Figure 1

* Collect data as a cart rolls
different distances down an inclined plane

* Analyze the graph of time (Dt) vs. distance (D) for the cart

* Analyze the graph of velocity (v) vs. distance for the cart

* Analyze the graph of time (Dt) vs. distance (D) for the cart

* Analyze the graph of velocity (v) vs. distance for the cart

computer

Vernier Photogate

Vernier computer interface

Vernier Dynamics System

Logger Pro

Flag cut from Index Card

Vernier Photogate

Vernier computer interface

Vernier Dynamics System

Logger Pro

Flag cut from Index Card

2. How would your predicted graph change if you changed the angle of the incline? Explain.

2. Adjust the photogate so the flag on the moving cart will move through it and cause the LED indicator to turn on as it goes through.

3. Connect the photogate to the interface and then connect to the computer. Launch Logger Pro. A default file should open up ready to collect data with the attached photogate.

4. Click on File > Open > Probes & Sensors > Photogates. Then open the file “Gate vs Event.cmbl”

5. In the window labeled “PhotogateDistance1”, double-click and change the value from 0.1 m to 0.02 m, the width of your flag.

6. Place the cart on the track near the bottom with the leading end at a specific position. Move the photogate so it is at the front edge of the flag. The LED on the photogate will light up when the flag just eclipses the beam. Mark this position with a piece of masking tape if necessary.

7. Move the cart so it’s distance D from the position you identified in Step 4 is 10 cm up the inclined track*. Start data collection. Release the cart so it moves down the track and through the photogate. Note the Gate Time and Velocity in the Data Table included in these instructions along with the distance (D).

8. Repeat your run at the 10-cm distance three times and compare your results. Are they consistent? Why or why not? Once you have perfected your procedure, you may not need to do repeated trials at the other distances.

9. Move the cart up the inclined track in 10-cm increments, noting the three data values each time you make a data run. Once you obtain 5-10 sets of data points, stop data collection. Go on to ANALYSIS.

2. Enter the data from your data table. Double-click at the top of each table, entering the labels and units for each.

3. The first graph that will appear will be Gate Time vs Distance. In general, how did the time for the cart to go through the photogate change as you increased the distance it moved? Would you characterize this as a “direct” or an “inverse” type of relationship?

4. Click and drag across your data points then choose Analyze > Curve Fit from the main menu bar. If you think the data is a “direct” relationship, try fitting it with Linear. Click the button next to “Linear” then click [Try Fit]. If you think it is “inverse”, scroll down to the choice “Inverse”, click the button, then [Try Fit]. You can also try “Inverse Square”. How did your curve fitting go?

5. Cancel out of the curve fitting. Click on the y-axis label (Gate Time). In the menu that appears, choose “Velocity”. Click on the Autoscale button -

6. In general, how does the velocity of the cart change as you increased the distance it moved? Would you characterize this as a “direct” or an “inverse” type of relationship?

7. Click and drag across your data points then choose Analyze > Curve Fit from the main menu bar. If you think the data is a “direct” relationship, try fitting it with Linear. Click the button next to “Linear” then click [Try Fit]. If you think it is a curve of some sort, try some of the other options. If you think it’s an “inverse” relationship, scroll down to the choice “Inverse”, click the button, then [Try Fit]. You can also try “Inverse Square”. How did your curve fitting go? We’ll return to this analysis below.

Distance
(D) m |
Gate
Time (t) s |
Velocity (v) m/s |

2. Go to Data > New Calculated Column. Label it “Velocity Squared”, short name: “v^2”, and units of “m^2/s^2” (or m

3. On the graph of velocity vs distance, click on the y-axis label. On the menu that appears, click on “Velocity Squared”. How does your data look now? Is it linear? How could you test? If it is linear, then you know the relationship is v

4. Velocity (speed) is distance divided by time or d/Dt. Develop an argument for why doing an inverse square fit for Gate Time vs Distance yields a good straight line fit.

* Best results are achieved if you move the cart the distance D less 1 cm up the track. This will cause data collection to start 1 cm before the cart is at the designated spot and stop once it’s 1 cm past there. The result is you get an average time for the cart to go through the photogate.

This lab is based on Lab 3 in Physics with Vernier. It takes a slightly different approach.

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C. Bakken

September 2012