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Terminal Velocity

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                02-12-08

Investigating terminal velocity

The aim of this experiment is to investigate the terminal velocity of a falling coffee filter. The equipment we uses was 5 coffee filters, tape measure, GLX explorer with motion sensor and PC with Data Studio.

We first measured the length from the glx explorer up to about 2.5 m height. Than we dropped coffee filters in different size and different amount down to measure the terminal velocity. We than dropped the small coffee filters adding one at a time up until five filters to see whether this affected the terminal velocity. Also, we dropped one large filter twice to see whether size matters when finding the terminal velocity.

Raw data
- Graphs, finding the terminal velocity.

image00.png

Figure 1: Graph of 1 small coffee filter ( terminal velocity from just before 1 sec until 3.5 sec  )

image01.pngFigure 2: Graph of 2 small coffee filters ( terminal velocity from just before 1 sec until about 2.5 sec. 1.1 sec at the graph is wrong, it could have occur if the beam missed at the coffee filter and hit something else. Upthrust will be physical impossible under the fixed circumstances we had )

image07.png

Figure 3: Graph of 3 small coffee filters ( terminal velocity from just after 0.6 sec until 2.1 sec. Same problem as the graph above. At 0.9 sec the beam might have hit something else.  )

image08.png

Figure 4:Graph of 4 small coffee filters ( terminal velocity from just after 0.6 sec until 2 sec. Same error as the graphs before, now at about 0.62 sec  )

image09.png

Figure 5: Graph of 5 small coffee filters ( terminal velocity from around 0.7 sec until 1.9 sec. Same error as the graphs before, now at about 0.9 sec  )

image10.png

Figure 6: Graph of 1 large coffee filter, 1st run ( terminal velocity from just after 0.6 sec until just before 3.6 sec.  )

image11.png

Figure 7: Graph of 1 large coffee filter, 2nd run ( terminal velocity from just before 0.6 sec until just before 3 sec. Same error as some of the first graphs, now at about 0.62 sec  )

Processing the data:

Terminal velocity occurs when the net force on a falling object goes to zero. The coffee filters reaches its  terminal velocity when the downward force of gravity (Fg) equals the upward force of drag (Fd). We can see terminal velocity on a graph by observing when the graph gets linear. When the net force equals zero of an falling object it will have terminal velocity. Due to the shape of the coffee filters they are suitable to this investigation. It will maintain it until its the ground.

To calculate the terminal velocity we use the formula:

image12.png

-

Calculations for figure 1 (1 small filter):

Putting the observed numbers into the equation above, we get that image13.png

Calculations for figure 2 (2 small filters):

image14.png

Calculations for figure 3 (3 small filters):

image02.png

Calculations for figure 4 (4 small filters):

image03.png

Calculations for figure 5 (5 small filters):

image04.png

Calculations for figure 6 (1 large filter, 1st run)

image05.png

Calculations for figure 7 (1 large filter, 2nd run)

image06.png

Presenting the processed data

We have quite a few uncertainties to take into consideration when doing this report. Although, we will just be mentioning them, not actually utilizing them.

First the lack of equipment we used. We should have used some sort of device that kept the coffee filter exact above the motion sensor. As explained  under the graphs, the filter sometimes was not above the beam. This made some uncertainties. We adjusted the motion sensor to a wide beam, thus making it less accurate than f we had used a smaller one, but due to lack of equipment. We was not capable to make this as accurate as we wanted it. At last it was quite difficult to read off the graph values accurately. The beam width, coffee filter when it fell etc.

Number of small coffee filters

Terminal velocity

ms-1 ( + 0.01)

1

0.94

2

1.34

3

1.58

4

1.86

5

2.0

As you may notice, the terminal velocity increases when weight increases. This may explained by the fact that, as you may recall, the terminal velocity is defined as follows: Downward force of gravity (Fg) equals upward force of drag (Fd). Downward force increases when weight increases, thus the upward force of drag increases proportional.

Number of large coffee filters

Terminal velocity

ms- ( + 0.01)

1

0.88

1

0.88

Well, as you can read out of the table our two runs were quite accurate. Both times we got 0.88 ms1..

Conclusion

Based on what we did in the experiment we can sum up the following: The terminal velocity of a free falling object depends on the weight of the object. It will also depend on the shape of the object as seen with the differences in terminal velocity of the large and small coffee filters.

It was not any huge weaknesses in this experiment. The biggest must be that the coffee filters did not fall straight down, but rather wave through the air  from side to side. Another weakness was that the coffee filter lost its shape during the experiment. This might have effected the results.  
We can solve the first problem if we had use ha cylinder that could have guided the filter to be exactly above the beam. Than we also could have used a beam with lower width. This would have given us a more precise measurements and the graphs would have been more accurate. The last problem could we have fixed using new filters after each measurements or using harder material. But also, this will have an effect on the velocity.

If we had dropped the filters from the same height all the time we may got more accurate results. We should have dropped it from the same height all the time and measured it. Still the experiment was intelligible and we can draw conclusions  out of it. With the uncertainties we still had good enough experiment to understand the basics of terminal velocity.

This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.

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