Projectile Motion PHYS_111 (3)

PROJECTILE MOTION: AN EXPLORATION WITH RAMPS AND BALLS

Author(s)/Collaborators -Everett Beck, Tyler Brumbles, Matthew Bryant, Amanda Carrizo, Ivana Fernandez Rosas, Jack Franco Date 3/22/2023 Keywords Newton’s Laws, Oscillation, Pendulum, Kinetic Energy, Potential Energy, Time, Experimentation, Excel Institution Physics 111L, Department of Physics, University of Idaho, Moscow, 8384 Introduction In this lab we will expand our explorations on projectile motion. We will be measuring the distance traveled by the projectile in the horizontal direction. We will then translate that data to predict the maximum travel distance of a projectile with that specific volume and potential energy. We will be using 3 different balls as projectiles, a ramp as our ‘gun’ and a measuring stick to… well… measure the travel distance. By calculating the potential energy of an object, we can directly predict where it will end up, being one of if not the main learning goals of this experiment. Hypothesis  With the goal of the lab being understanding projectile motion, we believe that a projectile’s motion directly depends on the kinetic and potential energy it has before it is released.  The projectile’s horizontal distance depends on the potential energy of the projectile’s height and density, because of this a lighter projectile will travel further. Procedure This experiment utilized the calculations of a ball's velocity overtime, the Hight at which it falls and the location of the impact of the ball as a key topic. We measured the effects of different variables, such as angle, weight, and Hight, to analyze the effects they had over time to the point that it hits the ground. This was tested three times with changing verbal's every trial. The results of these observations were then recorded and analyzed in the report below. Materials Used : • Graduated Ramp (sloped at 45 o ) • Meter (or three-meter) Stick • 3 × Balls: Plastic, Wood & Metal • Carbon Paper • White Paper Formulas  calculation of potential energy PE = mgh  calculation of kinetic energy KE = 1 2 m v 2  conversion of potential energy to kinetic energy PE = KE mgh = 1 2 m v 2  initial launch velocity v = √ 2 gh  Calculation of initial velocity over a horizonal direction v ax = √ 2 gh  Maximum horizontal distance ∆ x = v ax t + 1 2 a x t Page | 3

Plastic Ball 40 79 28 28 31 29 Trial 1 31.5 79 26.4 29 29.5 28.3 Trial 2 25 79 22.6 25.5 29.5 25.86666667 Trial 3 29 28.3 25.87 Average Δx 27.085 Percent error 263.66% Calculations were performed using the equations above as indicated and are as follows: Wooden Ball h (±0.1cm) Δ y (±0.1cm) x 1 ( ± 0.1 cm x 2 ( ± 0.1 cm x 3 ( ± 0.1 cm Δ x (±0.1cm) Trial # 40 79 46 47.5 48.8 47.43 Trial 1 31.5 79 43 40.5 45.25 42.91 Trial 2 25 79 33.6 34.5 36 34.7 Trial 3 47.4 42.9 34.7 Average Δx 41.66 Percent error 141.97% Steel Ball h (±0.1cm) Δ y (±0.1cm) x 1 ( ± 0.1 cm x 2 ( ± 0.1 cm x 3 ( ± 0.1 cm Δ x (±0.1cm) Trial # 40 79 28 28 31 29 Trial 1 31.5 79 3 29 29.5 28.3 Trial 2 25 79 22.6 25.5 29.5 25.86666667 Trial 3 29 28.3 25.87 Average Δx 27.085 Percent error 195.25% Page | 3

Results As you can see from the tables and calculations above, we have a massive percent error. This can be explained though, as we have multiple variables at work that were not included in our calculations. Observation and Discussion 1.) How well do experimental results agree with theoretical predictions and why? Quantify the % error. The results agree with the theoretical predictions as if a ball is denser, and or has a lower starting height, the ball will have a lower travel distance on the horizontal axis. The same goes for the opposite, as lighter balls with a larger height travel much further. The error % seems to be about __% as veritable results were only variable by human error, air resistance, and the ramp not being perfect. 2.) Explain with a physical description how friction and the rolling motion of the ball contribute to this error. (Hint: Refer to a modified version of (9.3), the law of conservation of energy). While the ball is rolling and transferring potential energy to kinetic energy, the ball also loses some of its energy to friction as it glides down the metal surface. In addition to this, some grooves and imperfections in the metallic surface (hidden to the naked eye) cause small imperfections in the projectile’s motion, adding to the way friction messes with the overall experiment. 3.) How could these errors be minimized? Errors can be minimized by conducting the experiment in a controlled environment to reduce the impact of external factors, such as air resistance, and ignoring the friction and other forces that could potentially make a difference in the results. Also running a minimum of three trials per ball and concluding if the results measurements are somehow equivalent and taking the average of the results. 4.) Does the material have an impact on the maximum horizontal distance? Why or why not? (Hint: refer to the previous discussion question on friction and rolling). Yes, the materials can have an impact on the maximum horizontal distance traveled due to its effect on friction and rolling resistance, and as mentioned previously in question 1, we stated that depending on the density of the ball and placement in the vertical axis makes a great difference on the results, this being distance traveled in the horizontal axis. Conclusion After performing three different trials with each ball, we collected enough data to show that we cannot reliably recreate the Δx without more information. We did have consistent data however, and recorded results did not appear to break any expectations or rules. Recommendations Being a worksheet, and relatively straight forward; we couldn’t really come up with much that could improve on this experiment. Some of the measuring was confusing but eventually we got it done, all the objectives required in this lab felt very achievable. Contributors -Introduction  Jack -Hypothesis  Jack Page | 3