Lab Assignment 2: Projectile Motion Instructor’s Overview Projectile motion is a part of our everyday experience. When you strike a baseball or softball, you are creating a projectile motion scenario. Similarly, you yourself are a projectile when you jump into a pool to cool off on a sweltering summer day. In this lab you will get some hands-on experience with projectile motion and apply the two-dimensional kinematic equations that we have developed. You will perform experiments and compare your results to theory. This activity is based on Lab 7 of the eScience Lab kit. Although you should read all of the content in Lab 7, we will be performing a targeted subset of the eScience experiments. Our lab consists of two main components. These components are described in detail in the eScience manual (pages 83-88). Here is a quick overview:  In the first part of the lab, you will launch a marble off of a table or other elevated surface and measuring the horizontal distance that the marble travels. From this distance, you will calculate the launch velocity of the marble. You'll then repeat the experiment using a different launch height and try to predict the new horizontal distance using the velocity that you derived from the first part of the experiment.  In the second part of the lab, you will launch small foam rockets. The first part of this experiment involves measuring the flight time of the rocket and deriving launch speed. In the second part of the experiment, you will explore the dependence of range on launch angle. Note: In the rocket experiment, perform and document steps 1-7. Then launch your rocket at three angles: 30 degrees, 45 degrees, and 60 degrees. Record all of your data in the tables that are provided in this document. Don't use the tables in the eScience manual. Take detailed notes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of your experimental methods and observations. Experiment Tips: Marble on a ramp  Although you are welcome to use the water and corn starch technique outlined in the eScience lab manual, I used a slightly less messy technique. Take a towel and fold it into several layers. Place the towel in the marble landing area and smooth the surface with your hand. When the marble hits the towel, its landing is deadened and you will see a slight impression of where it landed. Measure to this impression to determine the range of the marble.  Make sure that you place your marble at the same position on your ramp. This helps insure the repeatability of launch speed. Rocket experiment  I had the best results when I didn't squeeze the launch bulb excessively. The rocket flies more consistently and travels a manageable distance from a measurement perspective.  Before collecting data, make sure you practice you launch technique. Try to squeeze the launch bulb in a consistent manner to minimize experimental variation.  Launch the rocket close to the ground for your range measurements. Date: Student: Abstract Introduction Material and Methods Results Data table for marble experiment (Procedure 1): 1 Height = 0.15_meters Trial Number Distance (meters) Calculated velocity (m/s) 1.12 meters t=0.478 — V=sqrt(2dg) or 4.685 m/s =sqrt(21.12*9.8) 2 1.13 meters — t=0.480 4.706 m/s=sqrt(2*1.13*9.8) 3 1.14 meters — t=0482 4.726 m/s= sqrt(2*1.14*9.8) 4 1.13 meters — t=0.480 — 4.706 m/s=sqrt(2*1.13*9.8) 5 1.125 meters — t=0.479 —- 4.695 m/s =sqrt(2*1.125*9.8) 6 1.135 meters — t=0.481 — 4.716 m/s =sqrt(2*1.135*9.8) 7 1.115 meters — t=0.477 — 4.674 m/s =sqrt(2*1.15*9.8) 8 1.12 meters t= 0.478 — 4.685 m/s =sqrt(2*1.12*9.8) 9 1.125 meters t=0.479 — 4.695 m/s =sqrt(2*1.125*9.8) 10 Average 1.14 meters t=0.482 — 4.726 m/s= sqrt(2*1.14*9.8) 1.128 meters t=.479 — V= 4.701 m/s =sqrt(2*1.129*9.8) Standard Deviation 0.00856 Data table for marble experiment (Procedure 2): Height = 0.16 meters from the table (0.9_meters from the floor) Trial Number Observed Distance (meters) Predicted Distance (meters) Difference between observed and predicted distances (meters) 1 1.16 meters 2 1.18 meters 3 1.165 meters 4 1.16 meters 5 1.18 meters 6 1.18 meters 7 1.155 meters 8 1.165 meters 9 1.16 meters 10 1.18 meters Average 1.1685 meters Standard Deviation 0.01029 Data table for rocket experiment - vertical launch Trial Number Flight time (sec) Calculated velocity (m/s) 1 2 3 4 5 6 7 8 9 10 Average Standard Deviation Data tables for rocket experiment - angle experiments Angle = 30 degrees Trial Number Predicted range (meters) Measured range (meters) Difference (meters) 1 2 3 4 5 Average Standard Deviation Angle = 45 degrees Trial Number Predicted range (meters) Measured range (meters) Difference (meters) 1 2 3 4 5 Average Standard Deviation Angle = 60 degrees Trial Number Predicted range (meters) Measured range (meters) Difference (meters) 1 2 3 4 5 Average Standard Deviation Analysis and Discussion Marble experiment calculations Show your calculation of the launch velocity of the marble as a function of height and distance travelled (needed for Procedure 1 in the eScience manual): Use your equation above to solve for the range as a function of launch velocity and height (needed for Procedure 2 in the eScience manual): Rocket calculations Show your calculation of the launch velocity of the rocket as a function of flight time. Describe how you came up with your predicted ranges. What relation did you use? Based on your experimental results, please answer the following questions: Marble Experiment  Suppose you altered your existing ramp so that the marbles had twice their initial velocity right before leaving the ramp. How would this change the total distance traveled and the time that the marbles were in the air?  Did your prediction in Procedure 2 come close to the actual spot? Find the percent error of your predicted distance (expected) compared to the actual average distance (observed). What are some sources of error in this experiment? % error = [ (observed value ‐ expected value)]/ expected value X100 Rocket Experiment  Of the three angles that you tested, what angle gave the greatest range? The least?  Draw a FBD for a rocket launched at an arbitrary angle (assume the rocket has just only barely left the launch tube, and neglect air resistance).  What role does air resistance play in affecting your data?  Discuss any additional sources of error, and suggest how these errors might be reduced if you were to redesign the experiment.  How would a kicker on a football team use his knowledge of physics to better his game? List some other examples in sports or other applications where this information would be important or useful. Conclusions References
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