lab 3

Lab 3: Projectile Motion Analysis Clayton McCall 22 September 2023 PHY 211 – C01

OBJECTIVE: Create an experiment where you use an object, time, and the objects motion through time. Create a representation of how the object is moving through time, how fast the object is going, and the distance it travels. Use this experiment to understand how physics works in the real world and how you can use it to understand the world better. Data collection: for my first data collection I used a ball and threw it straight in the air at a starting point of about 29 inches high. I did 5 separate trials and inputted the data that I received in an excel sheet.

Trial Maximum Height Maximum Flight time Range Range (meters) Height (secs) (Inches) (meters) 1 15" 0.381 0.46 41" 1.0414 2 16" 0.4064 0.5 39" 0.9906 3 15" 0.381 0.44 40" 1.016 4 14.5" 0.3683 0.46 33" 0.8382 5 15" 0.381 0.47 32" 0.8128 The graph above shows the data I received in the video on an excel sheet. With the video I collected the max height, distance the ball traveled horizontally and the time it took for the ball to travel. To find the height I paused the video and looked at the distance it traveled vertically. To find the distance it traveled horizontally I looked at where the ball stared and where it ended up in the end and subtracted the two. With the data received from my first collection where I threw the ball straight up in the air, I can find the velocity of the ball in two separate ways. The first formula I can use to find an estimate of the velocity is v=gt/2. The second formula I can use to find an estimate of the velocity is v=√2gh. With the value of the two separate estimates of velocity I can find the average of the two, the difference of the two, and once I have found both I can also find the % difference. Trial H (m) Time (s) from Table 1 ( m/s) (m/s) Average of Difference of % Difference from Table 1 (1 st ) (2 nd ) (from previ- ous two col- umns) (from previ- ous two col- umns) ( m/s) (m/s) 1 0.787 0.83 4.067 3.927 3.997 0.14 3.5 2 1.0033 0.94 4.606 4.434 4.52 0.172 3.81 3 0.9144 0.89 4.361 4.233 4.297 0.128 3.02 4 0.8128 0.81 3.969 3.991 3.98 0.022 0.55 5 1.1176 0.98 4.802 4.68 4.741 0.122 2.57 With the formulas that I have learned to find the estimate of velocity I have plugged in my

answers to my excel sheet. V=(.83(9.8))/2 v=4.067 is the first estimate of the first value while v=√2(9.8)(.787) v=3.927 is the second estimate of the same trial. With the average and the difference of the two velocities I can use the formula difference *100/ average =% difference. (.14(100))/3.997=3.5%. I did the same process with each of the trial values and plugged in my answers to the excel sheet. With the data found from my second set of trials where I threw the ball at an arc, I can find the degree of the angle by first finding a certain ratio of 4h/r then finding the inverse tangent. From finding the angle I can also find the velocity of the ball with the formula v=(gt/2)*1/sin ϑ Trial Height Flight time Range (meters) (s) (m) (dimension- less) (deg) (m/s) 1 0.381 0.46 1.0414 1.4634 55.6536 2.73 2 0.4064 0.5 0.9906 1.641 58.6425 2.8691 3 0.381 0.44 1.016 1.5 56.3099 2.5912 4 0.3683 0.46 0.8382 1.7576 60.362 2.5933 5 0.381 0.47 0.8128 1.875 61.9275 2.6101 The data above shows what I found when using both formulas. In the dimensionless ratio In the first trial, I did 4(.381)/1.0414=1.4634. Once I have found the ratio all I need to do is find the inverse tangent of the ratio to find the angle that the ball was thrown in tan^-1(1.4634)=55.6536 degrees. Now that I have found the angle that the ball is thrown in, I can also find the velocity that the ball is going during its flight. Using the formula v=(9.8(.46)/2)*(1/sin( ϑ )) you get v=2.73. I did the same thing with each of the other trials and plugged it into the data sheet above. With both sets of data I received from throwing the ball straight up in the air and at an arc I can find an estimate of gravity of both of each trial. The formula g=8h/t^2 shows an estimate of the force of gravity that is put on a certain object with its max height and flight time. In this case we are finding the estimate of the force of gravity that is put on an object when it is thrown straight in the air and when it is thrown in an arc.

harder to read on the video compared to the tape measure that showed the height. 2. Is your vertical Projectile data consistent with the expected trend that the longer flight times result in the largest height? In all my data pieces except for one this assumption is correct. I believe this is the case because the one data piece must have had more of an arc than height than the other trials. 3. How do your two estimates of the initial speed compare with each other? What might ac- count for any differences? It seems as if in my data that the second estimates of the velocity are larger than the first estimates. I believe this is true because without the time of flight the estimate is as if the ball is dropped out of the air at the height and its relationship with gravity shows its speed which would constitute the speed being higher. 4. Was your estimate of the launch angle reasonable? Yes, I feel that the estimate that I found was accurate to what it looked like I was throwing the ball in in the video. If you look at the video, you can see that I throw the ball a little steeper than a 45-degree angle which is accurate to my estimates. 5. Discuss your two estimates for the gravitational constant. What might account for these errors? I feel that the errors that have appeared may have happened when I added the horizontal aspect of gravities force. When I threw the ball straight up the ball is almost never at a consistent height while when I throw the ball at an arc there is an aspect where the ball might be closer to having the same height in a decent interval. This makes me believe that the force of gravity is being used more on the ball that is thrown straight up while the ball that is thrown in an arc the force of my hand throwing it is more evident. Summary of error: I feel that throughout the lab my error has been less than how I believed it would be up until the last data set which was the estimation of gravity. The lowest percent difference in my estimation for gravity was 33% which is a very high percent difference. I believe that this error was not because of an error in my calculations although it is an error. I believe that this an error in the comparison of these two separate situations which are very different in physics even though it doesn’t seem like it if you were doing it normally without looking for the error. Results and interpretation: The point of doing this lab was to understand how values and data can be found of an object that is in motion with enough information. With the information that I used in my experiment I was able to find many things. I was able to find the speed of the ball in multiple different situations, the height of the ball in different trials, the distance the ball was thrown, an estimation of what the angle that the ball was thrown in was, an estimation of what the force of gravity that was put on the ball in different situation was, and what the percent difference error of each of my

calculations was. I feel like this lab has helped me better understand the world and the physics of the world which will help me in the future. Conclusion: Overall, I really enjoyed doing this lab the experiment was fun and I enjoyed learning how to find estimations for gravity and angles of how an object is being thrown. I also really enjoyed using excel and learning more on how I can use it in the future. This lab has really helped me better understand the force of gravity and how it can relate to objects in the air. Understanding the errors that are in this lab helps me understand the comparisons between an object being thrown in a horizontal direction and an object that is thrown in a vertical direction and how the forces of gravity can be different on them. I really enjoyed this lab and I hope to learn more in the future in these labs. Cutnell and Johnson. Physics , 9 th ed. 2012