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Name________________________Date_______________Partners________________________________
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
LAB 2:
ONE DIMENSIONAL MOTION
Slow and steady wins the race. –Aesop’s fable: The Hare and the Tortoise
OBJECTIVES
- To learn how to use a motion detector and gain familiarity with Data Studio.
- To explore how various motions are represented on a distance (position)-time graph
- To explore how various motions are represented on a velocity-time graph
- To discover the relationship between position-time and velocity-time graphs
- To begin to explore acceleration-time graphs
OVERVIEW
In this lab you will begin your examination of the motion of an object that moves along a line and how it can be represented graphically. You will use a motion detector to plot distance-time (position-time) motion of your own body. You will examine two different ways that the motion of an object that moves along a line can be represented graphically. You will use a motion detector to plot distance-time (position-time) and velocity- time graphs of the motion of your own body and a cart. The study of motion and its mathematical and graphical representation is known as kinematics. Marked distances
24 Lab 2 - One Dimensional Motion
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
INVESTIGATION 1: DISTANCE (POSITION) – TIME GRAPHS OF YOUR
MOTION
The purpose of this investigation is to learn how to relate graphs of distance as a function of time to the motions they represent.
You will need the following materials:
- motion detector
- masking tape marked on floor in meters
Questions to consider:
How does the distance -time graph look when you move slowly? Quickly? What happens when you move toward the motion detector? Away? After completing this investigation, you should be able to look at a distance-time graph and describe the motion of an object. You should also be able to look at the motion of an object and sketch a graph representing that motion.
ACTIVITY 1-1: DETERMINING THE INITIAL SPEED
- Be sure that the interface is connected to the computer. Open Data Studio. Click on Create Experiment on the opening page or under File, click on New Activity, which will go to the page where you can click on Create Experiment.
- Click on Digital Channel Input 1 on far left. A list of sensors appears. Find the Motion Sensor line, double click on the Icon beside the Motion Sensor line, and the software will connect the Motion Sensor to the 750 Interface. You should physically have the Motion Detector plugged into the Interface in the same manner. Close the Setup by clicking on the X in the upper right.
- On the left side of the screen under Data, click on Position and drag it down to the graph icon in the display window. A graph should appear on the right side of the screen displaying Position vs. Time.
- Note that you can change the scale on both axes by moving the mouse to the numbers, click and drag them to decrease or increase the scale. Try this for both scales.
Comment : “Distance” is short for “distance from the motion detector.” The motion detector is the origin from which distances are measured. The motion detector
- detects the closest object directly in front of it (including your arms if you swing them as you walk).
- transfers information to the computer via the interface so that as you walk (or jump, or run), the graph on the computer screen displays your distance from the motion detector.
- will not correctly measure anything much closer than 20 cm. When making your graphs don’t go closer than 20 cm from the motion detector.
26 Lab 2 - One Dimensional Motion
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
- When you are satisfied with your graph, print one copy of the graph for your group.
Question 1-1: Is your prediction the same as the final result? If not, describe how you would move to make a graph that looks like your prediction.
- Everyone should gather around the computer for the next few steps to make sure everyone learns how to do these manipulations with Data Studio.
- Keep the previous graph of your motion on the screen. Change scales as desired or use the Autoscale (scale to fit) icon on the Graph window toolbar on far left. Click the Autoscale to see what happens.
- Click on the Smart Tool and drag the crosshair to individual data points to read the data at that point.
- To highlight regions of data, go to a beginning spot and “click-and-drag” a window around the region of interest. Data will be highlighted with yellow background. Highlight the first region of data when you walk away from the motion detector.
- To fit data, click on the Fit icon and choose the function you desire, in this case Linear Fit. Note the parameters (slope and y-intercept) are immediately given on the screen. To remove them, go back and “unclick” Linear Fit.
- Note that if you leave Linear Fit on, but choose a different highlighted region, the fit will be applied to the new region.
- Let's now examine the region where the person was at rest. Highlight the second region of your data which should be level. Then click on the Statistics icon (which appears as a Σ). Click on Mean and the mean value over that region will be displayed. Note the varying functions that can be obtained with the Statistics functions.
- If you have multiple runs on the screen, note that the various tools work on the run that is highlighted in the box in yellow. You can choose which data runs are displayed by clicking on the Data icon and clicking on and off the runs as you desire.
- Now find the slopes of the two regions in which you were walking. Remember that the return path was supposed to be twice as fast as the initial path. Use the Tools to find the velocity (slope) of each path:
First path slope: _________________ Second path slope: __________________
Lab 2 – One Dimensional Motion 27
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
Question 1-2: How did you do? Was the speed in the second path about twice that in the first?
INVESTIGATION 2: POSITION-TIME GRAPHS OF MOTION
The purpose of this investigation is to learn how to relate graphs of position as a function of time to the motions they represent.
You will need the following materials:
- motion detector
- number line on floor in meters
ACTIVITY 2-1: MATCHING A POSITION-TIME GRAPH
By now you should be pretty good at predicting the shape of a position-time graph of your movements. Can you do things the other way around: reading a position-time graph and figuring out how to move to reproduce it? In this activity you will move to match a position graph shown on the computer screen.
- In Data Studio , select “Open” and navigate to the “203” folder. Do not try to save the previous activity (you will be prompted to do this). Open the experiment file called L02.A2-1 Position Match. A position graph like that shown above will appear on the screen. Clear any other data remaining from previous experiments. It is a good idea to always click on the “Setup” icon on the computer screen to see if your cables are correctly connected to the PASCO interface, now and in the future.
- Try to move so as to duplicate the Position Match graph on the computer screen. You may try a number of times. It helps to work as a team. Each person should take a turn.
0
1
2
3
4
0 5 10 15 20 25 Time (s)
Position (m)
Comment : This graph is stored in the computer so that it is persistently displayed on the screen. New data from the motion detector can be collected without erasing the Position Match graph.
Lab 2 – One Dimensional Motion 29
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
- Print out one graph that includes all the data you decide to keep. Make sure you denote on your print out with letters a) – d) to indicate what you were trying to do.
Question 3-1: What is the most important difference between the graph made by slowly walking away from the detector and the one made by walking away more quickly?
Question 3-2: How are the velocity-time graphs different for motion away THAN FOR motion towards the detector?
Prediction 3-1: Each person draw below in your own manual, using a dashed line, your prediction of the velocity-time graph produced if you, in succession,
- walk away from the detector slowly and steadily for about 5 s
- then stand still for about 5 s
- then walk toward the detector steadily about twice as fast as before.
Do the predictions before coming to lab. Label your predictions and compare with your group to see if you can all agree. Use a solid line to draw in your group prediction.
- Test your prediction. Open experimental file L02.A3-1 Velocity Graphs Two. Be sure to think about your starting point! Begin graphing and repeat your motion until you think it matches the description. -
0
1
0 5 10 12.5 15 Time (s)
Velocity (m/s)
2.5 (^) 7.
30 Lab 2 - One Dimensional Motion
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
- Print out one copy of the best graph for your group report.
ACTIVITY 3-2: MATCHING A VELOCITY GRAPH
In this activity, you will try to move to match a velocity-time graph shown on the computer screen. This is much harder than matching a position graph as you did in the previous investigation so do not spend a lot of time on this activity. Most people find it quite a challenge to move so as to match a velocity graph. In fact, some velocity graphs that can be invented cannot be matched!
- Open the experiment file called L02.A3-2 Velocity Match to display the velocity- time graph shown below on the screen.
Prediction 3-2: Describe in words how you would move so that your velocity matched each part of this velocity-time graph. Do this before coming to lab. 0 to 4 s:
4 to 8 s:
8 to 12 s:
12 to 18 s:
18 to 20 s:
- Begin graphing , and move so as to imitate this graph. Try to do this without looking at the computer screen. You may try a few times. Work as a team and plan your movements. Get the times right. Get the velocities right. It is quite difficult to obtain smooth velocities. We have smoothed the data electronically, but your results may -
0
1
0 4 8 12 16 20 Time (s)
Velocity (m/s)
32 Lab 2 - One Dimensional Motion
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
Prediction 4-1: Do this before coming to lab. Determine the velocity graph from a position graph. Carefully study the position-time graph that follows and predict the velocity-time graph that would result from the motion. Use a dashed line to sketch what you believe the corresponding velocity-time graph on the velocity axes will be.
- Test your prediction. Begin graphing , and do your group’s best to make a position graph like the one shown. Walk as smoothly as possible. When you have made a decent duplicate of the position graph, sketch your actual graph over the existing position-time graph. Use a solid line to draw the actual velocity-time graph on the velocity graph where you drew your prediction. Do not erase your prediction or your data in the computer.
Question 4-1: How would the position graph be different if you moved faster? Slower?
Question 4-2: How would the velocity graph be different if you moved faster? Slower?
Prediction (^0) Results
Time (s)
Position (m)
Velocity (m/s)
Lab 2 – One Dimensional Motion 33
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
ACTIVITY 4-2: CALCULATING AVERAGE VELOCITY
In this activity, you will find an average velocity from your velocity-time graph in Activity 4-1 and then from your position-time graph.
- Here you will find your average velocity from the velocity graph that you obtained in Activity 4-1. Choose a region where your velocity is relatively constant and pick 10 adjacent velocity values. Do not choose a region where the velocity is zero. Use the Smart Tool in Data Studio to read values of velocity and write them in the table below. Use these values to calculate the average (mean) velocity using a calculator. For reference, note the time at the first and last points. You will need them later. Time at first point ___ _________ Time at last point _______________
Average (mean) value of the velocity: _______________ This is method 1 of determining the average velocity.
- Calculate your average velocity from the slope of your position graph in Activity 4-1. Make sure you use the same time region here that you just used in step 1. Use the Smart Tool again to read the position and time coordinates corresponding to the two end points (of your ten-point velocity region).
Position (m) Time (s)
Point 1
Point 2
Comment : Average velocity during a particular time interval can also be calculated as the change in position divided by the change in time. (The change in position is often called the displacement .) For motion with a constant velocity, this is also the slope of the position-time graph for that time period. As you have observed, the faster you move, the steeper your position-time graph becomes. The slope of a position-time graph is a quantitative measure of this incline. The size of this number tells you the speed, and the sign tells you the direction.
Velocity values (m/s) 1 6
2 7 3 8
4 9
5 10
Lab 2 – One Dimensional Motion 35
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
Next, use the fit routine , select a linear fit, y = mx + b, and then find the equation of the line. Record the equation of the fit line below, and compare the value of the slope ( m ) to the velocity you found in Activity 4-2. This is method 4.
Question 4-5: What does b represent?
ACTIVITY 4-4: PREDICTING POSITION GRAPHS FROM VELOCITY GRAPHS
Prediction 4-2: Carefully study the velocity graph shown above. Using a dashed line , sketch your prediction of the corresponding position graph below. (Assume that you started at the 1 m mark.)
Prediction _ _ _ Results ____
0
1
2
3
4
(^0 1 2) Time (s) 3 4 5
PREDICTION AND FINAL RESULT
36 Lab 2 - One Dimensional Motion
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
Test your prediction.
- First shut off the analysis features (fits and statistics), and adjust the time axis to 0 to 5 s as needed before you start.
- Each person has already made a prediction. Your group should try to duplicate the velocity-time graph by walking. Try to do it without looking at the computer monitor. When you have made a good duplicate of the velocity-time graph, draw your actual result over the existing velocity-time graph.
- Use a solid line to draw the actual position-time graph on the same axes with your prediction. (Do not erase your prediction.)
Question 4-6: How can you tell from a velocity-time graph that the moving object has changed direction? What is the velocity at the moment the direction changes?
Question 4-7: How can you tell from a position-time graph that your motion is steady (motion at a constant velocity)?
Question 4-8: How can you tell from a velocity-time graph that your motion is steady (constant velocity)?
INVESTIGATION 5: INTRODUCTION TO ACCELERATION
There is a third quantity besides position and velocity that is used to describe the motion of an object: acceleration. Acceleration is defined as the rate of change of velocity with respect to time (just like velocity is defined as the rate of change of position with respect to time ). In this investigation you will begin to examine the acceleration of objects.
Because of the jerky nature of the motion of your body, the acceleration graphs are erratic. It will be easier to examine the motion of a cart. In this investigation you will examine the cart moving with a constant (steady) velocity. Later, in Lab 3 you will examine the acceleration of more complex motions of the cart. You will need the following:
- motion cart without friction pad
38 Lab 2 - One Dimensional Motion
University of Virginia Physics Department Modified from P. Laws, D. Sokoloff, R. Thornton PHYS 203, Fall 2008 Supported by National Science Foundation
Question 5-1: Did your position-time and velocity-time graphs agree with your predictions? Discuss. What type of curve characterizes constant velocity on a position- time graph?
ACTIVITY 5-2: ACCELERATION OF A CART MOVING AT A CONSTANT VELOCITY
Prediction 5-2: Do this before coming to lab. Sketch with a dashed line on the axes that follow your prediction of the acceleration of the cart you just observed moving at a constant velocity away from the motion detector. Base your prediction on the definition of acceleration.
- You will use the data you took in the previous activity. Display the real acceleration graph of the cart by “dragging” acceleration data from the left column onto existing graph. Sketch the acceleration graph using a solid line on the axes above. Ask your TA for help if needed.
- Print out one copy of the graph for your group report. Label it.
Question 5-2: Does the acceleration-time graph you observed agree with your prediction? Discuss.
- Find the average acceleration of the car using one of the techniques that you used earlier to find the average velocity. Show your work. -
0
1
(^0 1 2) Time (s) 3 4 5
PREDICTION AND FINAL RESULTS
Acceleration (m/s
2 )
