Ballistic Pendulum Investigation Back to Research Page

Lindsey Pierce & Angela Buck – 2005

Contents

Background

Statement of Problem

Review of Literature

Hypothesis

Method

Data Collection

Analysis/Conclusion

Bibliography

Background: Back to the top

Energy is conserved, but many factors come into play when calculating energy after a collision.  The farther the pellet from an air soft gun has to travel; air friction will act on it longer, therefore displacing the energy.  With a ballistic pendulum, one is able to measure velocity of the projectile before the collision by using the concept of conservation of energy.  Two formulas are needed.  The first being Ek=1/2*M*V^2, which is the formula for kinetic energy.  The second is Ep=mgh, which is the formula for potential energy.  With a ballistic pendulum, kinetic energy is converted into potential energy after the collision.  Therefore, one may set these two formulas equal to each other, then solve for velocity. 

Statement of the problem: Back to the top

The purpose of this investigation is to find out the relationship between the distance an air soft pellet travels and the velocity with which it hits a ballistic pendulum. 

Review of literature: Back to the top

First, it’s important to understand how an air soft gun works.  Robinson explains, “Spring guns are driven by a spring, a potential mechanical energy source. The spring propels a piston, which is drawn back by manual force and is internally locked in a rearward position by a gear. When the trigger is pulled, the sear releases the piston creating pressure in the cylinder, which is then channeled through a nozzle and onto the bb which is then propelled out of the barrel”.  In addition, “Most of the stock air soft gun is rated a little under 300 feet per second”(Airsoft FAQ).

Air resistance will also come into play in our experiment.  “All matter is made from atoms and/or molecules. The air is no exception. When something moves through the air, it bumps into the atoms and molecules…Even though atoms and molecules are very tiny and very light, each collision causes a force on the moving object…The force from each individual collision is therefore very tiny. There are however millions of these collisions each second so millions of tiny forces add up to make a large overall force”(“Air Resistance”).  Because the pellet is moving through a distance of air, it will be affected by air resistance.  We must take this into account when analyzing the results. 

In our experiment we will also be using a ballistic pendulum.  “The ballistic pendulum is a device used to measure the speed of a projectile, such as a bullet.  The projectile of mass m is fired into a large block (of wood or other material) of mass M, which is suspended like a pendulum.  (Usually, M is somewhat greater than m.)  As a result of the collision, the pendulum projectile system swings up to a maximum height h” (Giancoli).

“The height of the swing can be related to the velocity of the projectile” (Tedeschi).  Based on this information, we will be able to find the velocity by measuring the height of our pendulum after the collision.

Hypothesis: Back to the top

We believe that the velocity of the pellet right before collision will exponentially decrease in relation to the distance the pellet travels.  We believe that the angle that the pendulum will travel will be between 10 degrees and 0 degrees, decreasing as the distance the air soft gun is from the pendulum increases.

Method:  Back to the Top

            When designing our experiment we used multiple models for our pendulum.  Initially we used a design that involved a cardboard box hanging from pieces of wood.  The box had one open end to catch the BB from the airsoft gun.  In preliminary testing we found that the box was too heavy and would not move.  Next we created a pendulum with a clay weight on the end of it.  This was also too heavy.  Eventually we came to our final design for the pendulum, which is described below.

For our experiment a pendulum and an airsoft gun is needed.  For safety, goggles are needed when firing the gun.  For the pendulum, we used a 2 ¾ inch by 3 7/8 inch by 3 7/8 inch block of Econofoam®.  Also, we used children’s toy construction straws and connectors to create the apparatus for the block to hang from.  On the bottom of the block, small wire loops are used to hold a felt tip pen.  Multiple colors of pens are needed, going from light to dark.  In addition, two level surfaces are needed to hang the pendulum between.  One of which has to have a flat side.  Legal-sized paper is needed as well as a ruler and a protractor. Finally, one needs a piece of yarn, tape, and a level.

             First, you must set up the pendulum.  Next, measure ten distances from the pendulum, each ten centimeters apart.  So, the farthest distance should be 100 centimeters away from the pendulum.  Mark each distance with tape.  On the legal size paper draw a perpendicular line and attach it to the flat side of one of the supports.  Attach a ballpoint pen to the bottom of the pendulum and swing the pendulum by hand to mark its path on the paper.  Use this paper as a template, and trace the markings onto ten more sheets.  Measure the angle from the top of the perpendicular line to points on the path of the pendulum.  Using the protractor, mark every 5 degrees on the path.  Do this on all of the sheets.  Then, attach one of the sheets to the flat side of the support.  Put a light-colored felt tip pen in the wire loops.  Get the piece of yarn, lift up the piece of tape at the first distance marked, and tape down one end of the yarn.  One experimenter holds up the yarn, and uses the level to make sure the yarn is perpendicular to the ground.  The other experimenter, wearing goggles of course, aims the gun so the tip is matched up with the yarn, and shoots the pendulum.  Record the angle that the pendulum swings.  Repeat ten times for each distance, increasing the darkness of the pen color for each trial.  If it becomes difficult to read the angle reached by the pendulum, change the sheet of paper.  

            The independent variable is the distance from the pendulum that the airsoft gun is fired.  The dependent variable is the angle to which the pendulum swings. 

Data Collection: Back to the top

Calculations for velocity: ½ (m+M) v^2 = (m+M) g*h h=x*cosθ

*masses cancel out because they are on both sides of the equation

½*v^2=9.8*.319*cosθ 

v=√2*9.8*.319*cosθ

m=.12g (mass of BB)

M=49.78g (mass of pendulum)

g=9.8ms^-2

x=31.9cm (length of pendulum)

θ=the angle the pendulum reaches

h=height the pendulum reaches

v=velocity (what we’re trying to find)

10cm: v=√2*9.8*.319*cos4.982=2.52109

• repeat this with each value, all velocities are in the table below

  Uncertainty:

Of the angle: (5.6-2.5)/2=1.55 degrees *we took the largest difference between two angles at 80cm and subtracted them and divided them by 2 (this will be done for all distances) Of the gravitational constant: 0.01 ms^-2

Δy/y=Δa/a+Δb/b

80 cm: Δy/2.4956=1.55/4.06+.01/9.8=.9553ms^-2

• repeat this with each value, all uncertainties are in the table below

Analysis/Conclusion : Back to the top

            We were not able to completely prove our hypothesis that the velocity would decrease exponentially as the distance from the pendulum became greater.  However, if one refers to the graph of velocities one can see that we were slightly correct starting at a distance of 60 cm going to 100 cm.  We found that all of our velocities were around 2.49 m/s and our average uncertainty was .5272 m/s.  This is a fairly high uncertainty.

    There are many reasons why we believe the uncertainty was so high.  First, we contemplated the effect of friction between the pen and the paper and the straws and the connectors while the pendulum was swinging.  However we decided that the amount of friction would be fairly consistent during each trial so it probably wouldn’t cause that high of an uncertainty.  Then we realized that the air soft gun was probably not firing at the exact same speed every single time.  This is because how far back the shooter cocks the gun affects how condensed the spring inside the gun is, which eventually propels the BB, the speed of the BB would not be that consistent.  Also the air soft gun that we were using was fairly used so it might not have been working at its original quality.  We believe this was the best explanation for the discrepancies in our data.  Another problem that may’ve affected the velocity of the BB was air currents within the house we were experimenting.  The BBs only weighed .12g so they could be greatly affected by any air currents in the experimenting environment.             If we could do the experiment over again there are multiple things that we would change.  Firstly, we would’ve tried obtaining a gas air soft gun instead of a spring action one.  We learned after our experiment was already complete that the gas air soft gun is more consistent because it does not need to be cocked.  This takes out the human error of cocking the gun at different distances.  Also, we would choose distances to shoot from that were farther apart and farther away from the pendulum itself so that we would be more able to see the effect on the velocity of the pendulum.  Because our shooting points were only 10 cm apart, and at most 100 cm from the pendulum, our velocities were very similar and in some cases, practically the same.

Bibliography: Back to the top

  “Air Resistance.” Science for All. 2004. Fortune City. 27 Oct. 2004            <http://www.fortunecity.com/business/redstone/1574/index.htm>  - Interesting Analysis of Air Resistance

“Airsoft FAQ.” Nippon Hobbies. 2004. Nippon Hobbies. 27 Oct. 2004            <http://www.nipponhobbies.com/airsoft_faq.php> -Information on airsoft guns

Giancoli, Douglas. Physics Principles with Applications. 5^th Ed. New Jersey: Prentice Hall,         1998.

Robinson, Jason ‘Kornkob.’ “Challenge: How do Airsoft Guns Work?” Airsoft Retreat.  2001. Airsoft Retreat. 27 Oct. 2004 <http://www.airsoftretreat.com/chal-howtheywork.asp> -Descriptions of different types of airsoft guns

Tedeschi, David Dr. “Ballistic Pendulum.” July 1999. University of South Carolina. 27 Oct.       2004
< http://solomon.physics.sc.edu/~tedeschi/demo/demo20.html>  -Explanation of a ballistic pendulum