Daniel Guzman
Physics 4A.
Ballistic Pendulum Lab
The purpose of this lab was to determine the firing or initial speed of a steel ball from a spring loaded cannon.
Theory Introduction: In this lab we were trying to determine the firing speed of a ball from a spring loaded gun or cannon, due that we do not have an apparatus or equipment that measured the speed of the firing gun, we had to use a different approach to determine the initial speed of the sphere. In this case we used two important concepts: the conservation of mechanical energy and the conservation of momentum in an inelastic collision. Using these two concepts one is able to determine the speed at which the ball was fired. The approach here is to determine the final speed of the system using the conservation of mechanical energy, because if the final speed of the system is known one can use the conservation of momentum to determine the speed at which the sphere was fired.
For the second case the approach is different due that the bullet in this case is going to be fired but it is not going to collide with anything; therefore, we treated just like a projectile. Therefore, to determine the initial speed of the bullet we only had to know a couple things: the distance in the x direction that the bullet traveled, and the height at which the bullet was fired, having these two measurements one can determine the initial speed of the bullet.
Description of the apparatus: The apparatus for this experiment was quite simple due that it only consisted of a ballistic pendulum, which is composed of a small cannon, a small steel ball, a pendulum and a protractor
that measures the angle at which the pendulum moves. The cannon in this apparatus is used to fire the steel sphere,which gets embedded in the pendulum. Once the sphere gets embedded in the pendulum, the pendulum rises, which makes a lever in the protractor move to a certain angle, depending on how fast the steel sphere was fired.
Experimental Procedure: The experimental procedure was quite simple due that it did not require of putting the apparatus together, which made it quite simple. The first thing done in the lab was to verify if the firing ball would get embedded in the pendulum once it was fired, if the ball would get embedded immediately no adjustments had to be done and one could start making recording the measurements of the angles at which the pendulum would be displaced. In our case the sphere did not get embedded in the pendulum so we had to adjust it by using the two knobs that are right behind the cannon. Once the cannon is adjusted and the ball gets embedded in the pendulum, one can start recording the different measurements of the angles. Once all the measurements of the angles are recorded one can proceed and measure the length of the strings of the pendulum, the mass of the block and the mass of the sphere, which are important measurements because they are going to be used to determine the initial speed or firing speed of the sphere. Once all the measurements are taken one can proceed and determine the initial speed of the bullet by using the approach described before in the theory introduction.
For The second part of the experiment the measurements are much easier, in these part the only two measurements made were the horizontal distance that the bullet traveled and the height above the ground where the cannon was placed. To measure the horizontal distance that the bullet travels we used a carbon paper that was taped to a blank piece of paper, so every time the bullet would hit the carbon paper it will make a mark on the withe paper, for this part of the experiment we measured a total of 5 horizontal distances, to then take the average that will be used in the projectile motion equations to determine the initial velocity of the bullet.
The data collected in the first experiment was the angle at which the pendulum moved and the final height of the pendulum after the inelastic collision.
The data collected for the second part of the experiment was the horizontal distance that the sphere traveled, the height above the ground and the distance from the table at which the canon was placed.
Table of Calculated Results
Calculated Results part 1
The calculated results for part 1 were made using two important concepts : the conservation of mechanical energy and the conservation of momentum. The calculations made were based on the data collected
Calculated Results part # 2
The calculations made in part two were made using the projectile motion equations, and were based on the data collected
Propagated Uncertainty Calculations
Conclusions
In this experiment the firing speed of the bullet was calculated using two different approaches, one was using a ballistic pendulum. In this approach two important concepts were used to calculate the initial speed of the bullet, one was using the conservation of mechanical energy and the other one was the conservation of momentum. After using these two important concepts the speed found was 4.187 m/sec. In the second part of the experiment a different approach was used in this part we used the the projectile motion equation to found the initial speed of the bullet, we were able to determine the initial speed of the bullet by measuring different distances and taking the average of them, from these distances and some other data collected we found the time it will take the ball to hit the ground, and there we determine the initial speed of the bullet which came out to be 4.98 m/sec, which is slightly higher than the speed found in the first part of the experiment. The propagated uncertainty found for the initial speed or firing speed for the first part was much smaller than in the second part of the experiment. The propagated uncertainty for the first part was = +- 5.76 , while in the second part was +- 8.9, which lets one infer that the first part of the experiment was carried out much better than the second part of the experiment. There are different sources of error for this experiment, which might be; making wrong or not precise measurements, another source of error that could have affected the results can be a miss calculation, which would affect other calculations and increase the error in the calculated results.
No comments:
Post a Comment