ACTIVITY 1: Measuring Speed

Transcription

1 CYCLE 1 Developing Ideas ACTIVITY 1: Measuring Speed Purpose In the first few cycles of the PET course you will be thinking about how the motion of an object is related to how it interacts with the rest of the world. In order to gather evidence to test your ideas you will need a reliable method to determine one particularly important aspect of the motion of an object its speed. For example, it may be important to know if the object is moving at a constant speed or is its speed changing? In many activities your group will use a device called a Motion Sensor, connected to a computer, to gather this evidence. In this first activity you will find out how to use the Motion Sensor, and the computer program used to run it. You will also begin thinking about how the information from the Motion Sensor tells you about what is happening to the speed of an object during short periods of time. How can you represent motion involving speeding up, slowing down and constant speed? Initial Ideas Imagine taking a short trip in your car. When you first start out, you push on the gas pedal, the car starts moving and then picks up speed as you pull away. Once you reach a reasonable speed you set your cruise control and your speed then remains constant for a while. However, as you approach your destination you use the brakes to slow the car down and make it stop PET Modified by Dr. Armen Kocharian 1-1

2 Cycle 1 How could you represent the motion of your car in order to indicate how it is different in these three situations (speeding up, constant speed, and slowing down)? Think about the first question below individually. On your own, try to think of two different ways to represent the motion of the car, that could be used to indicate how its speed is behaving during the three segments of the short trip described above. (In the past people have used pictures, math symbols, charts, diagrams, graphs, equations, arrows etc.) Sketch your representations below. Now share your ideas with your group members. Also, listen to their ideas and try to agree on two representations that are most informative about what is happening to the speed of the car during each part of the trip. Illustrate these representations on a large presentation board. Your instructor will now lead a short whole-class discussion about all the groups ideas. Be prepared to explain your group s representations and also make a note of any ideas you think are useful that are different from those of your group. 1-2

3 Activity 1: Measuring Speed Collecting and Interpreting Evidence Experiment #1: How does a speed-time graph represent speeding-up and slowing-down? You will need: Cart Track Wood blocks of various thickness (or similar) Copy of the handout, How to use the Motion Sensor Access to a Motion Sensor connected to a computer Color pencils STEP 1: Examine the Motion Sensor. The part that does the measuring is inside the circular opening, covered by a grille. Note that you can adjust the tilt of the sensor mechanism using the dial on the side of the sensor housing. The sensor works by emitting short pulses of high-frequency sound (beyond the range of human hearing) that then reflect back to the sensor from any object in front of it (within a limited range). The sensor then sends information about these pulses to the computer, which uses it to determine the speed of the object. There is a switch on the top of the sensor that can be used to select either short or long range, depending on how far away the object of interest is likely to move. For all the situations you will investigate in this course, the switch should be on the short range setting. (On some sensor models this setting may be indicated by a small picture of a cart, like the one you will be using.) STEP 2: Open the data collection file on your computer for this activity. (See the separate handout for details on how to open files and operate the data collection program on the computers in your classroom.) When the file opens you will see a blank speed-time graph. It is set to measure speeds between 0 and 120 centimeters per second (cm/s) for a period of three seconds. 1-3

4 Cycle 1 Place the Motion Sensor on the table and set the switch to the short range (if it is not already). One member of your group should now place their hand about 30 to 40 cm in front of the sensor and then move their hand slowly toward and away from the sensor while you collect data. (Refer to the handout again.). Watch the graph being drawn on the computer as the hand is moved. The data collection will stop on its own after three seconds. Repeat the experiment, only this time your group member should not move their hand, but keep it stationary at 30 cm from the sensor until the computer has stopped recording data. How does the speed-time graph look when the hand is not moving? Does this make sense to you? Briefly explain why. STEP 3: Slot the Motion Sensor on to the end of the track. Now place a wood block under the track at the sensor end to raise it up. (How you do this will depend on how your track is supported. If your track has legs put the block under one of these.) Place the cart on the track about cm in front of the sensor and release it. (Do not give it a push of any sort.) The cart should start to move on its own, and clearly speed up as it moves along the track. (If the cart does not move, or if it does not seem like it is speeding up as it moves, add one or more wood blocks to raise the end of the track a bit more and then try again. Add as many blocks as necessary until you are sure that the cart is speeding up as it moves.) 1-4

5 Activity 1: Measuring Speed Once your are satisfied that the cart is speeding up as it moves, return it to the starting point and record speed-time data with the Motion Sensor as you repeat the experiment. Note: It takes about a second for the computer to start recording data after you click on the relevant button (or hit the Enter key). To make sure you see the start of the cart s motion on the graph it is a good idea to watch the computer screen and only release the cart when you see the very start of the graph appear on the screen. (If you are having trouble collecting good data, your instructor may be able to give you some more tips.) Sketch the speed-time graph for the motion of the cart below. How does the graph indicate that the speed of the cart was increasing as it moved? At many points in this course you will be asked to think about what might happen if you were to change something about an experiment, or performed a different, but closely related, experiment. Such questions will ask you to Imagine... or Suppose It is very important that you take the time to think about these questions and explain the reasoning behind your responses before you perform the new experiment. 1-5

6 Cycle 1 Imagine you were to make the track steeper, by raising the end of the track even higher than it is now, and then repeat the experiment. Do you think the cart would speed up in exactly the same way as it did before, or would anything be different about the way its speed behaves? If so, what would be different, and how would this difference be represented on the speed-time graph? Explain your reasoning below and, using a different color pencil, sketch your prediction on the speed-time graph above. Label this line Prediction for steeper track. STEP 4: Before testing your idea it is a good idea to store the previous data so that you can compare the new data to it directly. (The data collection program you are using may do this automatically. If not, see the separate handout for how to do this.) Now, raise the sensor end of the track slightly higher by adding one or two more thin blocks of wood, and then repeat the experiment Using two different colors sketch the two speed-time graphs for the motion of the cart below. Label the lines so that you can distinguish between them. 1-6

7 Activity 1: Measuring Speed Does the speed-time graph for the cart on the steeper track indicate that the cart s speed changed differently, in any way, than before? If so, what was different, and how does the graph represent this? STEP 5: Remove the extra block(s) you added in STEP 4 and set them aside. Move the original block(s) so that they are under the other end (or leg) of the track, so making the track tilt in the other direction. Now place the cart about cm in front of the Motion Sensor and give it a quick push with your hand so that it moves along the track away from the sensor. (One of your group should stop the cart just as it starts to move back toward the sensor, or just before it hits the end of the track.) Do not record motion sensor data yet. Describe how you think the speed of the cart changes (if at all) as it moves along the track, away from the sensor, after your initial push. Practice this procedure until you can make the cart travel almost to the end of the track, before it slows to a stop on its own. (Remember to have one of your group hold it at this point so that it does not start moving back toward the sensor.) Suppose you were to record Motion Sensor data for the cart, including the short period while you were giving it the initial push. What do you think a speed-time graph of its movement would look like? Sketch your idea on the blank graph below. 1-7

8 Cycle 1 Explain your reasoning for drawing the graph as you did. Now, suppose you were to add the extra blocks you set aside, to make the track even steeper and then repeat the experiment, trying to make sure that just after your initial push the cart started out at the same speed as before. On the same graph above, sketch what you think the speed-time graph would look like now (use a different color and label the two lines accordingly) and explain your reasoning below. STEP 6: Before testing your idea you will need to erase the data from the previous steps. (Again, see the separate handout for how to do this.) Now test your ideas from STEP 5 by performing the two experiments. (Remember to store the data from the first run if necessary and add the extra block(s) for the second one.) Sketch the speed-time graphs below and label the lines appropriately. 1-8

9 Activity 1: Measuring Speed Do your predicted graphs from STEP 5 agree with those from the experiments? (Note: Precise numbers are not important, but you should pay attention to the general shape.) If not, discuss any major differences with your group and try to understand them. Describe any changes in your thinking as a result of these discussions. Experiment #2: How can you make the cart move at a constant speed? You will need: Cart Track Wood blocks of various thickness (or similar) Copy of the handout, How to use the Motion Sensor Access to a Motion Sensor connected to a computer STEP 1: In the previous experiment you saw what speed-time graphs for the cart looked like during periods of time when its speed was changing (either increasing or decreasing). 1-9

10 Cycle 1 What do you think the graph would look like if the speed of the cart were constant (not changing) for a period of time? Sketch your idea below and briefly explain your reasoning. STEP 2: Your task now is to make the cart move at a constant speed (or as close to constant as you can make it). You may use any combination of manual pushes, or blocks to tilt the track, to achieve this. (Hint: You may need to give the cart a push to get it moving to start with, but if you do, it should then move at a reasonably constant speed for a period of time after that initial push.) Use the Motion Sensor to check whether the speed is really reasonably constant. When you are satisfied that the cart is moving at a reasonably constant speed (for at least a short period of time) sketch the actual speed-time graph below, and indicate the section(s) where its speed is constant. 1-10

11 Activity 1: Measuring Speed Briefly describe what strategy you used to make the cart move at a reasonably constant speed. Summarizing Questions Discuss these questions with your group and note your ideas. Leave space to add any different ideas that may emerge when the whole class discusses their thinking. S1: Return to the description of short car trip in the Initial Ideas section at the beginning of this activity. Below, sketch what you think a speed-time graph of the complete trip would look like, and label the different segments of your graph according to how the speed of the car is behaving during that period. 1-11

12 Cycle 1 S2: Suppose your car had failed to start and had not moved at all. Below, sketch what you think the speed-time graph would look like in this case, and explain why you drew the graph as you did. S3: Write a few sentences to describe the behavior of the speed of the object represented on the speed-time graph shown below. In your description you should also explain briefly how you determined this information from the graph