Lab Partners: Max McCandles and Vincent Mele
Date of Completion: 03-24-14
Date of Completion: 03-24-14
Purpose
The investigation of relations between values in a perfectly inelastic collision where energy is conserved.
Theory
The Principle of Conservation of momentum (which states that the momentum of the objects before they collide will be equal to the momentum of the objects after they collide), and the Law of Conservation of Energy (which states that the Kinetic Energy at the moment of collision will be equal to the Potential Energy at the top of the pendulum's swing), along with the formula for cosine, allow for an equation to be derived that solves for the initial velocity of the projectile. The potential energy of a system is equal to 'mass x height x gravity'. The kinetic energy of a system is equal to '.5 x mass x velocity^2'. The formula for cosine is that 'cos(theta) = adj/hyp'. In our case, the variable standing for h will be equal to the value of L minus h2
When the equations are rearranged as seen above, they can be combined and put into the energy equation to solve for the initial velocity of the projectile.
Experimental Technique
1. Build a pendulum by bolting a threaded rod to a plastic box and adding weight to make the center of balance near the center of the box. The center of mass should be carefully marked. One can test this by balancing the apparatus on a pencil.
2. Create a foam insert that can catch the metal sphere projectile
3. Mass the metal sphere projectile and the pendulum apparatus, as well as both of them combined
4. Bolt the apparatus to the Rotary Motion Sensor
5. Set up the Data Studio to measure the angle of the apparatus when the projectile is fired
6. Fire the projectile at the first second and third click and record results
7. Set up photogates to record the actual velocity, compare results to calculated results
2. Create a foam insert that can catch the metal sphere projectile
3. Mass the metal sphere projectile and the pendulum apparatus, as well as both of them combined
4. Bolt the apparatus to the Rotary Motion Sensor
5. Set up the Data Studio to measure the angle of the apparatus when the projectile is fired
6. Fire the projectile at the first second and third click and record results
7. Set up photogates to record the actual velocity, compare results to calculated results
Data
Analysis
The calculated values very closely matched the measured values for the velocity. The derived equation was used and each time the angle was the only part that varied. These results were then taken and the percent difference was found.
Conclusion
The Law of Conservation of Energy and the principle of conservation of momentum combined with trig functions could indeed be combined in a way that allowed the system to solve for the muzzle velocity of the projectile. The results of testing these predicted velocities with photo gates for accuracy showed that there was very little error between the two measurements. The only one that had a relatively larger error was the first setting and this was likely due to the fact that the angular sensor could not be very precise when dealing with such a small change. One challenge to overcome was the vibration caused in the plastic box when the projectile was fired. This was tweaked by re-measuring the center of balance of the box and making a foam catching mechanism that would stop the projectile in a consistent manner. Some sources of error would be imperfect measuring tools, inconsistency with the shot (firing straight, catching consistently, etc.), and the error encountered when rearranging equations several times. All in all, this lab yielded very successful results, and it helps to confirm the idea that the muzzle velocity of a projectile can be figured out by using the angle that is created when the shot is fired.
References
Momentum Conservation Principle. The Physics Classroom.com. Retrieved on April 1st, 2014, from http://www.physicsclassroom.com/class/momentum/u4l2b.cfm.
Momentum and its Conservation. The Physics Classroom.com. Retrieved on April 1st, 2014, from http://www.physicsclassroom.com/class/momentum
Momentum and its Conservation. The Physics Classroom.com. Retrieved on April 1st, 2014, from http://www.physicsclassroom.com/class/momentum