Lab 8 Report

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University of Kentucky *

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Physics

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Jan 9, 2024

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docx

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Lab 8 Report PI: Isaac Madill DA: Luke Katalinic Introduction The goal of this experiment was to calculate the speed of a ball fired out of a projectile launcher using two different methods. One method used involved taking measurements of the final angle of the pendulum, the radius of the pendulum, as well as mass of the ball and pendulum. Using some basic equations to calculate the change in height, gravitational potential energy, and velocity of the pendulum and ball together, the researchers were able to isolate the velocity of the ball. For the other method used, the researchers calculated the velocity of the ball by gathering data from how far the ball was launched in a linear direction from a constant height. A piece of paper towel was used to identify exactly where the ball landed as the ball left an imprint. Both methods yielded sperate velocities respectively. Data Analysis – Method 1 Speaking on the systematic uncertainties of the first method when referring to the center of mass, if a wrong center of mass is picked, then the overall height change will be consistently incorrect. This is due to an incorrect measurement of the radius of the pendulum. This could cause a very large uncertainty if not properly measured. 0 1 2 3 4 5 6 7 0 2 4 6 8 10 12 Velocity V. Trial Ball Velocity Pendulum-Ball Velocity Trial Velocity v pendulum v ball (m/s)
ball (m/s) 0.46924538 5 2.154262903 0.46924538 5 2.154262903 0.46924538 5 2.154262903 0.45467237 1 2.087359522 0.46924538 5 2.154262903 Data Analysis – Method 2 As for the second method, systematic uncertainty can be seen to exist in the measurement of the height of the launch position. To solve the velocity of the second system we set the initial energy equal to the final energy. The initial energy is all potential and the final energy is all kinetic. The initial energy is equal to mass times acceleration due to gravity times the height, or mgh. The final energy is one half times the mass times the velocity squared, or 1/2mv^2. Setting these two equal we get that velocity is equal to the square root of two times the acceleration due to gravity times the height. The way we solved for velocity was using distance traveled over time elapsed and since we know the initial height, we know the time elapsed and can observe the distance traveled we solve for velocity this way. 0 2 4 6 8 10 12 0 2 4 6 8 10 12 Method 1 v Method 2 Velocity Method 1 Method 2 Trial Velocity (m/s) v ball (m/s) 6.443284877 6.513320582 6.548338434 6.583356287 6.600865213
Conclusion As you can see in the graph for method one, the velocity of the ball is significantly greater than the velocity of the pendulum. This is consistent with the idea that momentum is conserved throughout the system. So, the total of the masses times their respective velocities of the initial components of the system must be equal to the total of the new total mass times its resulting velocity. In this graph you can also see that our data is very consistent with itself, and this points to sound experimental design with few uncertainties. This graph points to and agrees with the idea that the velocity of the ball can be found through the ideas of conservation of momentum. In method two the idea was to use the initial potential energy and set it equal to the final kinetic energy and solve for velocity this way but then it made more sense to use the kinematic equations to solve for the time of the projectile and observe the distance traveled and then use displacement over time. This method is also very consistent with itself, but the two methods resulted in different velocities. Both methods use the ideas of conservation of momentum and conservation of energy. Group questions: 1. ) Yes the ball should be inside the pendulum for this measurement because when we are actually observing the momentum of the pendulum the ball is inside of it, so its mass should be considered. 2.) This could significantly impact the measurement of delta H because it moves the center of mass of the pendulum down significantly, which is used directly in the calculation of delta H. 3.) No, a significant amount of energy is lost to things like sound, and friction of the collision which often produces small amounts of heat. 4.) This momentum is also transferred out of our observed system in the form of things like heat and sound that come as a byproduct of friction. Because this is not a perfect ideal collision. 5.) We attempted to measure our height of the ball which determines the initial energy of the ball carefully but the measurement could have resulted in some uncertainty. Another way we attempted to reduce uncertainty was through clamping the launching system down, however we did not do this in method one.
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