# Explosions

## Abstract

The experiment showed the physics behind rocket propulsion. We found that total linear momentum before the explosion was in fact equal to the total linear momentum after the explosion. We also estimated the energy released in an explosion.

## Theory

We learned about rocket propulsion in this lab. When energy is released, other objects can utilize this energy. Rockets are an example of this. Although energy can be released in these rocket launches, total linear momentum is conserved. The momentum of individual objects can change, but in the total picture, nothing is lost or gained.

## Experiment

In this experiment, we used a set up similar to the picture below.

However, we used a cart with a spring on it and the carts started in the center contacting each other. We simulated explosions by compressing one cartŐs spring between the two carts and then releasing the spring. The carts them moved outwards towards the photogates, which measured the velocity. The spring had three different compression settings. We did this experiment multiple times with all three settings. We also varied the weight on the carts.

## Data Analysis

As seen below in Table 1, momentum is conserved in these explosions. Although the experimental momentum is not exactly equal to 0 as it is in the calculated momentum, the result is in the realm of possibility when you take into account the error derived from the three different velocity readings. The graph below also shows that for the first four points, momentum was conserved. This is a graph of velocity. We can show that momentum was conserved through a graph of velocity by breaking down the equation of momentum:

Momentum = (mass1 * velocity1) + (mass2 * velocity2) iff mass1=mass2 then velocity1= -velocity2

The first four points of this graph are mirror images of each other. However, the points after point 4 are not because unequal mass was introduced by the addition of weights.

### TABLE 1

 runs V1 error V2 error momentum exp Momentum calc energy after energy before avg 1-3 0.57 0.03 -0.58 0.01 -0.006 0 0.2 0 avg 4-6 0.37 0.03 -0.39 0.01 -0.02 0 0.04 0 avg 8 10 11 0.15 0.03 -0.16 0.02 -0.009 0 0.03 0 avg 12-14 0.33 0.04 -0.65 0.03 0.002 0 0.16 0 avg 15-17 0.64 0.05 -0.34 0.02 -0.02 0 0.16 0 avg 18-20 0.22 0.01 -0.72 0.02 -0.03 0 0.17 0 avg 22-24 0.65 0.01 -0.23 0.02 -0.02 0 0.15 0

In Table 1, one can see that the energy of the average of runs 1-3 is bigger than the energy of the average of runs 4-6, which, in turn, is bigger than the average of runs 8, 10, 11. This is because in runs 1, 2, and 3, the spring was fully compressed giving these runs the most energy released. Runs 4-6 had moderate spring compression since it was set to the middle setting. Runs 8, 10, 11 had the least compression possible given the spring design. We were also able to prove that mass had no bearing on the amount of energy released. This can be proved by comparing the energy released of the average of 15, 16, and 17 and the energy released of the average of 22-24. If one looks at these two numbers in Table 1, there is no significant difference in the amount of energy released. However, in runs 15-17, we had one mass block on one cart, and in runs 22-24 we had two mass blocks on the same cart. The compression settings were the same.

Conclusion

In this lab, we learned that explosions similar to those we performed and rocket propulsions conserve momentum and release energy. The higher the compression of the spring, the more energy released. Mass has no effect on the amount of energy released, nor does it have an effect on the conservation of momentum.

Remarks

This lab was fun, but maybe you should try using actual rockets out on the quad. Video analysis perhaps?