Lab Experiment 3 PDF

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physics lab about projectile motion ...

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Projectile Motion Physics 12 Experiment 3 Lab Report Fall 2020 Purpose/Goal: The purpose of this experiment is to use a projectile simulation program to become familiar with characteristics of a projectile. The range and initial height of the projectile will be measured, initial velocities will be calculated from specific heights and ranges, and the range of a projectile will be predicted using projectile motion equations. Finally, a graph will be created to show the relationship between the height and range of a launched projectile. Procedure A: 1) Determine how long the projectile is in the air (with error) using Min/Max and the other equations provided in this lab. 2) Determine the initial velocity (with error) using Min/Max and other equations provided in the lab. 3) Adjust the initial velocity of the projectile so that it lands in the bullseye at 21.1m and record this value in your lab report. 4) Calculate the percent difference between the experimental and theoretical value for vo if the theoretical value isn’t within the range of the experimental value with probable error. 5) Determine the time it takes for the projectile to land at the bull’s eye when launched at a height of 3 meters. 6) Calculate the percent difference between the experimental and theoretical value for the time if the theoretical value isn’t within the range of the experimental value with probable error.

Procedure B: 1) Set the launcher angle at 30°, set the height at 3 m, set the velocity to the value determined in part A, launch the projectile, and measure its horizontal displacement. 2) Launch the projectile again with the same exact settings and determine how long the projectile is in the air. 3) Write an equation for vx,o and vy,o in terms of vo and the angle it makes with the horizontal angle. 4) Substitute the previous expressions into the projectile equations for horizontal and vertical displacement to obtain equations for x and y. 5) Using the vo , calculate the theoretical value of t (the time the projectile is in the air). 6) Calculate x using the calculated value of t. 7) Calculate the percent difference between the experimental value and the calculated value from step 6. 8) Discuss and explain any discrepancies in your results. Procedure C: 1) Create a table in excel with one column labeled x (meters) and the other labeled y (meters) 2) Set the cannon in the simulation to launch with an initial speed of 15 m/s 3) Set the height at 1m, launch the projectile, determine the horizontal range of the projectile, and record these values in the Excel 4) Repeat the launch while increasing the height by 1m each time until you reach 15m; record these values in the Excel 5) Create a graph of y vs. x for this projectile launched at a speed of 15 m/s 6) Describe the relationship between the height and range of the projectile Part A Calculations and Results: Projectile Flight Time (With Error): ∆y = vy,o(t) - ½(g)(t2) yf – yo = 0 - ½(9.81)(t2) 0 – 3 = -4.905(t2) 0.782 sec = tavg

tmin = -2.95 = - ½(9.81)(t2) = 0.776 sec tmax = -3.05 = - ½(9.81)(t2) = 0.789 sec

terror = (tmax - tmin) / 2 = 0.0065 t = tavg +/- terror = (0.78 sec +/- 0.007) sec

Initial Velocity (With Error): ∆x = vot + ½(a)(t2) xf – xo = vo(0.782) + ½(9.81)(0.7822) 21.1 – 0 = vo(0.782) + 2.9995 vo,avg = 23.15 m/s vmax = 21.15 = vo(0.782) + ½(9.81)(0.7822) = 23.21 m/s vmin = 21.05 = vo(0.782) + ½(9.81)(0.7822) = 23.08 m/s verror = (vmax - vmin) / 2 = 0.13 v = vavg +/- verror = (23.15 +/- 0.13) m/s

% difference = | 23.15 – 26 | / [(23.15 + 26)/2] = 11.6%

Part B Calculations and Results: Here you need to show all calculations and simulation results as asked for in the lab procedure. This includes calculations of flight time and horizontal range.

The observed horizontal displacement of the projectile is +64.49 m. The observed flight time of the projectile is 2.86 sec.

Theoretical Value of “t”: ∆y = 26sin(30°)(t) – ½(9.81)(t2) 0 – 3 = -4.905t2 + 13t t = 2.8639

Calculation of “x”: x = vx,o(t) x = 26cos(30°)(2.8639) = +64.485 m % difference: | 64.49 – 64.485 | / [(64.49 + 64.485)/2] = 0.007 % difference

Part C Calculations and Results:

Questions part A: 3) The initial velocity necessary for the projectile to be launched directly into the bullseye is 26 m/s. 4) !The!simulated!result!doesn’t!fall!in!the!range!of!my!calculated!value!for!vo.!! 5) The flight time of the projectile at a height of 3 meters to land at the bullseye 21.1 meters away is 0.78 sec. ! 6) The!simulated!value!does!fall!in!the!range!of!my!calculated!value!for!t.!!

Questions part B: 3-4) vx,o = 26cos(30°) ∆x = 26cos(30°) ∆y = 26sin(30°)(t) – ½(9.81)(t2) 6)!My!calculated/experimental!values!for!both!flight!time!and!displacement!of!the! projectile!are!almost!exactly!the!same.!This!goes!to!show!that!my!calculations!were! accurate!and!my!lab!proceeded!successfully.!!

Conclusion: My calculated values for initial velocity, time, and range are 23.15 m/s, 2.86 seconds, and 64.49 m, respectively. The percent differences I found for the initial velocity and displacement were 11.6% and 0.007%, respectively. I didn’t need to calculate the percent difference for the flight time because the theoretical value was within the range of the experimental value with probable error. With regards to almost every single calculated value of this lab, they almost exactly matched up to the theoretical values which signifies that my laboratory objectives were met very thoroughly, and my lab was completed successfully. With regards to the 11.6% difference for the initial velocity, I’m not entirely sure why it deviates from the theoretical value but I know it’s not a calculation error. The percent difference is relatively small, although not ideal, and isn’t a cause to reevaluate the entire experiment. According to the projectile range versus height graph, the relationship between these 2 values appears to be a slightly sloped parabola. There is obviously a strong correlation between the range and height of a projectile, where the range increases with increasing height but the range is increasing by smaller amounts as the height gets larger. Error Analysis: The main source of error in this experiment would be systematic error, which would be introduced by me and the projectile simulation program as I measure the distance between where the projectile landed and the cannon from which it was launched. The tape measurer on this program introduces similar error to measuring these same values by hand. The tape measurer is placed at the origin and I am to measure the projectile’s range, and it is up to me to put the end of the tape exactly where the projectile landed, which may not always be accurate. Also, this program introduces its own error because online programs are often susceptible to bugs which skew the measurements, although it is rare. If I measured the projectile’s range to be larger than it actually is, the calculations for flight time and velocity would both be larger than the actual values. The opposite is true if I measured the range to be smaller than it actually is....