Air+Resistance+and+Coffee+Filters


 * Lab Title: Air Resistance and Coffee Filters**


 * Primary Authors: Megan**
 * Contributing Authors: Anna and Paul**


 * Abstract:** The goal of this lab is to determine how mass and terminal velocity for a cross-sectional area are linked. Dropping coffee filters and letting them fall to the ground will provide enough data for the link between mass and terminal velocity to be seen.


 * Background Information/Introduction: As the filters fell, the acceleration decreased (eventually reaching 0 m/s/s), but the speed increased until it hit a certain speed and remained there, no matter how much farther it fell. This was when the filter had reached terminal velocity and the force of gravity was equal to the force of air. To complete the experiment, the program Logge **** r Pro was utilized to measure the terminal velocity and to see the velocity and position-time graphs of the falling coffee filters. Varying numbers of coffee filters were dropped over a sonic ranger on the floor so that it could record the coffee filters' change in position. Graphical analysis was used to analyze the path the filters took, from which we were able to determine the point where the velocity of the falling filters hit its constant terminal velocity. **




 * Methods:** Dropping the coffee filters proved to be difficult. The bottom had to be flat and the sides had to be turned up for it to fall smoothly. Also, using less coffee filters meant that air interfered with their flight, causing them to fall away from the sonic ranger, similar to the way a single sheet of paper falls. Therefore, it was difficult to get a good graph from which data could be extracted. The graphs kept turning out to be squiggles and had no sufficient data points. As a result, much of our data would be classified as outlying values, and we chose not to include them in our data charts because they would have thrown off our final numbers and led to inaccuracies in our conclusion. To counter this, we moved the sonic ranger and tried dropping the filters from higher up so that they could have more distance to reach their terminal velocity. These changes helped create a more accurate graph, which meant we were finally able to obtain usable data after many trials with the same number of coffee filters.

of Coffee Filters ||= **Terminal Velocity (m/s)** || By graphing the points and using linear regression, the line of best fit was found. Terminal Velocity= -0.237x-0.567. Alternatively, if power regression was used the equation was: Terminal Velocity =.552x.0.745  (with this equation the terminal velocity was a positive value). After completing the experiment, the groups were to consider what would be the terminal velocity if ten coffee filters were dropped. By plugging in ten for x, it is found that the terminal velocity for ten coffee filters would be about -2.9391 m/s. For the power equation, the terminal velocity would be -3.064m/s, which shows continuity in our data because there is little difference between those two theoretical velocities.
 * Results:**
 * ~ Number
 * = 1 ||= -0.493 ||
 * = 3 ||= -1.495 ||
 * = 5 ||= -2.025 ||
 * = 7 ||= -2.276 ||
 * = 9 ||= -2.475 ||


 * Conclusion:** For a given cross-sectional area, the more mass the object has, the greater the terminal velocity. Because there is more mass, there is more force of gravity. Due to this increased force of gravity, the terminal velocity is also increased (in the negative direction). Because mass is increased, gravity pulls the object at a faster rate towards terminal velocity. This makes sense because a larger mass would mean a bigger force of gravity on the object falling and thus a bigger upward force of air resistance needed to stop the object from accelerating at the rate of gravity, which is -9.8 m/s/s. Also, the more surface area, the more air resistance will occur. For example, skydivers open their parachutes which drastically increases their cross-sectional area, so more air is resisting the open parachute and the skydiver, causing the diver to slow considerably and safely land on the ground. The smaller the cross sectional area is and the more mass and object has, the larger the terminal velocity will be (in the negative direction).