Experiment two_ Projectile motion

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University of Illinois, Urbana Champaign *

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102

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Physics

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Apr 3, 2024

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pdf

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Alexis Ortiz A20532815 Experiment two: Projectile motion Part 1: (a) What are the two initial velocities for the first two firing settings (the first two “clicks”)? Make a table consisting of the initial velocities, its components vx and vy, the launch angles, the time of flight, and the horizontal range. (Setting 1) Trials Launch angle ( º) Time of flight (m/s) Range (m) Initial Velocity (m/s) V ix (m/s) V iy (m/s) Trial 1 20 0.400 1.027 3.957 3.718 1.353 Trial 2 20 0.600 1.018 3.940 3.702 1.348 Trial 3 20 0.550 1.019 3.942 3.704 1.348 Average 20 0.517 1.021 3.946 3.708 1.350 The average initial velocity of the ball on setting one is 3.946 meters per second. (Setting 2) Trials Launch angle ( º) Time of flight (m/s) Range (m) Initial Velocity (m/s) V ix (m/s) V iy (m/s) Trial 1 20 0.3 1.186 4.252 3.996 1.454 Trial 2 20 0.3 1.174 4.231 3.976 1.447 Trial 3 20 0.32 1.179 4.240 3.984 1.450 Average 20 0.31 1.180 4.241 3.985 1.450 The average initial velocity of the ball on setting two is 4.241 meters per second. (b) Consider the angle that gave you the longest range. Using the angle and initial velocity calculate the maximum height (ymax) reached at this angle? What is the overall maximum height reached in your experimental data? Which angle gave you the maximum height? (*These results came from Part 2 of the lab due to time constraints resulting in a lack of full data in part 1) (c) Make a graph of launch angle vs. horizontal range for the second experiment. Label the axes appropriately with correct units. (on Setting 1)
Alexis Ortiz A20532815 The overall maximum height reached from this data was 0.201 meters high. An angle of 65 gave the maximum height. An angle of 55 gave the maximum range. ° (d) For the third experiment, how do your measured values of the gravitational acceleration compare to the accepted value of g = 9.8 m/s2 ? What are possible sources of error for this experiment? (* Due to equipment malfunction, Part 3 of this experiment had no data taken.) To find the experimental value of gravitational acceleration, a free fall experiment would be conducted. Acceleration would be calculated using equation 1, with the initial height being the height of the table ( , the time measurement being the time to hit the ground (t), and the 𝑦 𝑖 ) final height being 0 meters ( ). Had the experiment been conducted, the ball would be released 𝑦 ? from rest over a photogate, which will start the measurement of total time. Then, the ball would pass the time of flight sensor on the ground. This time would be used in equation 2 to determine gravity. Possible sources of error that could arise from this experiment include air resistance dragging on the ball, resulting in a higher acceleration than is accurate, or the ball falling at an angle due to it being let go improperly.
Alexis Ortiz A20532815 (e) If the steel ball is shot vertically upward, how long would it take for it to hit the floor below? Calculate for both initial velocities. Assuming the ball starts at 0 meters and ends its trajectory at 0 meters, the time it would take for the ball to hit the floor would be 0.272 seconds for setting one and 0.296 seconds for setting two, based on the equation (equation 1) 𝑦 ? = 𝑦 𝑖 + 𝑣 0 𝑡 + 1 2 𝑎𝑡 2 2. Ideally, what kind of mathematical curve is the projectile motion trajectory? Describe two examples of projectile motion which you have observed or experienced outside of this physics lab that follow this mathematical curve. The mathematical curve of projectile motion trajectory is a parabolic curve. Two examples of parabolic curves are the path of fireworks and the path of a punted football. They both reach a maximum height, then fall to their original position height. 3. Are there two different launch angles that would give you the same range? Are there two different launch angles that would give you the same height? Explain. Yes, two different launch angles can result in the same range if they add up to 90 ° (complementary angles), as range is calculated with two times the sine of . This is due to the smaller angle going faster, thus having less time in the air, and the larger angle going higher, thus having less distance covered. Also, two different launch angles result in the maximum height if they add up to 180°(supplementary angles), as height is calculated with the sine of . This can be shown with their hypotenuses being the same. 4. If the steel ball is shot horizontally off the table, how much time would it take the ball to hit the ground for each of the velocity settings of the launcher? Explain your answer using the equations of motion and your experimental data. How does this relate to the ball being dropped vertically from the table top to the floor below? (equation 2) 𝑡 = 2𝑦 𝑖 ? The time to reach the ground could be calculated by taking the square root of two times the initial height divided by the gravitational acceleration. The time to reach the ground cannot be calculated with the partia data from this experiment, due to a missing measurement of the height of the table.
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