Free Fall by Area - calhoun.k12.al.us



Free Fall, Area Under the Curve

Materials/Equipment:

|Equipment |QTY |Equipment |QTY |

|Computer |1 |Photogate |1 |

|USB Link |1 |Small Ring Stand |1 |

|Digital Adapter |1 |Picket Fence |1 |

|Printer |1 |Wireless Router |1 (optional) |

Procedure:

Do not connect the USB link to the computer until instructed.

1. Attach the photogate sideways on the ring stand so that you can drop a picket fence vertically from above the photogate and have the picket fence move through the photogate’s opening without hitting the photogate. Some students find it easiest to move the photogate down to the lowest point on the ring stand rod.

2. Plug the photogate jack into the Digital Adapter.

3. Carefully align and connect the Digital Adapter to the USB Link.

4. Turn on the computer and Launch the software DataStudio using the shortcut on the desktop.

5. From the DataStudio home screen select Open Activity.

6. Open the template FreeFall_Area from within the ASIM folder. The file should open with a graph display showing a plot of “Position vs Time” and “Velocity vs Time” plus a Table for Acceleration. Notice that the Start button is not active (It’s grey) because the sensor is not connected to the computer yet.

7. Now that the file is open, connect the USB link to the computer. After a few moments, the software should detect the photogate and the start button should go active (green triangle)[pic]. If the button does not turn green, ask for help.

8. Prepare to drop the picket fence through the photogate beam. Hold the picket fence at the top end between your thumb and forefinger so the bottom edge of the picket fence is just above the photogate. Practice dropping and catching the picket fence making sure it does not hit the floor. If preferable, use a pad from the computer box to cushion the impact instead of catching the picket fence. Do not let the fence directly strike the floor or it will break.

9. Click on “START” [pic]to begin recording data and then drop the picket fence through the photogate beam. Data collection begins when the photogate beam is first blocked. When the picket fence is through the beam, click “STOP.” [pic] Data should appear in the Graph displays and “Run #1” should appear in the Data Sets list. Each person in the group should drop the picket fence for at least two data runs. Each group member should also run the computer during data collection.

10. Review your runs and determine which to use for the Analysis portion by finding the run with a Mean Acceleration closest to gravity, 9.8 m/s2 in the Acceleration Table. The average or Mean acceleration should be at the bottom of the table in the statistics.

11. Once you have selected your best run. Maximize the Graph window.

Notice that either the Velocity or Position graph is active, indicated by the yellow highlighted run number. To move between graphs, simply click on the graph you want to be active. The run number on that graph will be highlighted in yellow.

12. Now use the Data [pic] pull down menu to remove all but your best run from each graph. Select the run numbers to remove and make sure your best run has a check next to it. At the end of this step, only the best run should appear in both the Position vs Time and Velocity vs Time windows.

Analysis:

First, you will use the software graphing tools to find the area under the velocity time curve. Recalling your prior knowledge in math, what are the equations used to find the area of a rectangle and the area of a triangle? See question #2 in the Student Data section.

Next, you will use the software to add a curve fit (best fit line) to the Velocity vs Time graph. And finally, you will use the software to find the change in velocity from the Velocity vs Time graph and the corresponding change in Position from the Position vs Time graph.

1. Autoscale both graphs.

• Click on the Velocity graph, the run number should become highlighted. Click on the Scale to Fit button [pic].

• Click on the Position graph, the run number should become highlighted. Click the Scale to Fit button [pic].

2. Click on the Velocity curve again to continue analyzing the Velocity vs Time graph.

3. Click on the Statistics button [pic] and select Area from the menu. A shaded area should appear blow your Velocity data with the value of the area displayed in a text box. Record this Area on the Data and Calculations sheet. Be sure to note the units. What do the units suggest this area represents? (See question 1 following the Data sheet)

4. Now have the computer draw a “best fit” line through the highlighted velocity data by selecting Linear Fit from the Fit[pic] pull down menu. Record the Slope on the data sheet. Again, be sure to note the units.

5. With the Velocity curve selected (run number highlighted) select the Smart tool[pic]. A cross of dashed lines should appear with the (x,y) coordinates displayed above their intersection.

6. Now click on the Position graph and add a Smart tool to the Position graph. Note that the two Smart tools should lock together on the same time coordinate since both graphs share the same time (x) axis.

7. Click on the Velocity curve again. Now drag the Smart tool over to the final velocity data point. The coordinates of the point (time, velocity) should be displayed above the tool. Record these coordinates in the data table as the final velocity. Note that the Smart tool on the Position graph moved over to the same time coordinate on the Position curve.

8. Now, from the Position curve, get the corresponding position at the same time coordinate as the final velocity data point from step 7. Click on the Smart tool on the Position graph. Use the keyboard’s down arrow key to move the Position Smart tool straight down until it intersects the line segment on the Position curve. Record the (time, position) coordinates of this point in your data table as the final position. If the time coordinate shifts slightly, ask your instructor for help or try tweaking the smart cursor on the Velocity graph to lock them together on the correct time.

9. Now get the initial velocity from the Velocity graph. Click on the Velocity curve again. Drag the Smart tool over to the initial velocity data point. The coordinates (time, velocity) of the point should be displayed above the tool. Record these coordinates in your data table as the initial velocity. Note that the Smart tool on the Position graph moved over to the same time coordinate on the Position curve.

10. Now get the initial position at the same time coordinate as the initial velocity data point. Click on the Smart tool on the Position graph. Use the keyboard’s up arrow key to move the Position Smart tool until it intersects the Position data. Record the (time, position) coordinates of this point in your data table as the final position.

11. If a printer is available, print your graphs. Use the File pull down menu to select Print. Be sure to select the correct printer. Note both graphs will automatically print together.

12. Complete the calculations and answer the questions found on the Student Data Sheets.

Before closing DataStudio or shutting down your computer, ask your teacher about completing the extensions for this activity.

Extension 1: Adding the Acceleration vs Time graph.

Extension 2: Investigating the effect of mass on acceleration in Free Fall.

Student Data Sheet

Data:

• (Analysis Step 3) Record Area from the Velocity vs Time curve:

• (Analysis Step 4) Record Slope of the Velocity Linear Curve fit:

| |(x-coordinate) Time (s) |(y-coordinate) Velocity (m/s) |

|Final Velocity | | |

|Initial Velocity | | |

|Change in Velocity | | |

| | | |

| | | |

| |(x-coordinate) Time (s) |(y-coordinate) Position(m) |

|Final Position | | |

|Initial Position | | |

|Change in Position | | |

Complete the following calculations:

• Calculate the changes in velocity and position as indicated in the table above.

• Calculate the percent difference between the change in position by area under the velocity time curve (Analysis Step 3) and the change in position taken by direct measurement from the position time curve as indicated in the table above.

% difference:

• Using your velocity data in the table above, calculate the average acceleration between the Final and Initial Velocity points.

Average Acceleration =

• Calculate the percent difference between the Ave Acceleration and the slope of the Velocity curve from Analysis Step 4

% difference:

Questions:

1. What does the area under the Velocity vs Time curve represent?

2. Look at your graph of Velocity vs Time. What simple AREA equation(s) do you think the computer might have used to determine the area under the curve of the Velocity vs Time graph?

3. What does the Slope of the Velocity vs Time curve fit represent? Hint: Slope is change in y divided by change in x. Look at the units for your ∆y/∆x.

4. How could you an Acceleration vs Time graph to estimate the change in velocity during a given time interval?

-----------------------

[pic]

[pic]

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download