Motion with Constant Acceleration
- to investigate motion in one-dimension with constant acceleration
- to learn the characteristics of kinematics graphs for motion with constant acceleration
In this lab, you will use a Pasco motion detector to gather data on the motion of a fan-powered cart.
IMPORTANT: Yes, if you put your finger in the path of the fan blade, it will hurt. Don't do that.
You will then use DataStudio software to transform the data into graphs of position versus time, velocity versus time, and acceleration versus time for the motion, and analyze the graphs using the DataStudio software.
|Pasco ScienceWorkshopTM 500 Interface (CI-6760)
||Pasco USB/Serial Converter (CI-6759)
|Pasco Motion Sensor II (003-06758)
||Pasco Collision Cart (ME-9454)
|Pasco 2.2-meter Dynamics Track
||Pasco Fan Accessory (ME-9491)
|Pasco mass for the Collision Cart
- The set-up for this experiment (steps 1-5) is exactly the same as the previous lab Motion with Constant Velocity, so you can refer to the handout for that lab to set up and test your experiment. Don't add any extra mass to the cart for your testing or initial trial run.
- Run the experiment.
- Place the fan cart approximately 15-20 cm in front of the motion detector, so that it will move away from the detector along the dynamics track. For the initial run, do not add any extra weight to the fan cart. Release the cart and press the "Start" button on the interface screen.
- Collect data until the cart nears the end of the dynamics track, then press "Stop".
- Repeat steps "6a" and "6b" two more times, first adding the two silver-colored weights to the cart, and lastly adding the large black weight to the cart. Notice that the fan needs to be near the end of the cart in order to not hit the black mass.
- Save the experiment/data file.
- Since we only have one fan cart, you can move your experiment file to another computer to calculate the experimental results and let another group have a turn.
- Print a copy of each data table for your lab record.
- Scale your graphs to fit the available space and add an appropriate title. It would probably be a good idea to pull down the "Settings" menu at the top of each graph and un-check "Connected Lines".
- Draw best-fit lines for your velocity versus time and acceleration versus time graphs if you feel that it is appropriate. Notice that a straight line would not be appropriate for your position versus time graphs.
- Print a copy of each graph for your lab record.
- It is easiest to deal with the position versus time graph using an Excel spreadsheet. Hopefully, you are familiar with Excel. Here is an outline of what to do.
- First, get the data out of DataStudio. In the position versus time table, use your mouse to highlight all of the data in the time and position columns (in yellow), and Copy the data to the clipboard.
- Paste the time and position columns, in a new Excel spreadsheet.
- Insert a column to the right of the time data column - between the two data columns. Label the column "Time squared".
- In the first data cell in the new column, enter a formula to calculate the square of the time. For example, if you have your first time value in cell A4, you could enter "=A4*A4", or "=A4^2".
- Copy this formula to all of the cells in the rest of the column.
- Highlight the time-squared data column and the position data column, and use the Chart Wizard to create an XY-Scatter plot of the data. Add appropriate labels and a title to the graph.
- In the Chart menu, Select "Add Trendline..." and add a Linear best-fit line. Click on the Options tab of the Trendline dialog and check "Display equation on chart" and "Display R-squared value on chart".
- Repeat Steps 5a-5g for your other position versus time data sets.
- Print the Excel data tables and graphs and add them to your lab notebook.
- Go back to your DataStudio position versus time graph and select the "Slope Tool" from the graphs tool bar. Use the slope tool to measure the slope of each position versus time graph at t = 1s, 2s, and 3s, and record this data in a data table.
- Using DataStudio's Area tool, calculate the area under each of your velocity versus time graphs over some reasonable time interval, just as you did in the last experiment.
- Repeat step 7 for each acceleration versus time graph.
Here are some questions to help you draw some useful conclusions from this experiment:
- To what extent is the velocity versus time graph for this motion a straight line? Why is this so?
- To what extent is the acceleration versus time graph for this motion a horizontal line? Why is this so?
- What is the significance of the slope of the position versus time graph? (The units of the slope are a big hint.)
- What is the significance of the slope of the velocity versus time graph? (The units of the slope are a big hint.)
- What is the significance of the area between the velocity versus time graph and the time axis (the area "under the graph")? (Again, the units of the area are a big hint.)
- What is the significance of the area between the acceleration versus time graph and the time axis (the area "under the graph")? (Again, the units of the area are a big hint.)
- To what extent is the position versus time squared graph a straight line? Why would it be reasonable to expect this graph to be a straight line?
- What is the significance of the slope of the position versus time squared graph? (Do you really need another hint?)
- Suppose we took the fan cart and placed it at the opposite end of the 2m dynamics track - away from the motion detector, and let it move toward the detector. What would the position versus time, velocity versus time, and acceleration versus time graphs for this motion look like? (Yes, of course it's ok to try it and see if your prediction is correct!)
last update August 21, 2006 by JL Stanbrough