Results and Discussion
In analyzing our six photos, we found the average acceleration to be –1.0 *105 m/s2. The acceleration may have differed from picture to picture for several reasons. The main variation across our pictures was probably due to the inconsistency of the Jell-O. The Jell-O was frozen at the beginning of the shoot, but melted throughout our experimentation. This change in consistency could possibly have allowed the BBs to travel more quickly through the Jell-O as time went on. Also, the barrel of the gun heated as it was fired more which may have caused the initial velocity of the BB to vary. Shown below is a data table of our initial measurements taken from our photographs:
Table 1. Measurements taken from photographs and computer.
| Picture # |
072 |
081 |
083 |
084 |
093 |
094 |
| X1i (cm) |
4.65 |
4.65 |
4.65 |
4.55 |
6.35 |
6.25 |
| X2i (cm) |
0.00 |
0.25 |
0.25 |
0.76 |
2.22 |
1.61 |
| X1f (cm) |
0.00 |
1.25 |
0.45 |
0.74 |
0.31 |
0.81 |
| X2f (cm) |
2.20 |
2.76 |
2.20 |
2.69 |
3.80 |
4.05 |
| D (cm) |
2.30 |
1.79 |
2.10 |
1.89 |
2.61 |
2.70 |
| T (ms) |
.90 |
.90 |
.87 |
.87 |
.87 |
.87 |
Table 2. Scale Factors and actual distances found using scale factors.
| Picture # |
072 |
081 |
083 |
084 |
093 |
094 |
| X1i (cm) |
9.72 |
12.46 |
10.65 |
11.56 |
11.68 |
11.13 |
| X2i (cm) |
0.00 |
0.67 |
0.67 |
1.93 |
4.09 |
2.87 |
| X1f (cm) |
0.00 |
3.35 |
1.03 |
1.88 |
0.57 |
1.44 |
| X2f (cm) |
4.59 |
7.39 |
5.04 |
6.83 |
6.99 |
7.21 |
| Dreal (cm) |
4.80 |
4.80 |
4.80 |
4.80 |
4.80 |
4.80 |
| Scale fact. |
1:2.09 |
1:2.68 |
1:2.29 |
1:2.54 |
1:1.84 |
1:1.78 |
| T (ms) |
.900 |
.900 |
.870 |
.870 |
.870 |
.870 |
Table 3. Results for velocities and acceleration found using formulas.
| Picture # |
072 |
081 |
083 |
084 |
093 |
094 |
| Vi (m/s) |
108 |
138 |
122 |
133 |
134 |
128 |
| Vf (m/s) |
51.0 |
82.0 |
58.0 |
79.0 |
80.0 |
83.0 |
| T1 (ms) |
0.00 |
.049 |
.055 |
.145 |
.305 |
.224 |
| T2 (ms) |
0.00 |
.409 |
.178 |
.238 |
.071 |
.173 |
| Ad (m/s2) |
-6.3*104 |
-1.3*105 |
-1.0*105 |
-1.1*105 |
-1.1*105 |
-9.5*104 |
As you can see our final values for the acceleration of the pellet varied between -6.3*104 m/s2 to -1.3*105 m/s2. As we stated before we believe this to be caused by the inconsistency of the Jell-O as it melted and the growing inconsistency of the gun from continual use. While we took measurements for each piece of Jell-O, there could also have been thickness variations across the Jell-O depending on where it was penetrated.