Physics Research Project
Air Friction a Velocity?
Matt Mellinger Dan Maynard
IB Physics II
The purpose and goal for this Research Project is to discover if air friction is proportional to velocity. The method used to unveil this was a pendulum built to measure the velocity of a paintball after air friction had acted on it over a distance. By measuring the movement of the pendulum a velocity can be established and that velocity compared to the muzzle velocity. By performing this experiment at varying velocities, a comparison of the change due to air friction can be found to be either proportion or constant.
- Measuring Utensil
- Paintball Marker (and accessories)
- Pendulum
- Paintballs (identical spherical .68 caliber)
- Duct tape
- Dry-erase board
- Dry-erase markers
- Stop watch
- Calculator
- CO2
- Computer
- Microsoft Word
- Excel
The construction of the Pendulum is in such a fashion that a wooden plate sits directly beneath the beam connected to the foundation (fig 1) on double hook hinges. The hinges allow for a smooth stable swing of the plate while also permitting a fast removal for cleaning and measurement collection. A white board is added to the post so that it is along side the path of the swinging plate. On the side of the plate opposite of the intended impact, is an attached dry-erase marker. The marker is overly extended past the plate so as to allow for continuous contact to the white board (fig 2) with minimal friction.
Modifications were made to the gun so that it would fire in an unaffected action. A traditional barrel replaced the curved, backspin-enabling barrel. This made for a shot that would not reduce the air friction that any normal flying sphere would have.
At a distance of 8 yards from the plate of the pendulum was located the end of the muzzle. We made sure to hold the exit height of the paintball at the congruent height of the target. After a few preliminary trials we found that a splatter guard was a necessity since the oily paint was obstructing the surface of the white board and restricting the dry-erase marker from operating properly. A folded piece of thick paper was sufficient since it would not be contacted directly with a projectile (though, it would have to be replaced after a few unfortunate stray shots).
In-order to begin solving the air friction; we had to first figure out certain variables. The first of which was the muzzle velocity of a paintball in order to compare to the velocity upon impact. To calculate this we fired a single ball straight up into the air and timed its arrival back to ground level. By taking the average of six shots we formulated that the ball was traveling at an average speed of 37.2 meters per second. To do this we used V = U + AT (calculation in excel). By taking half the time it traveled, since an object spends an equal amount of time going up as it does coming down, and knowing that the velocity at the apex of flight is 0 m/s, we solved the initial velocity. Later on we are able to use this velocity in comparison to our ball that underwent friction. The following is the formula that would give us the velocity of a paintball an instant before it strikes the pendulum arm.
Mass Bullet x Velocity Bullet = (Mass Bullet + Mass Pendulum) x Velocity Pendulum
Velocity Pendulum = √(2 x Gravity x Height)
Rearranging and combining these two formulas produced the following formula.
Velocity Bullet = (Mass Bullet + Mass Pendulum) √(2 x g x h)
Mass Bullet
We now need to find the mass variables to work in our equation and since an accurate scale was tough to find, we sought a scale from the local Haggen’s meat market. According to the scale our meatless 50 paintballs, contained in a mass-less plastic bag, came out to .36 pounds, or .0029 kilograms per paintball. Similarly, our Pendulum arm weighed 1.02 pounds, or .4626 kilograms. Using the prescribed set up previously mentioned, we then shot the paintballs into the plate in our enclosed area. Between each shot we recorded the movement of the pendulum. This involved using the corner of a piece of paper as a template. Held at a perfectly perpendicular angle to the earth in respect to the pendulum, each point, both starting and ending, were marked (fig 3). After a lengthy period we finally got eight data points for the height, which were measured and calculated later.
After adjusting the velocity bolt, we went back outside and shot another salvo of paintballs up in the air to find the new velocity to retry our experiment to compare to our other data. However, to our dismay, the airtime of the paintballs did not change even though the velocity had been adulterated. We were recording the air times anywhere from 6.5 to 8.5 seconds just like we had received with our prior velocity. At first we thought that we had not turned the velocity up a noticeable enough amount but even on max settings we received similar results. Frustrated by these findings we went back inside and performed the same tests as before on the pendulum at the same distance and found that the velocity actually had become greater than the previous trial. Upon reaching this obstacle of not being able to determine an accurate muzzle velocity and not having another system of measurement, we put down our guns and began to ponder what went wrong.
Analyses/Margin of Error
(synonymous):
When we shot the paintballs outside to find the muzzle velocity, both times, it was raining and windy. This MUST HAVE contributed to the large amount of chaos in our times. Along with the inconsistency of airbursts due to the quality of paintball marker that was available. It is no wonder that combined with weather factors our results were no compliance to the laws of physics. And someone set up us the bomb.
This is not the only puzzle to our data since we confirmed that one of our final velocities from the pendulum tests equaled 232 m/s or 519 mph, making our data very improbable and unreliable since the usual speed of a paintball is around 200 mph. Not to mention the fact that a paintball cannot be fired much over 300 mph without bursting into a mist of splatter. We spent roughly an hour and a half examining, re-examining and rechecking our figure without any hint of the origin of our problem. Although our outside tests showed no variation in velocity, our second pendulum test did have an obvious increased. Upon re-measurement of our pendulum height data and re-computation of our formulas we begin looking to other variables for the answers. We did not, however, double check the masses of the pendulum arm and the paintballs because the trusty local fish guy already had measured them accurately for us. And we assumed that since the scale has to be accurate for meat sales that the fish guy was a reliable source. The place where the paintball stuck the target contributed to our data. At eight yards away it was highly improbable that we hit the target at the exact same place sixteen times in a row. Combined with the inconsistency of the paintballs and the inconsistence of aim, this can be some justification for our inability to retrieve reliable data.
Although our initial experimentation did not yield the expected results, due to the inability to calculate the muzzle velocity and other complications, we feel that we have supported our hypothesis: Air friction is proportional to the paintballs velocity. Since the airtimes did not change significantly, even though the velocities did, this may support the fact that the balls underwent more air friction as fired at a higher velocity, resulting in these similar times. We conclude that since our initial set up did nothing to help prove our hypothesis, it could still be supported by the outcome of the skewed muzzle velocity, instead using the actual pendulum.
| Physics Project | ||||
| Mass of Paintball | .0029 Kilograms | |||
| Mass of Pendulum | .4626 Kilograms | |||
| From Eight Yards (7.3152 m) | ||||
| Trial | Height diplacement on pendulum | Velocity of Pendulum | Velocity of Ball | Avg. of Trials |
| V = SQRT(2gh) | ||||
| 1 | 0.038 | 0.86301796 | 138.5292623 | 144.76032 |
| 2 | 0.058 | 1.06620823 | 171.1448046 | |
| 3 | 0.038 | 0.86301796 | 138.5292623 | |
| 4 | 0.034 | 0.81633327 | 131.0355638 | |
| 5 | 0.021 | 0.64156060 | 102.9815373 | |
| 6 | 0.045 | 0.93914855 | 150.7495346 | |
| 7 | 0.017 | 0.57723479 | 92.65613573 | |
| 8 | 0.107 | 1.44817126 | 232.4564558 | *** |
| From Eight Yards (Trial #2) | ||||
| Trial | Height diplacement on pendulum | Velocity of Pendulum | Velocity of Ball | Avg. of Trials |
| V = SQRT(2gh) | ||||
| 1 | 0.071 | 1.17966097 | 189.3559244 | 176.364338 |
| 2 | 0.069 | 1.16292734 | 186.6698887 | |
| 3 | 0.080 | 1.25219807 | 200.9993794 | |
| 4 | 0.090 | 1.32815662 | 213.1920363 | |
| 5 | 0.045 | 0.93914855 | 150.7495346 | |
| 6 | 0.083 | 1.27546070 | 204.7334332 | |
| 7 | 0.030 | 0.76681158 | 123.0864796 | |
| 8 | 0.040 | 0.88543774 | 142.1280242 | |
| Muzzle Velocity Measurements | ||||
| Times | Velocity | Avg. Velocity | ||
| 8.01 | 39.25 | 37.20 | ||
| 7.27 | 35.62 | |||
| 7.89 | 38.66 | |||
| 7.62 | 37.34 | |||
| 6.66 | 32.63 | |||
| 8.10 | 39.69 | |||
| ***- Money Spot which equals about 519 mph | ||||