lab report

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University of Mississippi *

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PHYS 223

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Physics

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Apr 3, 2024

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Uploaded by ProfessorField9095

Bernardino, Rene TA: Projectile Motion March 4 2024 Introduction This experiment involves launching a steel ball from a horizontal cannon and then repeating the launch with the cannon at an inclined angle. The objective is to predict the landing point of the ball from the launch point, considering the influence of gravity. Kinematic equations are employed to determine the missing values and forecast the ball's trajectory. To predict the landing point accurately, the experiment involves averaging the values obtained from six horizontal launches to determine the initial horizontal velocity (Vox) and horizontal displacement (Xtheo). This Vox value is then used to calculate the predicted horizontal velocity for the inclined launch. The actual horizontal displacement is determined by averaging the results from six inclined launches. Comparing the predicted horizontal displacement (Xtheo) based on the calculated initial horizontal velocity to the actual horizontal displacement from the inclined launches shows a close similarity between the predicted and actual values. This demonstrates the effectiveness of kinematic equations in predicting projectile motion. Results

Inclined Launch Prediction Inclined Launch Prediction Uncertainty Inclined Launch X Measurement X Standard Deviation % Difference Between X theo and X Xtheo= 3.15 Stheo= ± .05 Xincl= 3.34 Ox= .00534 % Diff= 9.5% Prior to conducting experiments with an inclined spring, it is essential to perform experimental trials with a horizontal spring. This allows for the determination of the relationship between velocity, gravitational acceleration, and the distance traveled. Understanding this relationship at a horizontal level provides valuable insights that can be applied to predict the distance traveled when the spring is at an angled position. The predicted launch result (Xtheo) was 3.15 meters, while the actual launch measurement (Xincl) was 3.34 meters. The uncertainty associated with this experiment was 0.05 meters due to the measurements not being analog with a 9.5% difference between the prediction and actual launch measurements. Discussions The results of this experiment showed that the steel ball traveled 2.53 meters when launched horizontally and 3.34 meters when launched at a 30-degree angle. Despite the gravitational pull toward the Earth remaining a constant value of -9.8 m/s², the distance traveled by the ball varied depending on the launch angle.

The objective of accurately predicting the landing point of the ball when launched at a 30-degree angle compared to when launched horizontally was successfully achieved using the provided equations. However, throughout the experiment, there were potential sources of human error. These may include measurement inaccuracies or slight adjustments in the cannon's angle during launch, which could affect the trajectory of the ball. Post Lab Questions 1) Discuss how your data and results would be affected if an aluminum ball were used instead of the steel ball. (Assume that the aluminum ball has half the mass of the steel ball that you actually used. Ignore air-resistance.) Using an aluminum ball instead of a steel ball would likely result in the ball being launched to a greater distance. This is because aluminum has a lower mass compared to steel, which means it would experience less gravitational force pulling it toward the Earth. As a result, the aluminum ball would be able to travel a greater distance once leaving the cannon. 2) What was the magnitude and direction of the steel ball’s acceleration at the instant that it became a projectile? Answer the same question about when the ball is at the vertical peak of its trajectory and when the ball is infinitesimally close to striking the ground. (Ignore air-resistance.) As the ball becomes a projectile, reaches its vertical peak, and approaches the ground, it experiences a constant acceleration. This acceleration has a positive magnitude because the ball is moving forward through the air. However, the direction of this acceleration is always negative because gravity continually pulls the ball downward toward the Earth.

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3) If we were able to “improve” these spring-guns with much stiffer springs so that horizontally fired steel balls traveled in the 𝑥 -dimension 10 times farther than they currently do, by what factor would that increase or decrease the time-of-flight? (Ignore air-resistance.) If the springs were stiffer and it caused the steel balls to travel farther, it would result in a larger displacement (x). Consequently, this would lead to a longer time-of-flight for the ball. When the ball travels a greater distance, it spends more time in the air to reach that distance. However, it's important to note that while the displacement increases, the acceleration remains constant, so it does not affect the overall factors of the motion.

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