process. Engineers communicate with team members, customers, and society in general. Engineers use models, write papers, and use many other methods to communicate their solutions. This helps society and customers understand a solution and allows future solutions to build on earlier solutions. Language Arts Connection Present a solution to a problem in two different ways, such as a paragraph and a demonstration. Ask the people to whom you present for feedback on which parts were clear and which parts were hard to follow with each method. Record which types of presentation styles are better for communicating different types of information. Evidence Notebook X-ray technology can be used to image industrial parts for inspection as well as the human body. Explain whether these solutions have the same criteria and constraints. Lesson 1 Engineering Design 15