Period Date
Name(s)
Chapter 2 Lab I-2:
ONE-DIMENSIONAL MOTION – CHANGING MOTION
Velocity and Acceleration Graphs
Motions can be very jerky and irregular. We are interested in having you learn to describe how some simple motions in which the velocity of an object is changing. In order to learn to describe motion in more detail for some simple situations, you will be asked to observe and describe the motion of a cart on a flat ramp. Although, graphs and words are still important representations of these motions, you will also be asked to draw velocity vectors - arrows that indicate both the direction and speed of a moving object.
In the last section, you looked at distance vs. time and velocity vs. time graphs of the motion of your body as you moved at a "constant" velocity. Your goal in this session is to learn how to describe various kinds of motion in more detail. It is not enough when studying motion in physics to simply say that "the object is moving toward the right" or "it is standing still."
You have probably realized that a velocity vs. time graph is better than a distance vs. time graph when you want to know how fast and in what direction you are moving as you walk. When the velocity of an object is changing, it is also important to know how it is changing. The rate of change of velocity is known as the acceleration.
In order to get a feeling for acceleration, it is helpful to create and learn to interpret velocity vs. time and acceleration vs. time graphs for some relatively simple motions of a cart on a ramp. You will be observing the cart with the motion detector as it moves at a constant velocity and as it changes its velocity at a constant rate. For the activities in this session you will need:
• a microcomputer • a LabPro• a motion detector • Logger Pro motion software • Constant motion buggy Pasco cart and track • a small block
IMPORTANT NOTE ON SAVING YOUR FILES: You may be asked to use the data collected in some of the activities for mathematical analysis in the future. For each activity that needs to be saved please save the data on your flash drive. It is recommend that you identify your files by the lab number and activity number for later reference along with your group initials. Thus, if Smith and Ricci work together on the LAB 2 activities, the file names might be, for example, I 2-1(SR), I 2-2 (SR), etc.
Activity 2-1: Distance, Velocity and Acceleration Graphs of Constant Velocity
Let's start by using the constant motion buggy along a smooth level surface and graphing its motion. Based on your observations of the motions of your body in the last lab, how should the distance and velocity graphs look if you move the buggy at a constant velocity away from the motion detector? Sketch your predictions in pencil on the axes that follow.
Open the program Logger Pro:
Go to “Insert”, “Movie”, then on the left hand side open “desktop” and “Physics Videos”and open the file “Buggy Constant” This movie shows a buggy in constant motion – you can play the video if you like, just make sure you rewind it to the beginning. Click and drag one of the corner squares of the movie to make the video bigger. Click on “Options”in the upper tool bar, then on “Movie Options”. Click on “override frame rate”and put in 100 as the frame rate then click O.K. On the bottom right corner of the movie window, click on “Enable video analysis”button (look for box with three red dots). A new column of buttons is now displayed on the right side, click on “set scale” (yellow ruler 4th button down).Findthe meter stick in the video. Click,hold and drag the cross hairs along the length of the meter stick. Define this length as 1 meter in scale pop up window. We will plot the position of the buggy at several points in time as it moves. We MUST use one specific part on the buggy for reference. In this lab we will use the center of the front wheel. To plot the position of the buggy select the “Add Point” buttonfrom the menu on the right (second button down). Place the cross hairs on the center of the front wheel and click the mouse to mark the location. Advance the video forward five frames using the next frame button located on the bottom left of the video window . Again align the cross hairs with the center of the wheel and mark the new position by clicking the mouse. Repeat this process at least ten more data points.
Go to “Insert”, and insert an additional graph. Go to “Page”, Auto Arrange. Make sure you are viewing the following 2 graphs:
x vs. t
x-velocity vs. t
Set “x velocity scale”at -1 and 1
Once your graphs are properly displayed sketch the line best represents the data on the above axis as dashed lines.
Analysis
(a) This video is titled constant velocity, how can you tell from the graph of x vs. t that this motion is constant velocity?
(b) For this motion what should the x velocity vs. t graph look like?
(c) Is this prediction confirmed on the graph?
Set up the motion detector at the end of a ramp and set up the distance and velocity graph axes as shown on the following graphs.
(a) Test your prediction for the velocity graph (plot velocity vs. time first.). Be sure that the buggy is never closer than 0.5 meter from the motion detector. Make sure that you get a fairly constant velocity and sketch your results with solid lines on the axes above.
(b) Did your distance vs. time and velocity vs. time graphs from the video and buggy agree with your predictions? What characterizes constant velocity motion on a distance vs. time graph?
(c) What characterizes constant velocity motion on a velocity vs. time graph?
(d) Acceleration is defined as the rate of change of velocity with respect to time. Sketch your prediction of the buggies’ acceleration (for the motion you just observed) on the axes that follow using a pencil line.
(e) Display the acceleration graph of the buggy by going to Insert, Graph and then go to Page, Auto Arrange and use a solid line to sketch the real acceleration on the axes above.
Activity 2-2: Finding and Representing Acceleration
To find the average acceleration of the cart during some time interval (the average time rate of change of its velocity), you must measure its velocity at two different times, calculate the difference between the final value and the initial value and divide by the time interval.
To find the acceleration vector from two velocity vectors, you must first find the vector representing the change in velocity by subtracting the initial velocity vector from the final one. Then you divide this vector by the time interval.
(a) Does the acceleration vs. time graph you just observed agree with this method of calculating acceleration? Explain. Does it agree with your prediction?
(b) The diagram below shows the distances of the cart at equal time intervals. (This is like taking snapshots of the cart at equal time intervals.) At each indicated time, sketch a velocity vector above the cart that might represent the velocity of the cart while it is moving at a constant velocity away from the motion detector (you should show 4 vectors).
(c) Explain how you would find the vector representing the change in velocity between the times 1.0 s and 2.0 s in the diagram above. From this vector, what value would you calculate for the acceleration? Explain. Is this value in agreement with the acceleration graph you obtained in Activity 2-1?
Activity 2-3 : Graphs Depicting Speeding Upat a Moderate Rate
In this activity you will look at velocity and acceleration graphs of the motion of a cart when its velocity is changing. You will be able to see how these two representations of the motion are related to each other when the cart is speeding up.
In order to get your cart speeding up smoothly you can use a small block under the ramp to incline the ramp so the cart will be accelerated. You need to create nice smooth graphs of distance and velocity vs. time of a cart that shows the cart starting from rest.
You should set up the cart, ramp, block and motion detector as shown in the following diagram.
(a) Set up the graphs on the computer so that theDistancegoes from 0 to 2.0 m and Velocitygoes from -1.0 to 1.0 m/sec for a total time of 5.0 sec. Create distance vs. time and velocity vs. time graphs of your cart as it moves away from the detector and speeds up. You might want to change the scale of the graphs so that the traces nearly fill the screen vertically. Practice several times before filling in your results.Sketch the graphs neatly on the axes below.
(c ) Save your data for analysis in the next activity by choosing Save As from the File Menu, decide on what you want to name it and save it to your flash drive.
(d) How does your distance graph differ from the distance graphs for steady (constant velocity) motion?
(e) What feature of your velocity graph signifies that the motion was away from the detector? How do you know?
(f) What feature of your velocity graph signifies that the cart was speeding up? How would a graph of motion with a constant velocity differ?
(g) Change the Distance display to Acceleration. Adjust the acceleration scale so that your graph fills the axes. Do a rough sketch your graph on the acceleration axes that follow.
Speeding Up Moderately
(h) During the time that the cart is speeding up, is the acceleration positive or negative? How does speeding up while moving away from the detector result in this sign of acceleration? Hint: Remember that acceleration is the rate of change of velocity. Look at how the velocity is changing.
(i) How does the velocity vary in time as the cart speeds up? Does it increase at a steady rate or in some other way?
(j) How does the acceleration vary in time as the cart speeds up (only analyze the portion where the cart was speeding up)? Is this what you expect based on the velocity graph? Explain.
Activity 2-4: Using Vectors to Describe the Acceleration
Let's return to the Vector Diagram representation and use it to describe the acceleration.
(a) The diagram that follows shows the distances of the cart at equal time intervals. At each indicated time, sketch a vector above the cart that might represent the velocity of the cart at that time while it is moving away from the motion detector and speeding up.
(b) Show below how you would find the approximate length and direction of the vector representing the change in velocity between the times 1.0 s and 2.0 s using the diagram above. No quantitative calculations are needed. Based on the direction of this vector and the direction of the positive x-axis, what is the sign of the acceleration? Does this agree with your answer to Activity 2-3 (h)?
Activity 2-5: Measuring and Calculating Accelerations
In this investigation you will analyze the motion of your accelerated cart quantitatively. This analysis will be quantitative in the sense that your results will consist of numbers. You will determine the cart's acceleration from the slope your velocity vs. time graph and compare it to the average acceleration read from the acceleration vs. time graph. You can display actual values for your acceleration and velocity data using the motion software. To do this activity you will need your experiment file from Activity 2-3 that you saved on your flash drive.
(a) Re sketch the velocity and acceleration graphs you found in Activity 2-3 using the axes that follow. Correct the scales if necessary.
(b) List 10 of the typical recorded accelerations of the cart. To find these values select the Acceleration vs. Time graph (by clicking on the acceleration graph) and then select Analyze, Examine from the Menu. Scroll along with the mouse to display the values at different times. (Only use values from the portion of the graph after the cart was released and before you stopped it.)
1 / 6
2 / 7
3 / 8
4 / 9
5 / 10
(c) Calculate the average value of the acceleration .
Average acceleration (mean): ______m/s2
(d) Since the average acceleration during a particular time period is defined as the change in velocity divided by the change in time - this is the average rate of change of velocity. By definition, the rate of change of a quantity graphed with respect to time is also the slope of the curve. Thus the (average) slope of an object's velocity vs. time graph is the (average) acceleration of the object. Find the data needs to calculate the approximate slope of your velocity graph. Click on the velocity graph and use Analyze, Examine to read the velocity and time coordinates for two typical points on the velocity graph. For a more accurate answer, use two points as far apart in time as possible but still during the time the cart was speeding up (try to pick your points from just after the beginning and near the end of the motion).
Velocity (m/s) / Time (s)Point 1
Point 2
(e) Calculate the change in velocity between points 1 and 2. Also calculate the corresponding change in time (time interval). Divide the change in velocity by the change in time. This is the average acceleration. Show these values in the next table and show your calculations below.
Speeding UpChange in Velocity (m/s)
Time Interval [t] (s)
Avg. Acceleration (m/s2)
(f) Is the acceleration positive or negative? Is this what you expected? Why?
(g) Does the average acceleration you just calculated agree with the average acceleration you calculated from the acceleration graph? Do you expect them to agree? How would you account for any differences?
Activity 2-6: Speeding Up at a Faster Rate - Calculating Accelerations
Suppose that you accelerate your cart at a faster rate by making the incline steeper. How would your velocity and acceleration graphs change?
(a) Re sketch the velocity and acceleration graphs you found in Activity 2-3 once more using the axes that follow.
(b) In the previous set of axes (activity 2-5a), use a dashed line or another color to sketch your predictions for the general graphs that depict a cart running on a greater incline. Exact predictions are not expected. We just want to know how you think the general shapes of the graphs will change. . Go to experiment on the menu bar and select “Store latest run” for comparison.
(c) Test your predictions by accelerating the cart on a greater incline. Repeat if necessary to get nice graphs and then sketch (using a different color) the results in the axes that follow. Use the same scale as you did for the sketch of the small incline graph.
(d) Did the general shapes of your velocity and acceleration graphs agree with your predictions? How is the greater magnitude (size) of acceleration represented on a velocity vs. time graph?
(e) How is the greater magnitude (size) of acceleration represented on an acceleration vs. time graph?
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