# Investigations for Chapter 1. How do we measure and describe the world around us?

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1 1 Chapter 1 Forces and Motion Introduction to Chapter 1 This chapter is about measurement and how we use measurements and experiments to learn about the world. Two fundamental properties of the universe that we want to measure are time and distance. A third important measurement, speed, tells us how time and distance relate to the motion of objects. Investigations for Chapter Time and Distance Science and Measurement How do we measure and describe the world around us? In the first Investigation, you will use electronic timers and other measuring tools to explore precision measurement of the fundamental quantities of time and distance. 1.2 Investigations and Experiments How do we ask questions and get answers from nature? Investigating a car rolling down a ramp may seem simple, but it is difficult to understand what is really happening. The key is learning to design careful experiments that test our ideas with observations. In this Investigation, you will examine the motion of a car on a ramp to explore the action of variables in experiments. 1.3 Speed What is speed and how is it measured? The words fast and slow are not precise enough for many questions in science. We need to know how fast is fast. You will learn to determine the speed of moving objects with great accuracy. This Investigation of speed will be the foundation for answering many questions about motion. 1

2 : Science and Measurement Learning Goals In this chapter, you will: Accurately measure time using electronic timers and photogates. Use decimals to represent fractions of a second. Develop a research question or hypothesis that can be tested. Identify the variables that affect motion. Develop an experimental technique that achieves consistent results. Draw conclusions from experimental results. Accurately measure distance. Identify metric and English units of distance. Convert between units of distance. Calculate speed in units of inches per second, feet per second, and centimeters per second. Vocabulary cause and effect experimental technique metric system time control variables experimental variable procedure trial controlled experiment hypothesis research question variables distance investigation scientific evidence velocity English system length scientific method experiment measurements second 2

3 1.1 Time and Distance In this section, you will learn about two fundamental properties of the universe: time and distance. Learning about how things change with time motivates much of our study of nature. We are born and our bodies change as time passes. The steady forward movement of time creates a present, a past, and a future. Another important quality of the universe is that it has three dimensions. To observe and learn about objects, their sizes, and their motion in the universe, we need units of length. Common measures for length are inches and meters. Other units of length are used for very small distances like atomic sizes and very large distances like those between cities. Two ways to think about time What time is it? How much time? There are two ways we think about time (figure 1.2). One meaning for time is to identify a particular moment. If we ask What time is it? we usually want to know time relative to the rest of the universe and everyone in it. For example, 3:00 PM, Eastern Time, on April 21 tells the time at a certain place on Earth. Another meaning for time is a quantity, or interval of time. The question How much time? is asking for an interval of time with a beginning and end. For example, we might measure how much time has passed between the start of a race and when the first runner crosses the finish line. Figure 1.1: The flow of time is an important part of our experience of life. To understand nature we need to investigate how things change with time. How is time measured? For most of physical science we measure and record time in seconds. Some other units of time you may see are hours, minutes, days, and years. Choose the unit most suited to the time you want to measure. Short races are best measured in seconds while the age of a person is best measured in years. Figure 1.2: There are two different ways to understand time. 1.1 Time and Distance 3

4 Time comes in mixed units Many calculations require that time be expressed in seconds. However, seconds are very short. Hours and minutes are more convenient for everyday time measurement. As a result, time intervals are often in mixed units, such as 2 minutes and 15 seconds. If you have a time interval that is in mixed units you will have to convert it to seconds before doing calculations. Table 1.1 gives some useful relationships between units of time. Why we have different units for time How do you read a timer? 4 How do you convert to seconds? Table 1.1: Some units for time Time Unit How Many Seconds How Many Days 1 second minute hour 3, day 86, year 31,557, century 3,155,760,000 36,525 How many seconds have there been since you were born? From the table you should see that for every year there are 31,557,600 seconds. To give your age in seconds would be silly. The number would be too big and change too fast. Years is a better unit for describing people s ages. Most timing equipment (including digital timers) displays time in three units: hours, minutes, and seconds. Colons separate the units into hours, minutes, and seconds. The seconds number may have a decimal that shows fractions of a second. To read a timer you need to recognize and separate out the different units. Figure 1.3 shows a timer display that reads 1 hour, 26 minutes, and seconds. To convert a time to seconds you have to first separate out all the different units. For physics problems, the starting units will often be hours, minutes, and seconds. Follow the list below to convert any amount of time to seconds. 1 Separate the total time into the amount of time in each unit. 2 Convert each separate quantity of time to seconds. 3 Add all the seconds. Figure 1.3: Electronic timers have displays that show mixed units. Colons (:) separate the units. Example: Convert the time in figure 1.3 to seconds. Solution: Separate time into each unit. 1 hour 26 minutes seconds Convert each different unit into seconds. 1 hour 3,600 seconds/hour = 3,600 seconds 26 minutes 60 seconds/minute = 1,560 seconds Then add all the seconds. 3, , , seconds

5 Measuring distance Distance is measured in units of length There are two common systems Distance describes how far it is from one point to another. Distance is measured in units of length. Like other measurements, distance always has a number and a unit. It is hard to say precisely how far something has moved without units. It would be silly to ask someone to walk 25. They would ask, Twenty-five what? There is a big difference between 25 feet and 25 miles! Without units, distance measurements are meaningless. There are two common systems of units that are used for measuring distance. You need to understand both systems. The English system uses inches, feet, and miles. The metric system uses millimeters, centimeters, meters, and kilometers. 1.1 Time and Distance 5

6 Why are there so many different ways to measure the same thing? Why units were invented Scientists use metric units Units were invented so people could communicate amounts to each other. For example, suppose you want to buy 10 feet of rope. The person selling the rope takes out a ruler that is only 10 inches long (instead of 12 inches) and counts out 10 lengths of the ruler. Do you get your money s worth of rope? Of course not! For communication to be successful, everyone s idea of one foot (or any other unit of measure) must be the same. Figure 1.4 illustrates a hot dog vendor trying to sell a foot-long hot dog that is only 10 inches long. If the girl were to buy a hot dog, would she be getting what the sign says that she is paying for? Almost all fields of science use metric units because they are so much easier to work with. In the English system, there are 12 inches in a foot, 3 feet in a yard, and 5,280 feet in a mile. In the metric system, there are 10 millimeters in a centimeter, 100 centimeters in a meter, and 1,000 meters in a kilometer. Factors of 10 are easier to remember than 12, 3, and 5,280. The diagram below will help you get a sense for the metric units of distance. Figure 1.4: The hot dog vendor and the girl have different ideas about how long a foot is. 6 We use units every day In your life, and in this book, we use both English and metric units. We measure some quantities, like power and wavelength, in metric units. We measure other quantities, like weight and speed, in both metric and English units. Science measurements are always metric, but you may use units of pounds and miles per hour in your daily experience. In many other countries, people use metric units for everyday measurements. Figure 1.5: In 1791, a meter was defined as 1/10,000,000 of the distance from a pole of Earth to its equator. Today the meter is defined more accurately using wavelengths of light.

9 The scientific method The scientific method Steps in the scientific method The process you use to figure out what is wrong with your car is an example of the scientific method. As you try to fix your car, you ask yourself questions (Is there any gas? Is the battery dead?) and formulate ideas (or hypotheses) about what is wrong. By testing your ideas, you are experimenting and collecting data. You may be able to use this data to fix the car. Even if you conclude that the car can t be fixed, you have learned information to use the next time you are faced with a similar problem. Table 1.2 shows the steps of the scientific method. Table 1.2: Steps in the scientific method Step Example 1 Ask a question. Why doesn t the car start? 2 Formulate a hypothesis. Maybe the battery is dead. 3 Design and conduct an experiment. Turn the lights on to test the battery. 4 Collect and analyze data. The lights go on. 5 Make a tentative conclusion. Battery is OK. 6 Test conclusion, or if necessary, refine the question, and go through each step again. Are the ignition wires loose or wet? Figure 1.7: Science is a process of collecting information through observation and experiment. The information is used to solve problems and test ideas about how things work. 1.2 Investigations and Experiments 9

11 Designing experiments Start with a good question Identify all the factors when designing experiments Variables Change one thing at a time Control variables and experimental variables Will a car roll faster down a steeper hill? This is a good research question because we can test it with an experiment. We could set up ramps at different angles and measure the speeds of cars as they roll down the ramp. Once you have a good question, you can design an experiment to help you find the answer. Suppose you find that a car on a steep ramp rolls faster than a car on a ramp at a lower angle. Can you say that your experiment proves steeper ramps make cars go faster? Maybe, and maybe not. Before you can design a good experiment, you must identify all the factors that affect how fast the car moves down the ramp. Maybe you pushed the car on one ramp. Maybe one car was heavier than another. Your observation of higher speed because the angle was steeper could be correct. Or, the speed could be higher for another reason, like a push at the start. Factors that affect the results of an experiment are called variables.you can think about variables in terms of cause and effect. The weight of the car is one variable that may have an effect on the speed of the car. Some other variables are the angle of the ramp and how far down the ramp you measure the speed. When you can identify more than one variable that could affect the results of your experiment, it is best to change only one variable at a time. For example, if you change both the weight of the car and the angle of the ramp, you won t know which of the two variables caused your speed to change. If you want to test the effect of changing the angle, keep ALL the other variables the same. The variable that you change is called the experimental variable. The variables that you keep the same are called control variables. When you change one variable and control all of the others, we call it a controlled experiment. Controlled experiments are the preferred way to get reliable scientific evidence. If you observe that something happens (like the car goes faster), you know why it happened (because the ramp was steeper). There is no confusion over which variable caused the change. Figure 1.8: Variables that affect a car rolling down a ramp. 1.2 Investigations and Experiments 11

13 1.3 Speed Just saying that something is fast is often not enough description for a scientist. You can easily walk faster than a turtle, yet you would not say walking was fast compared with the speed of driving a car. In this section, you will learn how to be very precise about speed. Fast trains What do we mean by speed? What is speed? Exactly how fast are you walking? How many meters do you walk for each second? Do you always walk the same number of meters every second? Objects in the world are rarely at rest for very long. Describing movement from place to place naturally leads you to think about speed. The speed of an object is a measure of how quickly the object gets from one place to another. Speed is a characteristic of all objects. Even objects that are standing still have a speed of zero. Fast trains are being used for transportation in several countries. In Japan, where cities are crowded, people have to travel from far away to reach their jobs. Japan s 500 Series train is the world's fastest, operating at a speed of 300 km/h (186 mph). In France, the TGV goes almost as fast. In the United States, Amtrak runs highspeed trains from Boston to Washington. Fast trains are also being considered in California and the Midwest. Fast trains offer benefits like performance and friendliness to the environment. As airports become more crowded, the use of fast trains for long-distance travel will probably increase. 1.3 Speed 13

14 Calculating speed Calculating speed Units for speed What does per mean? There are several ways to look at the concept of speed. In the simplest interpretation, speed is the distance traveled divided by the time taken. For example, if you drive 90 miles in 1.5 hours (figure 1.11), then your speed is 90 miles divided by 1.5 hours, equal to 60 miles per hour. To determine a speed, you need to know two things: The distance traveled The time taken Speed is calculated by taking the distance traveled divided by the time taken. Since speed is a ratio of distance over time, the units for speed are a ratio of distance units over time units. If distance is in miles and time in hours, then speed is expressed in miles per hour (miles/hours). We will often measure distance in centimeters or meters, and time in seconds. The speeds we calculate would then be in units of centimeters/second or meters/second. Table 1.3 shows many different units commonly used for speed. The word per means for every or for each. The speed of 60 miles per hour is really a shorthand for saying 60 miles for each hour. When used with units, the per also means divided by. The quantity before the word per is divided by the quantity after it. For example, if you want speed in meters per second, you have to divide meters by seconds. Figure 1.11: If you drive 90 miles in 1.5 hours, your speed is 60 miles per hour. This is calculated by dividing the distance traveled (90 miles) by the time taken (1.5 hours). Table 1.3: Some Common Units for Speed Distance Time Speed Abbreviation meters seconds meters per second m/sec kilometers hours kilometers per hour km/h centimeters seconds centimeters per second cm/sec miles hours miles per hour mph inches seconds inches per second in/sec, ips feet minutes feet per minute ft/min, fpm 14

15 Relationships between distance, speed, and time Mixing up distance, time, and speed Using formulas Three forms of the speed formula How far did you go if you drove for 2 hours at 60 mph? This seems like a fair question. We know speed is the distance traveled divided by the time taken. Now we are given the time and the speed. We are asked to find the distance. How do you take the new information and figure out an answer? Let the letter v stand for speed, the letter d stand for distance traveled, and the letter t stand for time taken. If we remember that the letters stand for those words, we can now write our definition of speed much faster. Also remember that the words or letters stand for the values that the variables really have. For example, the letter t will be replaced by the actual time when we plug in numbers for the letters. You can think about each letter as a box that will eventually hold a number. Maybe you don t know what the number is yet. Once we get everything arranged according to the rules we can fill the boxes with the numbers that belong in each one. The last box left will be our answer. The letters (or variables) are the labels that tell us which numbers belong in which boxes. There are three ways to arrange the three variables that relate distance, time and speed. You should be able to work out how to get any of the three variables if you know the other two. Equation Gives you... If you know... v = d/t speed time and distance d = vt distance speed and time t = d/v time distance and speed Why v is used to represent speed in an equation. When we represent speed in a formula, we use the letter v. If this seems confusing, remember that v stands for velocity. For this chapter, it isn t important, but there is a technical difference between speed and velocity. Speed is a single measurement that tells how fast you are going, like 60 miles per hour. Velocity really means you know both your speed, and also what direction you are going. If you told someone you were going 60 mph straight south, you told them your velocity. If you just told them you were going 60 mph, you told them your speed. 1.3 Speed 15

17 Review Chapter 1 Review Vocabulary review Match the following terms with the correct definition. There is one extra definition in the list that will not match any of the terms. Set One Set Two 1. time a. How far it is from one point to another 1. metric system a. A series of experiments connected to a basic question 2. second b. A system of measuring that uses length units of inches, feet, and miles 2. investigation b. An observation that can be recorded and thought about 3. distance c. A type of distance measurement 3. experiment c. An observation that can be repeated with the same result 4. length d. A measurement that describes the interval between two events; the past, present, and future 4. measurement d. An observation that is reported in a newspaper 5. English system e. A system of measuring time based on the Babylonian number system Set Three 5. scientific evidence e. A situation that is set up in order to observe what happens f. A common unit used in measuring time f. A system of measuring that uses length units of millimeters, centimeters, meters, and kilometers Set Four 1. scientific method a. An educated guess about what will happen 1. experimental variable a. A variable that is kept the same in an experiment 2. research question b. When one variable affects another 2. control variable b. How an experiment is done 3. hypothesis c. A process used to solve a problem or test an idea about how things work 3. controlled experiment c. The running of an experiment 4. variables d. A process used to build a device 4. trial d. A variable that is not important in an experiment 5. cause and effect e. Factors that affect the result of an experiment 5. experimental technique e. An experiment in which one variable changes and all other variables are kept the same f. A question that can be answered by an experiment or series of experiments f. A variable that is changed in an experiment 17

18 Review Concept review 1. Units of time include seconds, minutes, hours, days, and years. Why are there so many units for time? 2. To make sense, a measurement must always have a and a. 3. How are an investigation and an experiment related to each other? 4. Experiments usually have a question associated with them. True or false? 5. List the steps of the scientific method. 6. When doing an experiment, you must change only one at a time. 7. A hypothesis is a random guess. True or false? 8. Scientific discoveries and inventions must always be verified by more than one person. True or false? 9. What is the definition of speed? 10. How are speed and velocity different? Use each in a sentence. 11. Write the speed equation that you would use in each of the following scenarios: a. You know distance and speed. b. You know time and distance. c. You know speed and time. 12. What is the speed of an object that is standing still? 13. Describe, in your own words, how you determine the speed of an object. Problems 1. Which one of the following times is equal to 75 seconds? a. 3 minutes (3:00) b. 1 minute, 15 seconds (1:15) c. 1 minute, 25 seconds (1:25) 2. How many seconds are in half an hour? Show your work Match the measurement in the first column to the corresponding equal measurement in the second column: a) 1 centimeter b) 1 foot c) 5, 280 feet d) 1000 millimeters 1) 12 inches 2) 1 meter 3) 10 millimeters 4) 1 mile 4. A student is 5 feet, 2 inches tall. What is her height in meters? 5. A model car is 30 cm in length. How many inches long is it?

20 Review 12. A bumblebee flies through two photogates that are spaced exactly 20 centimeters apart. The timer shows the measurement made for the time between gates in seconds. a. Calculate the speed of the bumblebee assuming it flies a straight line between the two light beams. Show your work. b. If the bumblebee flies a curved path in the same amount of time, will its actual speed be different? Explain your reasoning. 13. A car was timed as it passed through two photogates. The distance between the photogates is 35 centimeters. Calculate the speed of the car as it passed through the two photogates. The timer displays time in seconds. 14. A group of students is doing a speed experiment, and they measure the speed of a car rolling down a ramp five times at the exact same location on the ramp. Review their data below: 66.7 cm/sec; 70.5 cm/sec; 64.9 cm/sec; 67.8 cm/sec; 69.1 cm/sec What factors could explain the variability in their data? Applying your knowledge 1. Many old number systems were based on 12 s because of the following way of counting with the hands: By using the thumb on one hand, a person can easily count to twelve on the four fingers by touching the tip and then the first two joints of each finger. By using the same method on the other hand, the same person could keep track of how many times he or she reached 12 on the first hand. Try out this method and calculate how high it is possible to count using this method. 2. Research the number system and units of an ancient civilization and write a short report on what you learned. 3. Read an article in a science magazine and try to identify how scientists have used the scientific method in their work. 4. Research the speeds of many kinds of animals and make a table showing slowest to fastest. 5. Prepare a short report on important speeds in your favorite sport. 20

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