Part III - Gravitational Acceleration

A small constant force can be applied to the rider by inclining the track slightly. The component of gravity which acts on the rider parallel to the air-track is equal to , as indicated in Fig. 2.5.

  

Figure 2.5: Geometry for rider on air-track with a small angle.

Use a few of the shims provided to elevate the right side of the air-track.

NOTE: All of the shims are 1.24 mm thick, not 1.32 mm as marked.

Note that equals the height of the shims divided by the length of the track between the supports, which in this experiment is exactly 1.0 m (see Fig. 2.6).

 

Figure 2.6

A convenient method for taking data is as follows: proceed through the menus until the point when the empty graph is on the screen and the computer is ready to begin collecting data at the press of a key. At this point, set the rider on the track at a given point, say at the 100 cm mark, and release it. After the rider has bounced off the elastic bumper, begin taking data. You should be able to record the rest of the rider's trip up the track, and all of it's trip back down to the bumper again; if not, try taking this data again and waiting a little longer after the rider bounces off the end.

From this one series of measurements of the rider's position, there are many ways to analyze the data and calculate the acceleration of the rider. All of these ways are mathematically related, but for each one you are isolating and analyzing different pieces of the data, so the correspondence between different calculations will not be exact. There are four methods which you should consider:

Analyzing the data you just collected, calculate the value of , and in turn g, using different data points from the graph for each of the equations above. Is your calculation of g close to the accepted value?

Perform the same analysis on two more trials. For the first, use a different inclination of the air-track. For the second, start with the rider at the bottom of the track (using either inclination) and after you begin taking data, give it a gentle push up the track.

Can you observe any significant deviation in the results obtained from these different trials? Which of the four methods seems most accurate? Using all of your results, what is your average calculated value of g?