Day 14: Force Analysis of Air Resistance and g

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Today, the team continued working on the lab experiment write up -this included adding the data tables and procedures to do the lab properly.

In conjunction to this, the group also did trials in different locations in the lab room and used Pasco Capstone to find the g value like any other trials we did so far. From the trials and data collected today, we confirmed that the experiment can be conducted with any background as long there is enough contrast between background and object so that it shows up on the video. Furthermore, the camera should not be zoomed in since it causes the clarity of the video to drop; this can cause an error in determining where the ball and meter stick is in the video.

Finally, the group tackled the problem with air resistance. We wanted to confirm, using the data from our trials, what air resistance does to the acceleration of the object. First, we initialized the vertical force vectors as mg - (1/2)CApv^2 = ma. Then we simplified to get a = g - (1/2m)CApv^2 and plugged in values of velocity found from our trials. In our case, we used the values found from the golf ball trial. As shown below, we used Pasco Capstone to calculate all values of 'a' using its built in tables and functions.

Figure 1: Golf Ball Trial with Computed a values per given v values

Figure 2: Expanded Table of Force and a values

The table in figure 2 shows how air resistance plays a large role in determining the acceleration of the object in a given time. For example, at .101 seconds, air resistance is only 0.01 while at .499 seconds, its at 1.92 which caused the acceleration of the ball to go from 9.80 m/s^2 to 7.89 m/s^2. In theory, if the ball were dropped at a very tall height, the acceleration of the ball will reach 0m/s^2 since air resistance will be as large as g (-9.81m/s^2) thus causing a state of equilibrium.

However, in our tests, the ball should not reach scenario since we only need to dropped the ball from a height of 2 meters or so. Nevertheless, the data shown above explicitly shows the effects of air resistance, even at a short distance of 2 meters. 

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