The Dissection of a Paintball Explosion - Analysis
Tim Reibold and Brandon Winterling - 5/02

To see the photos we analyzed and the mathematical process we used to find velocity, momentum, kinetic energy, F_net and impulse for the paint splash at different points in the splash, click on the photo name below.

photo164	photo176	photo177
photo220                                     photo221

Why did we choose these pictures in particular?
We used these pictures in particular because part of the shell or paint splash appeared to be moving parallel to the Plexiglas. This was important so that we could accurately measure the distance the piece of shell or paint was moving. In other words, because pictures are two dimensional, we could not measure the distance traveled by a piece of shell or paint in a third dimension. So, we need pictures that had paint or pieces of shell only moving in the plane of the picture. Though we doubt that the pictures we picked were absolutely perfect in this respect, they were the best pictures we had to use.

How did we actually use our measurements to calculate velocity, momentum, kinetic energy, F_net, and impulse?
We started by measuring the distance traveled by a piece of paint or shell in each image of the photographs. We did this by printing the photographs and using a ruler to measure the marked distances.

Photo 164:

Photo 176:

Photo 177:

Photo 220:

Photo 221:

From the raw distance measured on the photographs, we converted to actual meters by using a scaling factor. We obtained our scaling fact by taking a picture of a meter stick at the same distance from the mirror as the paint ball.

Below is the picture we used for scaling:

The actual distance was 30 centimeters and we measure it to be 7.59 centimeters. So, we get our scaling factor from dividing 30 cm by 7.59 cm, which comes out to be 3.95. We then multiplied the distances measured in the photograph by this scaling factor and by 1m/100 cm to convert the distances to actual distances in meters. Please refer to the MathCAD documents to see exactly how this was done (link below).

From these distance we used many physics equations to calculate velocity, momentum, kinetic energy, F_net, and Impulse. Please click here to see the step by step process we used for photo 164. 

Results:
Key:
V₁ = Velocity 1, or the velocity found using the first two images in each photograph
V₂ = Velocity 2, or the velocity found using the last two images in each photograph
P₁ = Momentum 1, or the momentum found using the first two images in each photograph
P₂ = Momentum 2, or the momentum found using the last two images in each photograph
KE₁ = Kinetic Energy 1, or the kinetic energy found using the first two images in each photograph
KE₂ = Kinetic Energy 2, or the kinetic energy found using the last two images in each photograph
F_net = Net Force

 

Photo	V1 (m/s)	V2 (m/s)	P1 (kg*m/s)	P2 (kg*m/s)	P2-P1 (kg*m/s)	KE1 (Joules)	KE2 (Joules)	KE2-KE1 (Joules)	Fnet (Newtons)	Impulse (N*S)
164	45.5	38.6	0.145	0.123	-0.022	0.072	0.061	-0.011	-26.1	-0.022
176	60.0	41.8	0.191	0.133	-0.058	0.095	0.066	-0.029	-67.8	-0.058
177	78.5	24.2	0.25	0.077	-0.173	0.125	0.038	-0.086	203.4	-0.173
220	59.9	32.5	0.191	0.103	-0.087	0.095	0.052	-0.044	-103	-0.087
221	33.9	54.8	0.108	0.174	0.066	0.054	0.087	0.033	78.2	0.066

As you can see from our results, the values of velocity, momentum, kinetic energy, F_net, and impulse vary widely depending on the stage of the paintball explosion and the surface the paintball hits. Photos 164, 177, 177 are of the paintball hitting Plexiglas.  The first velocity of photo 177 shows the approximate speed of the paint erupting out of the paintball - 78.5 m/s. Also, photos of 220 and 221 are of the paintball hitting a ring stand and are an interesting comparison to the values of the paintball hitting the Plexiglas. 

All photos on this site are copyrighted by Brandon Winterling and Timothy Reibold, 2002. 
To inquire about picture use please contact Loren Winters at winters@ncssm.edu