Lab 1- Introduction to Motion

Transcription

1 Partner : Purpose Partner 2: Lab - Section: The purpose of this lab is to learn via a motion detector the relationship between position and velocity. Remember that this device measures the position of your body or another object. You should see that that the structure of the lab is very similar to your homework assignment. In Part, we will create and analyze position-time graphs. In Part 2, we will study velocity-time graphs and learn how to gain information from them. Finally, in Part 3, we will learn to relate both types of graphs together. Apparatus List Motion detector mounted to a stand Meter stick ScienceWorkshop 75 interface Introduction In this lab, you will use the motion detector to create position-time and velocity-time graphs from the motion of your own body. As you move in front of the detector, the computer will display information based on how far you are from the detector (the position-time graph) or how you quickly or slowly you are moving with respect to the detector (the velocity-time graph). There are a few conventions you should be aware of, as they will be referred to through this Minilab and through the rest of the course: Distance is short for "distance from the motion detector." The motion detector is the origin (the zero point) from which distances are measured. The motion detector works by measuring the closest object directly in front of it (such as your arms if they swing when you walk), so please be careful about how you walk! Note that it is best to avoid getting too close to the detector, since it may have issues detecting objects accurately from a distance less than approximately 2cm. If you have any problems with your program, don t hesitate to ask your TA for help. Also, please remember the following rules with respect to the computer programs: Generally, you do not need to save your work on the computer. However, if you do want to save some file, please first create a folder with your name within the Documents folder and then save the file within that folder. DO NOT turn off the computer, monitor or the black 75 interface box when you are done. This ensures that the equipment and computer will be ready to go for the next group that participates in the lab and it will avoid interruptions with regular scheduled system maintenance. University of Utah Department of Physics & Astronomy 7

2 Part One: Position-Time Graphs Procedure Activity Creating Distance-Time Graphs The motion detector should be plugged into the 75 interface with the yellow plug in port and the black plug in port 2. Open Internet Explorer, go to the lab website and click on the link Capstone. There, you will find links to lab activity files for Physics 25. Click on.cap to open today s project. A dialog window will appear somewhere on your screen and you should choose to Open the file. It will open with the Capstone software that is already loaded on your computer. Note: In case internet connections are interrupted, there is also a copy of the.cap file on your computer. Ask a TA for help finding it in that case. However, generally, you should attempt to load the Capstone activities from the website because they represent the most up to date versions of the activities. Near the top of the screen you should see one or more tabs. By clicking on a different tab, you look at different pages of the activity. Each Capstone file may contain several pages, some may be instructional, others for the actual data acquisition. To check that your equipment is functioning correctly, find the tab called Part A and click on it. You will see a position versus time graph and then you can press the Record button in the lower left region of the Capstone window. Note that there is a 2 second countdown before the program will start taking data (this is called a delayed start), then a 2 second clock will start while taking data. You will hear a clicking sound from the detector and see a plot of data on the screen during the 2 second period. Try walking away from the detector and make sure it records your movements (especially about 2-3 meters away). If you do not see anything on the screen, you may need to adjust where your detector is pointing until it does detect you. Delete this Run from the screen (there is a button at the bottom of the Capstone window). It will be important for you to check the scales on your graphs in your lab manual, since the axes may be different than those you see in Capstone. In this first section, create distance-time graphs for the four different situations listed below using Capstone. Then answer Questions and 2 that follow. Note that you can delete data sets from the graph using a button at the bottom of the Capstone window. This way you can go back to an empty graph and then do a new one. You can also record multiple graphs on top of each other. Please analyze the following situations and draw the graphs associated with them n the axes provided [.5 pts per graph] a) Start at ½ meter from the detector, and walk away from the detector at a slow, steady pace. Draw the graph that is created on the left. b) Again, start about ½ meter from the detector, and walk away from the detector faster than part a, but still steady. Draw the graph that is created to the right. University of Utah Department of Physics & Astronomy 8

3 c) This time, start about 3 meters away from the detector and walk towards it at a slow, steady pace. Draw the graph that is created to the left. d) Again, start from about 3 meters away and walk towards the detector faster than part c, but still steady. Draw the graph that is created to the right. Q. [.5 pts] What happens to the slope of the line when you walk faster as opposed to slower? Q.2 [.5 pts] How is the line different when walking away from the detector as opposed to walking towards the detector? In this next section, we will ask you to create a position-time graph based on the description of an object s motion. First, we ask you to draw a prediction of how you think the object will move on the left. Then, use Capstone to do the experiment and compare the experimentally recorded data with your prediction. Draw the following situation: A person starts at the meter mark, walks away from the detector slowly and steadily for 4 seconds, stops for 3 seconds, then walks back to the detector quickly. [Prediction is.5 pts for completing, Results is.5 pts for correctness] Prediction Capstone Results University of Utah Department of Physics & Astronomy 9

4 Philosophical Interlude (your grade directly depends on how you understand this) One of the main ideas we hope you will take from this lab is to use critical thinking skills to solve abstract problems. One way we do this is to ask you open-ended questions that ask you to describe or analyze a particular idea or situation. In order to answer a question like this correctly, you may wish to answer by sketching a graph and discuss specific features such as the slope steepness. You can also use words (a qualitative approach) or numbers (a quantitative approach) to answer these questions. It will be your choice which method to use in order to best answer these questions. Activity 2 Creating More Complicated Position-Time Graphs Below, there are three position-time graphs shown. Try to produce graphs like this using Capstone and observe how you need to move to achieve them. Describe how you have to move to produce the distance-time graphs shown the following graphs. Use Capstone to map this motion. [.5 pts per part] a) a) b) b) c) c) University of Utah Department of Physics & Astronomy

5 Procedure Part 2: Velocity-Time Graphs In this part of the lab, Capstone will plot velocity using the motion detector. Note that you learned in your homework that velocity is both a speed and a direction. Thus, it can be positive or negative depending on which direction you travel. As part of your procedure, you will need to find what makes velocity negative, and what makes velocity positive. Activity One Basic Velocity-Time Graphs Select the tab named Part 2. This is a velocity-time graph. In the following activities, you will be asked to create graphs for a couple of different situations. Once you have created the graphs, please answer Questions 3 and 4. Please create the following graphs [ pt per graph] a) Start about ½ meter in front of the detector, then move away from it at a slow, steady rate. Draw the velocity-time graph on the axes to the right (just draw smooth patterns and leave out smaller bumps that are mostly due to your steps). b) Start about ½ meter in front of the detector, then move away from the detector faster than before, but still steady. Draw the velocity-time graph on the axes to the left. V (in m/sec) c) Start a few meters away from the detector and walk slowly towards the detector. Draw the velocity-time graph on the axis to the right. Q.3 [.5 pts] What happens to your line when you start walking faster versus walking slower? V (in m/sec) V (in m/sec) Q.4 [.5 pts] What is different between when you move towards the detector versus when you are moving away? How do you move to create a negative velocity, and how do you move to create a positive velocity? University of Utah Department of Physics & Astronomy

6 Activity 2 Creating More Complicated Velocity-Time Graphs Below, you see a grey box with an empty velocity-time graph. First, read the description of the motion above the grey box, and draw what you think the motion will look like as a dotted line on the graph. Then, select again the tab Part2 in Capstone and create the graph of the motion. Draw that graph in the grey box as a solid line. Analyze the following situation [ pt (.5 pts for prediction.5 pts for actual data)] Walk away from the detector slowly and steadily for seconds, then stop for 4 seconds, then walk towards the detector about twice as fast as before for the final 6 seconds (or until you run out of room!) V (in m/s) Time (in s) Open the tab called Part2 Below, you see a graph that describes a difficult to reproduce, complicated motion. Use your own motion to try to produce the graph in Capstone. It may take you a few tries to get a good match, so plan out how to move to get the correct graph. Then, answer Questions 5 and 6 below. v (m/s) time (s) University of Utah Department of Physics & Astronomy 2

7 Q.5 [ pt] Describe how to move in the graph above to create an exact copy each segment. -4 Seconds, 8-2 Seconds, and 8-2 Seconds: 4-8 Seconds: 2-8 Seconds: Q.6 [ pt] You may have noticed that Capstone does not produce vertical (straight up-anddown) lines like we have used in many of the sample graphs in this manual. In fact, it is physically impossible for a vertical line to be created on a velocity-time graph and a distancetime graph. Why is this? (Hint: It may be helpful to look at the definition of velocity again to find the answer!) University of Utah Department of Physics & Astronomy 3

8 Part 3: Relating Distance-Time and Velocity-Time Graphs Procedure This section will be split into 3 activities. First, you will create a velocity-time graph when given a distance-time graph. Next, we will learn how to calculate average velocity using both a distance-time graph and a velocity-time graph. Finally, we will create a distance-time graph when given a velocity-time graph. Activity - Creating a Velocity-Time Graph from a Distance-Time Graph Below, you will notice both a distance-time graph and a velocity-time graph created from Capstone. The distance-time graph is filled out for you. The goal here is to generate a positiontime graph that has the same shape as the given position-time graph. At the same time a velocity-time graph will be generated that corresponds to the position-time graph. Make a prediction of the velocity-time graph using a dotted line, then select the tab Part 3 in Capstone, acquire data until your position-time graph looks good. Then draw your velocity results in a solid line into the velocity-time graph. Accuracy will be important on this graph, since you will use your graph to make some calculations in Activity 2. After drawing your graph, please answer Question 7. Keep only the best run on Capstone and delete the rest. Please create a velocity-time graph from the following information. [ pt] x (m) V (m/sec) Time (s) Time (s) Q.7 [.5 pts] How does the distance graph change if you had moved faster during the inclined portion? How would that have changed the velocity graph? Activity 2 Calculating Velocity In this activity, we will learn three different methods to calculate an average velocity from the graphs in Activity of this section. Average velocity is the total distance travelled by an object in a given period of time divided by that time period. Remember from the homework that this is the same as the average slope for a distance-time graph in a given time period. Thus, these methods are simply different ways to find a slope. Solve for all three methods, and then please answer Question 8. University of Utah Department of Physics & Astronomy 4

9 a) Using the slope formula to calculate average velocity [ pt] In this first approach, we will use the slope formula to calculate the average velocity for the given time period. For this portion, use the tool called Show coordinates and access Delta Tool of Capstone to find the rise and the run of two points along the section of the graph where you are moving. You will find it helpful hints to read the corresponding section in the Capstone Guide at the beginning of this manual. Record your results on the appropriate lines below: (Hint: The Show coordinates and access Delta Tool button looks like this: ) Change in distance: m Change in Time: s Average Velocity m/s b) Using a linear fit to calculate average velocity [ pt] A linear fit is a method that will create a best-fit line that will give us the slope of our position-time graph s steep section. You will find it helpful hints to read the corresponding section in the Capstone Guide at the beginning of this manual to help you perform this calculation. First click on the Select Range button, then adjust the range, and finally select the Linear Fit from the Select Curve Fits button. An equation is displayed on your graph. The slope, m, is the average velocity of the region. Velocity value (m) from the linear fit: m/s c) Using Statistical calculations to determine average velocity [ pt] A third way to calculate the average velocity is to calculate a mean value of all the points. You may have learned in your math class that an average or a mean is calculated by adding up a list of values, then dividing by the total number of values in the set. Thankfully, instead of doing this by hand, Capstone will do it for you. After selecting as many points as possible on your sloped line, using the Range tool, click on the small triangle to the right of the Statistics button ( ) and select Mean. The calculated mean will be displayed and it is the average velocity. Average velocity (mean) value: m/s. Q.8 [.5 pts] How do your velocity calculations from a) and b) compare with the results from c), which are based on the velocity graph? If there are any differences, explain why they are different (in 3 words or less). University of Utah Department of Physics & Astronomy 5

10 Activity 3 - Predicting Distance-Time Graphs from Velocity-Time Graphs Shown below is a velocity-time graph. Your task is to perform a motion that creates such a graph and also the corresponding distance-time graph. To simplify your work, you will want to plan out the steps to take in order to create the graphs, and then use Capstone to actually create the graphs. Once you have obtained sufficiently good results, please draw the positiontime-graph into the grey box below and answer Questions 9 and at the end of the lab. Please create a distance-time graph from the following information. [.5 pts].5.3 V (m/sec) Time (sec) Q.9 [.5 pts] How can you tell from a velocity-time graph that the moving object has changed direction? What is the value of the velocity at the moment the direction changes? Q. [.5 pts] How can you tell from a distance-time graph that you are travelling at a constant velocity? How about from a velocity-time graph? University of Utah Department of Physics & Astronomy 6