Ballistic Pendulum

Project

 

 

By:       Blake Reser, Tyler Snyder, Libby Banse-Fay, Nick Hines, Robbie Ellis, Robbie Price

 

 

 

 

 

 

Table of Contents .:. Go Up

 

 

Introduction:                                              

 

Method:                                                                 

           

Results:                                                                   

 

Errors and Improvements                                   

 

Conclusion                                           

                  

Related Links

 

Bibliography                                                      

 

 

 

 

 

 

 

 

 

 

 

 

Physics Research Paper

 

Introduction

 

Background:

To conduct an experiment that uses paintball guns to measure the velocity at which a paintball travels, there are many things to consider, evaluate, and calculate. The first step in the process is identifying the type of paintball guns. The two types that will be used for the experiment are a Tippmann 98 Custom and a Spyder Xtra. The Tippmann 98 Custom is a used gun, while the Spyder Xtra is a new gun. This is important to note because the Tippmann 98 paintball gun, could be functioning at a lower level, as compared to a new gun.

A paintball gun is a weapon designed to simulate an actual gun in a war simulation, while paintballs are easily identifiable when checking if a target was hit. A paintball gun works by releasing compressed air and causing propulsion upon the paintball firing it. The gas is usually Carbon Dioxide, while it could be pumped air. When the gas is released, it flows up the tube into the barrel, where it fires the projectile at a high rate of speed. 

Moving on, the next thing to consider is the ammunition that will be used, which is Inertia Paintballs. Each individual paintball is 0.68 Caliber and this will be kept constant throughout the experiment. Another aspect is testing the velocity in relation to the state of the paintball. Also, there will always be air friction, which is what causes the paintball to slow down, as well as gravity. In addition to air friction and gravity, we will ultimately be measuring how temperature affects the velocity of a paintball. We will be using three varying temperatures; a frozen state at 15 degrees Fahrenheit, a normal state of 60 degrees Fahrenheit, and a temperature of 30 degrees Fahrenheit.

To measure the velocity of a paintball we are going to use a ballistic pendulum. The ballistic pendulum is a device that is used to measure the velocity of an object by retaining the bullet upon impact, and its velocity is a function of the displacement of the pendulum.

We are going to use the formulas: (2gh)^(½) = V  &  (m+m)V=mV.  The “g”  in the first equation stands for gravity, which is equal to 9.81 m/s squared. As for the “h”, it represents the change in the height of the pendulum when it is hit by the paintball. Finally, the V is the velocity of the pendulum and paintball, which can be substituted into the second equation. For the second equation, the first “m” represents the mass of the paintball, and the second “m” represents the mass of the pendulum. As for the first “V”, it represents the velocity of the pendulum and paintball, which we can  find by using the first equation.  After the equal sign, the next “m” signifies the mass of the paintball. Finally, the last “V” stands for the Velocity of the paintball and the variable we are trying to find.

It has been shown that the temperature of a projectile can greatly affect the speed it travels. The paint ball will condense at a frozen temperature, while it will expand when heated to a hotter temperature. Not only does the condensing and expansion of the projectile increase mass, we believe that it will increase/decrease velocity. Overall, the paintball experiment will be very exciting and informative, and also provide us with a better understanding of velocity and air friction.

Statement of the Problem:

The purpose of this problem is to find the velocity of a paintball, shot by a paintball gun, in different physical states: 15, 30, and 60 degrees Fahrenheit.

 

Hypothesis:

We believe that the paintball is going to have a faster acceleration when it is in a colder temperature compared to a higher temperature. We believe this because the paintball will have less resistance when it is slicing through the air. Also, we believe that the frozen paintballs will withstand air resistance much more effectively than the warmer paintballs. Aerodynamics plays a big role in determining how fast an object travels.

We are going to measure the temperature of the paintball by using a temperature gun. As for the velocity of the paintball, we are going to make a ballistic pendulum and use mathematical equations to calculate the velocity. The controlled variables in the experiment include the two paintball guns, the type of paintballs, the target, distance, and the CO2. The dependent variable in the experiment is the velocity that we are going to calculate. Finally, the independent variable is the three different temperatures of the paintball. The temperatures we are going to use are 15, 30, and 60 degrees Fahrenheit.

 

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Method:

 

The set up of the experiment was quite simple and remained constant throughout the entire procedure. The first thing we had to do for this experiment was to set up a table to attach the ballistic pendulum. We began by making a table with two sawhorses and a sheet of plywood. Then we built a ballistic pendulum that would swing when it was hit by a paintball. The ballistic pendulum was made out of lightweight sheet metal and rivets. The sheet of metal was connected to two hinges on either side that produced little to no resistance on the sheet. The sheet of metal hung off the side of a table at a 90 degree angle, forming what is known as a ballistic pendulum.  After the ballistic pendulum was set up, we placed a 45 pound weight on the plywood so it would remain steady and not shift when the paintball would strike the ballistic pendulum. Fifteen feet from our ballistic pendulum, a stand was aligned where the paintballs would be fired from both of the paintball guns. Next to the pendulum stood a shovel embedded in the ground that stood in a perfect line, with a ruler taped onto it at the same level as the pendulum. A couple feet away from the shovel, a camera was placed to capture the movement of the pendulum after it was struck by the paintball. For each gun, three trials were conducted. The trials were done for the three states in which the paintballs were in. Ten shots were fired in each trial. So altogether, there were six trials and sixty data points gathered. Before the paintballs were shot, we used the temperature gun to ensure that they were the precise temperature we wanted. Also, keeping the distance the same was an imperative factor in order to find the exact velocity for each shot fired and obtain accurate data.

 

Diagram:

 

Supplies:

 

     Spyder Xtra gun

     Tippmann 98 Custom gun

     Paintballs

     CO2

     Ballistic Pendulum (sheet metal, two hinges, and arms to attach to table)

     Screws (to stabilize gun to table)

     Table (two sawhorses and a sheet of plywood)

     Measuring Tape

     Temperature Gun

     Ruler

     High Definition Camera

     Tripod for Camera

     Stand or Clamp (to stabilize gun)

     Towels

     Screw Driver

     Cleaning supplies for the Paintball Guns

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Results:

 

The results told us that the 30 degree Fahrenheit paintballs had a faster velocity than at the temperatures of 15 and 60 degrees Fahrenheit. This was true for the Tippmann 98 Custom and the Spyder Xtra paintball guns. All three temperatures had a significant amount of variance, but the averages made it clear that the 30 degree Fahrenheit paintballs were the fastest.

Data file: text .:. Excel

 

 

 

Average Velocities:


 

15º  =  133.51 mps


 

30º  =  149.86 mps


60º  =  120.09 mps

 

Data file: text .:. Excel

 

 

Average velocities:


 

15º  =  107.81 mps


 

30º  =  119.24 mps


60º  =  95.59 mps

 

Data Summary:

The Spyder gun shooting paintballs at 60 degrees moved the pendulum an average of .02784 meters and had an average velocity of 120.09 mps. The same gun with paintballs at 30 degrees averaged .04333 meters in height and a velocity of 149.857 mps, and the paintballs at 15 degrees had an average .03478 meters and velocity of 133.51 mps. The Tippmann gun shooting paintballs at 60 degrees moved the pendulum an average of .02747 meters and had an average velocity of 95.59 mps. At 30 degrees the pendulum moved an average of .02747 meters and velocity of 119.24 mps, and at 15 degrees the pendulum moved .02255 meters and had an average velocity of 107.81 mps.

 

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Errors & Improvements:

A few errors could have occurred during the length of our experiment. First of all, the experiment took place outside which means weather could play a role in the way our results turned out. The wind may have altered the direction of the paintballs, as well as, increased or decreased the rate at which it was traveling. Another factor that could alter the results is the location of impact by the paintballs on the ballistic pendulum. The paintballs did not always hit the same exact spot on the pendulum, making the uncertainty a little higher than it would be if the target was precise. Though the paintballs were not always impacting on the same location, the ballistic pendulum is not a huge target; therefore our data is still reliable.

Continuing, another potential error is the temperature of the paintballs. Since there were ten shots fired in each trial, the temperature of the paintballs may have increased or decreased while resting in the hopper waiting to be used. One last potential inaccuracy was the technology used to record the impact on the pendulum. Although we did have an HD camera and quality video editing software, analyzing video footage is not 100% accurate.

There were many ways we could have improved the procedure of our experiment. First off, we could have researched a video of a ballistic pendulum being used so then it would have been easier to make one. Also, making a list of supplies and equipment would have saved us time, since we found ourselves having to go and get equipment from a store or someone’s house. Another thing that slowed us down was using the camera to videotape the experiment. Improving our knowledge on how to set up the camera, import the videos into the computer, evaluate the videos on the computer, and use software to pause the video to measure the distance the ballistic pendulum swung would have helped.

 

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Conclusion:

 

From the results we can see that 30 degree Fahrenheit paintballs have faster velocities when compared to paintballs at 15 and 60 degree Fahrenheit temperatures. In our hypothesis we stated that the coldest paintball would have the fastest acceleration. In this experiment, that wasn’t the case. We thought that a paintball would have a faster acceleration the colder it was, but it turns out that a paintball around freezing has the fastest acceleration. Why is this the case? More research would need to be done to target this exact reason, but using prior knowledge one could relate this experiment to the height at which a ball rebounds. For instance, a marble, when dropped, would have a very minimal rebound. On the other hand, a rubber ball would bounce much higher. Part of the reason this occurs is because a rubber ball absorbs more energy on impact, thus giving it more energy to expend when it rebounds. A similar instance could occur when a paintball is struck by the spring or trigger used to launch the ball. The harder the object, like the frozen balls, the less energy absorbed. Then you ask why doesn’t the warmest paintball have the fastest velocities. A possible reason is because the warmer ball absorbs too much of the energy and doesn’t expend it all on impact. There has to be a middle ground, or in other words, a bell curve, and this experiment demonstrates that the 30 degree paintballs rests on the top of the curve in relation to the other two temperatures. Overall, the experiment was very engaging and useful. Being able to calculate velocities using less modernized equipment, allowed us to better understand the process, and served to be very educational.

 

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Related Links:

http://www.tippmann.com/98customplatinum.aspx             (Specifications of the 98 custom Tippmann)

http://en.wikipedia.org/wiki/Tippmann_98_custom                (Origin and more in depth specifications of the Tippmann 98 custom)

http://paintball-guns.findthebest.com/l/60/Spyder-Xtra            (Specifications and personal reviews of the spider xtra)

http://en.wikipedia.org/wiki/Drag_(physics)                           (The physics of drag and several formulas to calculate drag)

http://www.techpb.com/forum/index.php?showtopic=7641        (Reviews and opinions on paintball resistance)

http://www.ask.com/question/how-does-a-paintball-gun-work       (How to operate a paintball gun and different types)

 

 

Bibliography:

      "98 CUSTOM® PLATINUM." 98 Custom PS Paintball Marker. N.p., n.d. Web. 30 Oct. 2013. <http://www.tippmann.com/98customplatinum.aspx>

      "Tippmann 98 Custom." Wikipedia. Wikimedia Foundation, 16 Oct. 2013. Web. 30 Oct. 2013. <http://en.wikipedia.org/wiki/Tippmann_98_custom>

      "Spyder Xtra." Paintball Gun. N.p., n.d. Web. 30 Oct. 2013.      <http://paintball-guns.findthebest.com/l/60/Spyder-Xtra>

      "Drag (physics)." Wikipedia. Wikimedia Foundation, 29 Oct. 2013. Web. 30 Oct. 2013  <http://en.wikipedia.org/wiki/Drag_(physics)>

      "Drag Coefficient (air Resistance) on a Paintball? Mass?" Forums. N.p., n.d. Web. 30 Oct. 2013. <http://www.techpb.com/forum/index.php?showtopic=7641>

      “ How A Paintball Gun Works” Forums.  N.p.. Web. 6 Jan 2014. <http://www.ask.com/question/how-does-a-paintball-gun-work>.

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