Constant Velocity and Acceleration
OBJECTIVE: To investigate, by experimental and graphical procedures, the motion of objects during constant velocity and constant acceleration.
INTRODUCTION:
The motion of objects fall into one of two categories, namely accelerated motion and constant velocity. These motions can be determined and predicted accurately by mathematical formulas and calculations. By experimentation and graphical analysis, we will determine the actual velocity and acceleration of a cart on an air track.
METHOD:
A video camera will be used to save video images of a moving cart to a computer. The computer will save video images at a known, fixed frame rate of 10 frames per second, producing a QuickTime "movie" of the motion. A meterstick will be placed in the plane of the cart's motion to provide a scale factor for the movie. By using LoggerPro software to locate the screen coordinates of the cart in each frame of the movie and converting these coordinates to real units using the scale factor, the actual displacement of the cart during each frame interval can be found. By dividing each of these displacements by the time for each frame interval, the cart's average velocity during each interval can be found. Finally, by subtracting the velocities for successive intervals and dividing by the time between intervals, the acceleration of the cart between each set of intervals can be found.
In part I of this experiment (constant velocity), you will give the cart an initial constant velocity by simply giving it a slight push. After it is out of the influence of your hand, it will move at constant speed. A picture of what the analyzed video will look like is shown below. Unfortunately, there is no easy way of theoretically predicting what this velocity will be. Likewise, it is difficult to repeat the experiment with the same velocity to check your results. Thus, for part I, there is no possible %error calculation.
In part II of this experiment (constant acceleration), you will give the cart a constant acceleration by applying a constant force to it (by way of a suspended mass connected to it). A picture of what your analyzed video will look like is shown below. The acceleration the cart exhibits can be theoretically predicted by Newton's Second Law, allowing a %error calculation to be made.
In part III of this experiment, a second check of your results will be achieved by repeating the experiment and using a computer interface device (called a "smart pulley") to directly measure the cart's accelerationand compare the acceleration to that predicted by Newton's Second Law (Part II). You will use Logger Pro to plot x vs. t and v vs. t graphs for the constant velocity data,and you will plot x vs. t and v vs. t graphs for the constant acceleration data by hand. Make sure that you do a curve fit or linear fit (with calculated slope) for each graph.
Thus, the experiment consists of three parts:
-Quicktime movie of the cart moving at constant velocity
-Quicktime movie of the cart moving at constant acceleration
-Measure the acceleration directly using the smart pulley and compare it to part II.
DATA:
Part I: Constant Velocity
Measured Positions and Time Intervals
Position Number / Position (m) / Total Time (s)1 (origin)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Calculated Velocity and Acceleration
Interval Number / Velocity (m/s) / Acceleration (m/s/s)1
2
3
4
5
6
7
8
9
10
11
12
13
14 / XXXXXXXXXXXXX
Part II: Constant Acceleration
Measured Positions and Time Intervals
Position Number / Position (m) / Total Time (s)1 (origin)
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Calculated Velocity and Acceleration
Interval Number / Velocity (m/s) / Acceleration (m/s/s)1
2
3
4
5
6
7
8
9
10
11
12
13
14 / XXXXXXXXXXXXX
Part III: Smart Pulley Measurement: ______m/s2
DATA TREATMENT:
- Velocity of cart
- Acceleration of cart
- Include any additional calculations required to answer specific interpretations/analysis of errors questions with the answers to those questions.
- Be sure to include all four graphs, labeled to show which is for part I and which is for part II.
INTERPRETATIONS:
1. Why was an air track used for this experiment?
2. Suppose we did not have an available video capture card or LoggerPro software. How else might the cart's displacements during successive, equal increments of time be measured? Describe some of the sources of error using the method you've described.
3. Describe the shape of your computer x vs. t graph for Part I. What does this tell you concerning the motion of the cart?
4. According to the computer calculations, what was the slope of the x vs. t graph for part I? What does this slope represent?
5. Describe the shape of your computer v vs. t graph for Part I. (Approximately) what is its slope? What does this tell you concerning the motion of the cart? How does the average velocity for this graph compare with the slope of the x vs. t graph?
6. Discuss the shapes of your x vs. t and v vs. t graphs for Part II. What does each tell you concerning the motion of the cart?
7. What was the acceleration of the cart, according to your v vs. t graph for Part II? How does this compare with the average acceleration value from your data table for Part II?
ANALYSIS OF ERRORS:
- Calculate the cart's theoretical acceleration using Newton's Second Law. Find the % error between your experimental value from the v vs. t graph and this theoretical value.
- Calculate the % error between your experimental acceleration value from the v vs. t graph and the smart pulley measurement. Take the smart pulley measurement to be your accepted value.
- Why is it important to use as much of the paper as possible when graphing? Why is it important to use the plotted line to find the slope rather than collected data points?
- Which value, the theoretical or the smart pulley measurement, is closer to your experimental acceleration from the v vs. t graph? Which would you expect to be closer? Why?
- What error would have been introduced had the meterstick been farther away from the camera than the air track? Would the measured displacements have been too high or too low?
Physics Computer Lab. Software Guide
Using the Smart Pulley
- Navigate to the honors physics shared files folder (from either the school web site physics page or the Honors Physics I moodle page). Open the “Class Materials,” “LoggerPro” folders. Click on the file “Smartpulley” and open the file. Click on “Connect” to connect to the interface.
- Make sure that your smart pulley photogate is plugged into “DIG/SONIC 1” on the LabPro interface that is connected to your computer.
- Make sure that the cart is ready to release and that the smart pulley is not blocking the photogate (the red light should not be on).
- Click on the “Collect” button at the top, right of the toolbar.
- To begin timing, release the cart.
- Click on the “Stop” button before the suspended mass strikes the floor!
- Note that a graph of velocity versus time has been plotted for your data. Using the left mouse button, click and drag the cursor over all of the data points displayed on your graph.
- Click on the “Linear Fit” button at the top of your screen (box with blue curve and “R =”). The slope of the graph (acceleration) is given as “m:” in the floating box which points to the linear fit line.
- Select “Clear All Data” from the “Data” menu (and click on “yes”) after you have recorded the slope.
- When you are ready to collect new data, repeat steps 4-8.
- When you are completely finished, select “Exit” from the “File” menu (do not save your changes.)