KEY CONCEPTS AND PROCESS SKILLS

Measuring 74 40- to 2-3 50-minute sessions ACTIVITY OVERVIEW L A B O R AT O R Y Students use a cart, ramp, and track to measure the time it takes for a cart to roll 100 centimeters. They then calculate speed from their distance and time measurements. They explore the units used for speed and the concept of speed as a rate of motion. They further investigate speed by designing and conducting an experiment that relates the speed of the cart to its release height on the ramp. KEY CONCEPTS AND PROCESS SKILLS (with correlation to NSE 5 8 Content Standards) 1. The motion of an object can be described by its position, direction of motion, and speed. (PhysSci: 2) 2. Average speed is the distance an object travels divided by the time taken to travel that distance. (PhysSci: 2) 3. Scientists design and conduct scientific investigations. They communicate their procedures, results, and explanations to other scientists. (Inquiry:1) 4. Students should be able to design and conduct appropriate scientific investigations. This may include the use of experiments with multiple trials. (Inquiry: 1) 5. Good experimental design requires keeping as many variables as possible the same except for the one being tested so that any results can be ascribed to the variable changed. (Inquiry: 1) 6. Mathematics is important in all aspects of scientific inquiry. (Inquiry: 1, 2) KEY VOCABULARY distance evidence error controlled variable rate speed tested variable time interval variable E-11

Activity 74 Measuring MATERIALS AND ADVANCE PREPARATION For the teacher 1 Scoring Guide: DESIGNING INVESTIGATIONS (DI) For each group of four students 2 track pieces 1 cart 1 ramp 1 timer * 1 meterstick * 1 marker * masking tape * 1 book or heavy object (optional) For each student 1 Scoring Guide: DESIGNING INVESTIGATIONS (DI) (optional) 1 Science Skill Sheet 5, Elements of Good Experimental Design (optional) *Not supplied in kit Masters for Student Skill Sheets are in Teacher Resources II: Diverse Learners. Masters for Scoring Guides are in Teacher Resources III: Assessment. TEACHING SUMMARY Getting Started 1. Introduce students to the concept of speed. Doing the Activity 2. (MATHEMATICS) Students take measurements and calculate speed. 3. Discuss the experimental variables in the investigation. 4 (DI ASSESSMENT) Students design and conduct an investigation. Follow-Up 5. (MATHEMATICS) Discuss speed and its units. 6. (MATHEMATICS) Review the definition of rate.if this works) E-12

Measuring Activity 74 BACKGROUND INFORMATION An object in motion takes time to change its position. is the measurement of the rate of change in position and can be linear or rotational. The units for speed are a distance or an angle per unit of time, such as miles per hour or degrees per second. Many moving objects do not travel at a constant speed. Instantaneous speed is the term given to the speed of an object at any instant during its journey. Average speed is the distance the object traveled divided by the total time elapsed in traveling that distance. Objects can attain the same average speed through numerous different series of instantaneous speeds. For example, one car might travel a certain distance at a steady 40 mph, while another makes the same trip at a speed of 30 mph for the first half of the trip and 50 mph for the second half. At the end of the trip, both cars will have made the trip at an average speed of 40 mph although their instantaneous speeds were different. The term average in the context of average speed should not be confused with mathematical mean. In the example above, the average speed and the mathematical average of the speeds are the same, but this is not always the case. Another car making the same trip could also average 40 mph having traveled at speeds of 20 mph, 30 mph, and 60 mph, which gives a mathematical mean of 37 mph not equal to the average speed of 40 mph. Velocity (s) and velocity (v) are related concepts but are not the same thing. The velocity of an object includes both its speed and its direction. Whereas speed is a scalar quantity, velocity is a vector quantity, which means it must be described by an amount and a direction. This unit discusses the concept of speed only. Acceleration Negative acceleration, like any acceleration, is a vector quantity that has both magnitude and direction. In linear motion, the term negative acceleration refers to acceleration that is a result of either a slowing down in a positive direction or a speeding up in a negative direction. For example, a car that applies brakes while moving forward (positive direction) in a straight line has negative acceleration because the acceleration is in the opposite direction as the velocity. However, a car that is speeding up while moving backwards in a straight line (increasing negative values) is also said to have negative acceleration because, although it is speeding up, it is doing so in the negative direction. The term deceleration is used to refer to negative acceleration given in the first example above, that is, when the object is moving in a straight line in the positive (+) direction and has decreasing speed from an acceleration in the opposite direction (i.e., applying the brakes). Deceleration is a specific case of negative acceleration and reflects the situation presented in the activity. E-13

Activity 74 Measuring TEACHING SUGGESTIONS GETTING STARTED 1. Introduce students to the concept of speed. Ask students what things can contribute to a car accident. Make sure speeding or driving fast is mentioned. Explore students ideas of speed, using the units described in the introduction and everyday examples. For example, in the United States, car speed is typically measured in mph while km/h is used for car speed in other countries. Point out that scientists often measure everyday speeds in m/s but that in this activity, students will measure speed in cm/s. Have students read the introduction and Challenge to the activity. Ask them how they think speed is measured. If they respond with names of devices, such as a speedometer or radar gun, ask, How did people measure speed before those devices were invented? All speed-tracking devices, whether modern or not, measure the time interval it takes to travel a distance. A time interval is the elapsed time between two events, such as the start and finish of a race. To measure speed, the distance, or the length between two points, is also measured. Guide students to understand that the basic method of measuring speed must involve measuring both of these quantities. Point out that because of this, all speed-measurement units are a combination of a distance unit and a time unit. DOING THE ACTIVIT Y 2. (MATHEMATICS) Students take measurements and calculate speed. Distribute the materials for the activity and have students review the procedure. Ask students, Why do you think you are asked to do three trials? Students should have the sense that repeating a trial several times improves the quality of the data set, but have them try to articulate the reason why. Create a list of potential sources of error, or unavoidable inaccuracies that occur because no measurement can be made with perfect precision. In this activity timing errors will cause the measured time to be sometimes too long and sometimes too short. Sometimes students may stop the watch too soon, and sometimes too late. Either case introduces error in the measurement. A person s reaction time is not a mistake but a limitation of one part of the experimental process. Error can be reduced by finding the mathematical mean of several measurements taken under the same conditions. In this experiment student groups average results of three trials in an effort to minimize error. Point out that although some errors are beyond their control, students should try their best to be as precise as possible to minimize their own errors during the experiment. This includes being consistent about how they release the cart, how and where the track is set up, and how the timer is used. For example, viewing the cart from above when timing it across the start and stop points increases the timing accuracy. As a class, review various methods for timing the cart, and decide on a reasonably accurate one that all groups will use. Using the same method allows groups to most easily compare and pool their data. Emphasize that in any experiment, no matter how hard you try to do the procedure perfectly, there is almost always some error. Explain that by doing multiple trials which if done identically would give identical results you can see how much error you have in your experiment. Point out that if there is too much difference in measurements, you need to figure out why and make corrections to your procedure, equipment, or technique. Teacher s Note: Before students complete the procedure, make sure they have a way to prevent the cart from rolling off the track and falling to the floor. The cart will sustain damage and provide inconsistent results if repeatedly handled in this way. Either have students place a book or other heavy object at the end of the track to prevent a runaway cart, or have students perform the experiment on the floor. Ask students to complete Part A of the Procedure. They might notice that the cart slows down over the E-14

Measuring Activity 74 course of the track and may decide, in light of the previous discussion, that this introduces error in the experiment. If students raise this issue, point out that the cart should slow down consistently in each trial since the track is a controlled component of the experiment. Since the slowing is occurring across all trials, it is not a factor that will introduce noticeable error in the data. If appropriate, briefly discuss the friction between the cart and the track that slows the cart. Because friction is formally introduced later in the unit, it is sufficient at this point to merely identify it and its effects. In Procedure Step 7, students determine the speed of the cart for each trial. Point out the equation for speed: speed = distance / time Write the equation on the board, and introduce or review its use with several examples, by asking such questions as, What is the speed of a car that travels 100 miles in 2 hours? (50 MPH), and What is the speed of a car that travels 30 kilometers in 1/2 hour? (60 km/h). Reinforce the idea that the forward slash (/) is read as per and means divided by. When students finish the Procedure, have each group report its results, and compile them on the board. Students should find that the cart takes between 1 and 2 seconds to travel 100 cm, as shown by the sample data below. Results may differ depending on variations in the cart and track. Sample Results for Cart Trial Distance (cm) Time (s) (cm/s) 1 100 1.34 74.6 2 100 1.36 73.5 3 100 1.14 87.7 Average 78.6 If any group s results are significantly different but are consistent, try to determine the cause. If only a few times are really different, point these out, and discuss whether or not to discard these outliers as bad data or to keep them in the data set. Typically students want to discard the outliers. In either case, point out that although these times are significantly different, it doesn t necessarily mean they are wrong. 3. Discuss the experimental variables in the investigation. Explain that the factors that influence the speed of the cart are all variables, or factors that could all have any number of values, depending on the situation. In this experiment, there are many controlled variables, that is, variables the investigator holds constant or ignores in order to analyze a relationship between other variables without interference. In this investigation, students control some variables, such as the mass of the cart, the angle of the ramp, and the surface of the track. A tested variable is one that is systematically changed so the investigator can determine its effect. By changing only one variable in this activity, the release height students can observe and compare changes caused by that factor. Variables that are neither controlled nor tested are called uncontrolled variables, and they are the ones the investigator either ignores or is unable to control. In this investigation, for example, the levelness of the surface that students laid their track on is not controlled. 4. (DI ASSESSMENT) Students design and conduct an investigation. Have students begin Part B by predicting what would happen if they changed the release height and then writing down a procedure to test their prediction. Emphasize for them the importance of controlling all variables except the one they are testing ramp height. If appropriate, hold a class discussion to come up with a reasonable experimental design to test the effects of release height on speed. Once you have approved each group s procedure, distribute the equipment, and let students complete the investigation. Point out that if they realize that some part of their procedure is wrong, they should correct it as they go along and note the change in their notebooks. E-15

Activity 74 Measuring The DESIGNING INVESTIGATION (DI) Scoring Guide may be used to evaluate student work from Part B. If appropriate, provide each student with a copy of the Scoring Guide and/or Science Skills Student Sheet 5, Elements of Good Experimental Design. Or, you might hold off on the evaluation for now, and instead use the skill sheet to model how to control variables and create a procedure. Even if you decide to score this portion of the activity, you may still hold a class discussion to come up with a reasonable experimental design together. After students complete their experiment, encourage each of them to revise and rewrite their procedures before turning them in to be assessed. Let students know in advance how you will be providing feedback for this assessment. Level 3 Response: Procedure for Determining the Effect of Ramp Height on Cart 1. Connect the ramp and the two straight tracks. 2. Measure out and mark 50 cm point on the track. 3. Release the cart with its rear axle at the Notch A, and time it until it reaches the 50 cm mark. Sample student data for this response is shown in the tables below. Sample Student Data for Part B: Height and Cart Release Height A Trial Release Height B Distance (cm) Time (s) (cm/s) 1 50.43 116 2 50.40 125 3 50.39 128 Trial Distance (cm) average Time (s) 123 (cm/s) 1 50.52 96 2 50.57 88 3 50.62 81 average 82 4. Record the time taken and the distance traveled. 5. Calculate the speed, and record it in the table. Release Height C 6. Do two more trials, and calculate the mathematical mean of the speeds. Trial Distance (cm) Time (s) (cm/s) 7. Repeat the experiment for Notches B and C. 1 50.91 55 2 50.85 59 3 50.94 53 average 56 Briefly discuss students predictions and results. Most students will have correctly predicted that increasing the starting height will increase the speed of the cart. When they are reviewing the data, remind students of the error due to timing the cart. It may be helpful when comparing speeds of the carts that traveled over different distances that the timing errors are more significant in the slower speeds because it is a larger portion of the time measured. E-16

Measuring Activity 74 FOLLOW-UP 5. (MATHEMATICS) Discuss speed and its units. Although suggestions for introducing the terms median and mean in the investigation are not included here, they are referred to parenthetically in the activity. If your students are familiar with these terms, this activity provides a good opportunity to review and reinforce them. When discussing Analysis Question 1, some groups might have picked the middle (median) value. Others are likely to have found the average (mean) for their three trials, or perhaps even for all the trials by the entire class. Explain that averages are a mathematical way to find the middle value. If necessary, review how to calculate a mean. Point out that finding the average value helps take into account any errors. If one trial is extremely different than the others, however, it may be the result of a significant error and may skew the results. It is sometimes appropriate to discard such a value, especially if the experimenter is aware of a possible source of error in the value. Emphasize that more trials increase the likelihood that the average is representative. When discussing Analysis Question 2, emphasize that any combination of distance and time units is a legitimate unit for measuring speed. In the United States, most people are concerned with speed when driving their cars or motorcycles. The U.S. unit for road distances typically is miles, so it is most convenient to measure car speed in mph. The common unit for road distances in most other countries is kilometers, so it is most convenient for drivers in other countries to measure speed in kph. Scientists most often use m/s because that is the standard international (SI) unit. Point out that we often use units that are both convenient and give friendly numbers between 1 and 1,000. For example, common units for speed such as mph and kph, are measured per hour, instead of per second, minute, or year. Using seconds or minutes would make common speeds too small (e.g. 30 mph = 0.5 miles per minute), and using days or years would make them too big (e.g. 60 MPH = 1,440 miles per day). These units are not incorrect, just less desirable. To help get this point across, you can ask questions, such as, What unit would be most convenient to measure how fast your fingernails grow? Students should suggest such units as mm/month or cm/year as opposed to meters/month or miles/year. Analysis Question 4 provides practice in and reinforcement for using the equation speed = distance/time by requiring students, when given the time and the speed, to find the distance. To use the equation, many students find it easier to rearrange it: distance = speed x time If needed, demonstrate how to rearrange the equation mathematically. The discussion of Analysis Question 4 also provides an opportunity to introduce or review the conversion of units from centimeters to meters to kilometers and from seconds to minutes to hours. 6. (MATHEMATICS) Review the definition of rate. In conclusion, discuss the concept of rate by first asking students if they have ever heard the term rate, and, if so, if they know what a rate is. If needed, explain that a rate is a ratio of two different kinds of measurements., for example, is a rate that depends on the value of both distance and time. is the distance traveled in (or per) a given time. Rates, such as speed, are typically calculated by dividing one measurement by another. is calculated by dividing the distance an object travels by the amount of time it takes to travel the distance. The units for speed, such as miles per hour, reflect the fact that a speed is calculated by division. Challenge the class to come up with other examples of rates and describe the two measurements needed to determine the rate. Given the preceding example, many of the rates students come up with are likely to be time-related. If necessary, point out that there are other types of rates, such as miles per gallon for fuel consumption, the price per dozen for the cost of eggs, or the amount of Euros you would get for an American dollar. Show students an everyday example of a rate familiar to them. One example would be a simple demonstration of adding water drops to a container to illustrate the contrast E-17

Activity 74 Measuring between a slower and a faster rate. In the water drop example, neither the number of drops that have fallen into the container nor the length of time the drops have been falling are sufficient by themselves to indicate the rate at which the cup is filling. To determine the rate, you must know the number of drops and the time taken to add these drops. Both of these quantities must be known in order to determine the rate of drops per second. SUGGESTED ANSWERS TO QUESTIONS 1. According to your data from Part A, what is the speed of the cart? A typical time for the 100 cm distance is between 1 and 2 seconds. The speed would then be in the range of 50-100 cm/s. 2. According to your data from Part B, what is the effect of release height on speed? Student data will vary but should reflect a trend of the cart slowing down as release height decreases. For example, the sample student responses in the Teaching Suggestions show the speed went from 123 cm/s to 82 m/s to 56 m/s as the height was decreased from notch A to B to C. 3. List some common units for speed. Why are there so many different units? Three common units for speed are miles per hour (MPH), kilometers per hour (kph or km/h) and meters per second (m/s). Different speed units are used because there are many different units for distance and time, and some units are more convenient to use than others in different situations. 4. What part(s) of your experimental design in Part B: a. increased your confidence in the results? Students are likely to suggest that the repeated trials and averaging increased confidence. b. decreased your confidence in your results? Students are likely to suggest that using your eyes to judge where to start the cart and to determine when to start and stop the timer decreased confidence. They might have also noticed a lag time from seeing to stopping the timer. 5. What is a car s speed, in m/s, if it travels: a. 5 meters in 0.1 seconds? 50 m/s b. 5 meters in 0.2 seconds? 25 m/s c. 10 meters in 0.2 seconds? 50 m/s 6. Reflection: Why do you think speeding is a factor in about 20% of fatal car accidents? Answers will vary. Students are likely to suggest increased stopping distance, less time to swerve out of the way, and greater impact force. Or, they may suggest that a car that is not designed to go faster will be more difficult to control at higher speed. Extension 1 Teachers can post student data on the SEPUP website by clicking on the TEACHERS button located under SEPUP USERS on the home page, and selecting ISSUES AND PHYSICAL SCIENCE on the pull-down menu to find on-line forms for posting data. Students can access the posted data by clicking on the STUDENTS button located under the heading SEPUP USERS, and then selecting ISSUES AND PHYSICAL SCIENCE on the pull-down menu, and then clicking on COMPARE DATA to find tables with student data from SEPUP classrooms. Extension 2 Because this problem requires some fairly complicated unit conversions, it may not be appropriate for all students. It is most suitable for students who enjoy solving challenging math problems. The police could issue speeding tickets in Questions 5a and 5c because in both cases the car is going 112 MPH, but in 5b it is going 56 MPH. a. 50 m/s = (50 m/s) x (60 s/min) x (60 min/hr) = 180,000 m/hr 180,000 m/hr = 180 km/hr x (0.62 miles/km) = 112 MPH b. 25 m/s = (25 m/s) x (60 s/min) x (60 min/hr) = 90,000 m/hr 90,000 m/hr = 90 km/hr x (0.62 miles/km) c. same as a. = 56 MPH E-18