Projectile Motion lab 4 PDF

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lab report for projectile motion...

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Doyle 1 Projectile Motion: Launching a Ball Purpose: The purpose of this lab experiment was to observe an object moving in a projectile pathway, and analyze this motion through measurements taken and found. Introduction: The objective of this lab experiment was to visualize a ball launched in a projectile pathway. For this experiment, projectile motion involved a ball that rose after being launched at an angle, reached its peak, and then fell with a similar motion symmetrical to its upward motion. Then the lab showed the comparison between two sets of data—data recorded from the actual experiment (Part I) and data recorded from the movie graphed on the LoggerPro software (Part II). Equipment: Tape measure Launcher Ball Stop watch Video recorder LoggerPro Graphing Software Experimental Procedure: 1. The tape measure was spread out and taped down across the hallway. 2. The launcher was set up at one end and its angle was set to 55o. 3. The ball was placed into the launcher and plunged in. 4. The video recorder began the video. 5. The launcher was released and the ball flew across the hallway. 6. Three separate times were recorded from a stop watch. 7. The distance traveled was measured where the ball landed. 8. The video was uploaded the LoggerPro software. 9. The data sets were found and analyzed. Data: Data from experiment: Angle: 55o Distance traveled: 7.7 m Average time: 1.52 seconds Initial Velocity: 5.06 m/s , 506 cm/s Vox = dx/t Vox = 7.7 m / 1.52 s Vox = 5.06 m/s Vox = 5.06 m/s x 100 cm = 506 cm/s

Doyle 2

Initial Velocity from video Vox = 701.5 cm/s , 7.015 m/s Voy = 1029 cm/s , 10.29 m/s Percent Difference = Difference/Average 7.015 m/s – 5.06 m/s / [(7.015+5.06) / 2] 1.955 / 6.0375 = .32 .32 x 100 = 32% Angle measured from experiment: 55o Launch Angle from movie data: 55.7o Tan -1 (1029 / 701.5) = 55.7 Percent Difference: 55.7-55 / [(55.7 + 55) / 2] = .0126 = 1.26 % Time of flight: 1.52 s Range: 7.7 m Maximum height: 4.99 m Launch velocity: 12.45 m/s Maximum height: t total = 1.52 s t peak = .76 s y = voyt – 4.9 m/s2 t2 y = 10.29 x .76 – 4.9 x .762 y = 4.99 m Launch velocity: a2 + b2 = c2 7.0152 + 10.292 = c2 155.09 = c2 12.45 = c 12.45 m/s Analysis: After recording the data from the lab experiment and finding the data from the movie, the data sets were compared. The time and the range of the projectile motion did not change since they could only be found from recording them from Part I, actual experiment. The initial velocity from Part I was determined by dividing the recorded distance traveled by the time recorded. This velocity was in the x or horizontal direction. The initial velocity from the data from Part II, the movie, was found by marking points on the software to find the slope of the

Doyle 3 line. Since the movie was in the opposite direction, the negative sign was ignored. The data was then compared and the percent error was found. The percent difference shows that the ignored air resistance could have affected the data. Not marking the ball in the exact spots it moved on the software could have affected the percent difference as well. The percent difference for the launch angle was small but could have been from not measuring the angle in person precisely. The launch angle accounts for how high the ball rose to its maximum height. Since a trajectory has a symmetrical upward and downward motion, the time it takes to reach its peak is half the time it takes to complete the full motion. The time it took to reach its peak was .76 s. This is also when the ball reached its maximum height and the velocity was zero for an instant. Initial velocity in the x direction is the initial speed the ball had in the horizontal direction. Initial velocity in the y direction is the initial speed the ball had in the vertical direction. Both of these velocities are treated separately and then combined to find the launch velocity which the is hypotenuse of the motion. Acceleration in the y direction was accounted for because gravity was always acting on the ball. There was not acceleration in the x direction because air resistance was ignored for this experiment. Graphs: Graph I was produced from the LoggerPro software. The slope of the lines are the initial velocities. Graph II shows position and velocity graphs for the x- and y- direction. For the x direction, the position graph had a straight, diagonal line with a positive slope since the ball was moving away from the starting point. It had a constant velocity because air resistance was ignored. In the y direction, gravity is acting on the ball so the velocity graph has a negative slope. Since gravity is acting on the ball as it moves, it slows down in the positive direction until it reaches the maximum height where the velocity is zero and then it speeds back up as it is falling down in the negative direction. In the first half of position graph in the y direction shows that the ball reaches a higher and higher height until it reaches the maximum height and then speeds up in the negative direction until it reaches the ground. Error Sources: One error source from this experiment was not marking the distance traveled exactly for Part I’s data set. It was difficult to see exactly where the ball landed which could have affected the results. Next time, the ball could have been coated in a paint to see the mark where it landed. Another error source could have been not marking the ball moving in the movie on the LoggerPro software exactly to find the slope of the line. The percent difference in the velocities completely affected the maximum height. The maximum height found through the equations using initial velocity in the vertical direction was too high for the experiment. It would have hit the ceiling if I actually went this high. Another source of error was not accounting for air resistance when calculating the velocities. This could have affected the percent difference between the velocities calculated. Conclusion: Initial velocity in the horizontal and vertical direction are treated separately in order to understand projectile motion. Velocity in the horizontal direction does not involve acceleration and it is zero because air resistance is ignored. Velocity in the vertical direction involves

Doyle 4 acceleration because gravity is always acting on the ball. Since the ball produced a symmetrical motion, half the time it traveled was at its maximum height where velocity was zero for an instant. Overall, projectile motion shows how a moving object involves both horizontal and vertical velocities to understand its movement....