Lab Report Lab 5 Projectile Motion

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Mechanical Engineering

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Apr 3, 2024

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Name: Gandy, Lillian Partner: Parks, Webb TA: Wang, Jack, Section: 3 Name of Experiment Lab 5 -- Projectile Motion Date Experiment was performed 2/26/24 Introduction (10 Points): The objective of this experiment is to measure the parameters of a horizontally launched steel ball, to further our knowledge of projectile motion by predicting the landing point at an inclined angle. The basic principles of these experiments are kinematic equations, projectile motions, and standard deviation. The procedures of this experiment are to first make sure the degrees are at zero for the first part, fire the spring gun and place a piece of white paper under a taped piece of charcoal paper facing down in the observed area. Fire the gun once again and measure the distance and height from the gun. Record this data in your table and calculate for missing values. Repeat this process six times collecting the distances and averaging them to find the average distance. Get the angle used for part two from the TA and angle the gun with these degrees. Find the predicted value of the distance using your data and mark where it should land. Fire the gun five more times after the initial time and record your data. Theoretical Analysis (15 Points): See written for more. Y = Y o + V ot + 1 2 at 2

t = 0 √ − 126 + 0 − 4.9 x = − b± √ b 2 − 4 ac 2 a Data Plots/Charts (10 Points): N/A Results (10 points): Inclined launch prediction (Xtheo) Inclined launch prediction uncertainty Inclined launch x measurement X standard deviation % difference between xtheo and x Xtheo. = 2.26m Δtheo. = 0.5m Xincl = 2.261m σx = 0.006m % diff = 13.2% 1) Why is it necessary to do experimental trials with a horizontal spring gun before being able to make predictions about projections at inclined angles fired? To ensure that the gun is firing at a constant precise rate and location, and to have a bases to plug your values into an equation to find the projections with proven values, to then find predicted values. 2) Make a statement about whether your inclined launch prediction and your inclined launch measurement overlapped given their uncertainties. My inclined launch predictions and measurements do overlap when the theoretical value of 2.58 is negative 0.5 uncertainty and the measured 2.26 value is positive 0.5 uncertainty.

Discussion of Results (30 Points): Increasing the angle also increases the distance. These results meet the objective of the experiment by involving the measurements of a horizontally launched steel ball, furthering knowledge of projectile motion by predicting the landing point at an inclined angle, using kinematic equations, projectile motions, and standard deviation. Some sources of experimental error include incorrect measurement using the meter stick, not pushing the ball back at the same distance in the barrel, or not measuring the impression of the ball on the ground at the same point. One suggestion on a way to improve the experiment is to make sure everyone is measuring the distance of the ball from the centermost position of the charcoal impression. Post-Lab Questions (15 Points): 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.) The balls would both fall at the same acceleration because of gravity so their times would theoretically be the same. The aluminum would go a greater distance because it has a smaller mass than the steel ball. 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.) The magnitude of the steel ball is 9.81 and the direction is downward from the instant it becomes a projectile, and at the peak, to when it is about to strike the ground.

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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.) It would decrease the time of flight because the velocity would be faster therefore it would hit the ground faster based on the velocity-time equation. Raw Data/Sample Calculations (10 Points):