9/26/95

Goals: To practice the picket fence method of determining acceleration and to use the method to determine acceleration in several situations

Introduction: You have already learned two methods of measuring acceleration. One method used a plexiglass strip--divided into 3 regions--dropped through a photogate. Three time intervals and two displacements were measured and used to calculate the acceleration due to gravity. In another method, you found the acceleration of a glider on an inclined air track using a spark tape. In this method, your raw data was position at uniform intervals of time, and you used the data to obtain velocity as a function of time.

The picket fence method has similarities to the previous two. A plexiglass strip is divided into alternating dark and clear strips of equal width. When the strip moves through a photogate interfaced to a CBL and calculator, time intervals are measured for the passage of successive dark strips through the gate. The raw data can then be converted to a graph of velocity vs. time.

For each of the steps below, make predictions, record data, and answer questions as you go along. Refer to the Data Collection Information and Data Analysis Instructions sections of this instruction sheet as necessary.

1) Taking data with the glider on a horizontal track:

Measure the distance in meters from the beginning of each dark band to the next on your picket fence bar. The default value used in the calculator program is 0.050m. Check that your picket fence matches the default value.

Level the air track. Then lay a picket fence in the groove on the top of a red glider and secure it with small pieces of tape on both sides. Turn on the air and practice giving the glider a short-lived push to send it through the gate. However, make sure to stop pushing before the glider enters the gate. Don't let the glider bounce back through the gate! Be sure to position the photogate so that the picket fence can pass unobstructed through the photogate. Be sure that the photogate beam is perpendicular to the plane of the strip.

Predict approximately what the acceleration of the glider should be as it passes through the gate; write down your prediction! Now collect and analyze the data for the glider on the horizontal track.

a) What does the slope of your v-t graph represent? Is the value what you expected? Explain.

b) What does the intercept represent? Be specific.

2) Taking data with the glider traveling down a tilted track: Now tilt the air track with riser blocks. Record the height of the blocks you used to the nearest 0.5mm You may have to readjust the photogate to make sure the pickets pass through unobstructed. Release the glider just above the gate and catch it before bouncing. Collect and analyze the data for the glider going down the tilted track.

a) What does the slope of your v-t graph represent?

b) What does the intercept represent? Be specific.

3) Taking data with the glider traveling up a tilted track: In this part, you will give the glider a push from the bottom of the track so that the picket fence passes all the way through the gate (but not while you are pushing it). But once again, before taking data, predict the approximate value of the acceleration that you should obtain in this part. Collect and analyze the data as before.

a) Compare the slopes from steps 2 and 3. Are the results what you expected? Explain.

b) Compare the intercepts from steps 2 and 3. Are the results what you expected? Explain.

4) Taking data with a different glider traveling down a tilted track: In this part you will mount the picket fence on a blue glider, and then release the glider above the photogate as in part (2) above. Keep the height of the riser blocks the same. Once again, before taking data, predict the approximate value of the acceleration that you should obtain in this part. Collect and analyze the data as before.

Compare the slopes from steps 2 and 4. Are the results what you expected? Explain.

5) Taking data for a picket fence in free fall: Position a photogate on its stand sideways so that it extends over a table end. Put a foam pad or box on the floor below the gate. Drop a picket fence lengthwise through the gate while collecting data. Analyze the data as before.

Is the acceleration within 1% of the expected value (show calculation)? If not, try again. Record all attempts.

Data Collection Information:

Link your calculator to another which has the program PICKET. Download the program to your calculator.

Attach your calculator to the CBL using a link cable and connect the photogate in the channel 1 port of the CBL. Select and run the PICKET program on your calculator.

Select the CHECK GATE option in order to test your photogate. The photogate should have an "Unblocked" status. Slowly slide the picket fence through the gate to see if the screen alternately displays BLOCKED and UNBLOCKED. If the gate appears to not be working, ask for help. Otherwise, return to the main menu.

To properly set the CBL/calculator for data collection, select the COLLECT DATA option. Follow the on-screen directions to arm the gate (timing will begin when the first dark band begins to break the beam).

Once the time data has been collected, the program stores all collected and calculated data in the following lists on the calculator:

L1 time bar has traveled (used for d-t plot)

L2 displacement of bar

L3 time bar has traveled (used for v-t plot)

L4 velocity of bar

L5 time bar has traveled (used for a-t plot)

L6 acceleration of bar

At this point, the program will allow you to view the d-t, v-t, and a-t graphs individually. After predicting the shape (and possibly even the value of the slope) of each graph, have a look at each graph. A sketch of each graph (one below the other so that the time axes line up properly and a description/discussion of the reason for the shape of each will help to make your data record more complete.

While the program does allow you to see the plots of the data, it does not do a fit for any of the graphs. Thus, you must exit the program to continue your analysis.

Data Analysis Instructions

Once you exit the PICKET program, examine the data is still in lists 1-6. Why are some lists shorter than others? Set your calculator so that it will use only the velocity and corresponding time data to display a graph and do any statistical calculations.

Once you have the v-t graph displayed, go through the steps on your calculator to do a linear fit (ax + b ) for the graph. Set your calculator to display the fitted graph so that it takes up the whole screen. Show your graph to your instructor. Sketch the graph and record both the math and physics form of the fit equation (include units!).

Also record the r value for the fit. The correlation coefficient, r, is a measure of the probability that the variables are actually correlated in a linear relationship. A value of 0 means no correlation; 1 (or -1) means perfect correlation. Expect all the fits to be very good (r nearly +/-1). If they are not, assume that you made a mistake and try again (exception: if the value of the acceleration is very nearly zero, the correlation coefficient may not be near 1 because the fit has a hard time deciding whether the acceleration is positive or negative; in this case don't worry about the value of the correlation coefficient).

CLEARLY LABEL EVERYTHING YOU RECORD AND INCLUDE UNITS!

Summarize all you have learned by doing these activities.