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: Sheena Beierman Abstract The purpose of this lab is to apply what I know about projectile motion and use kinematics to predict how far a projectile will travel. This is performed by launching a marble off of a table or other elevated surface and measuring the horizontal distance that the marble travels. The second part will look at a rocket being launched at different angles and the influence of gravity. I will determine the relationship between the angle at which a projectile was launched and the time of flight of the rocket. Introduction Background: A projectile is an object acted on by gravity alone.  A projectile is any object which, once projected, continues in motion by its own inertia and is influenced only by the downward force of gravity. In this lab, it can be assumed that projectiles are fired either vertically or horizontally.  Objective: The objective of this experiment is to predict the range of a projectile set in motion. Learn how to solve projectile motion problems. Understand that the acceleration due to gravity is constant (9.8 m/s2) and downward toward the center of the Earth. Understand that the horizontal motion and the vertical motion are disconnected. Hypothesis: My hypothesis for the marble experiment is that as the initial height of the marble increases the horizontal distance will also increase. For the rocket launch experiment, my hypothesis is that as the angle of the projectile decreases the time of flight will also decrease.   Material and Methods The materials needed for this lab are provided below: Experiment 1: Ramp Marble Corn starch 4 sheets of black construction paper Tape measure Monofilament line Fishing sinker Paper towel* Water* *You must provide Procedure: 1. Place the ramp on a table and mark the location on at which you will release the marble. This will ensure the marble achieves the same velocity with each trial. 2. Create a plumb line by launching the fishing sinker to the monofilament line. 3. Hold the string to the edge of the ramp, and mark the spot at which the weight touches the ground. Note: The plumb line helps to measure the exact distance from the edge of the ramp to the position where the marble “lands.” 4. Lay down a runway of black construct on paper. 5. Wet the marble all over with water, and drop into the cornstarch bag to coat. Roll on a paper towel to achieve a smooth, even coat of corn starch all over the marble (you do not want any chunks as it will affect the path of motion.) When the marble hits the construction paper, the force will cause some of the corn starch to come off, and leave a mark on the construction paper so you can see the point of first contact! 6. Begin the experiment by releasing the marble at the marked point on the ramp. 7. Measure the distance traveled to the first mark made on the carbon paper using the tape measure. Record this value in Table 1 on the following page. 8. Repeat steps 5-7 nine more times and record your data in Table 1. 9. Next, use your data to calculate the velocity of the marble for each t Experiment 2: 4 Squeeze Rockets™ 1 Squeeze Rocket™ Bulb Protractor Tape measure Stopwatch Procedure: 1. Mark the spot from which the rockets will be launched. 2. Load a Squeeze Rocket™ onto the bulb. Note: The Squeeze Rocket™ is a trademark product name. The “rocket” itself does not use a self-propelled mechanism. ACer a rocket is launched, gravity is the only major force which acts upon the “rocket”. 3. Using a protractor, align the rocket to an angle of 90° (vertical). 4. Squeeze the bulb (you will need to replicate the same pressure for each trial), and simultaneously start the stopwatch upon launch (alternatively, have a partner help you keep time). Measure and record the total time the rocket is in the air. Repeat this step three or more times, and average your results. Record your results in Table 3. tavg=_1.38 sec_ 5. Calculate the initial velocity of the rocket (vinitial = voy) using the kinematics equations. 6. Record your calculation in Table 3. (Hint: you can take the initial height as zero. The vertical velocity is zero at the peak of the flight, when the time is equal to t/2.) 7. Repeat this trial two more times, and record the values in Table 3. 8. Choose four additional angles to fire the rocket from. Before launching the rocket, calculate the expected range using the vertical velocity and the angle from which the rockets will be fired. Remember that you can use zero for any initial positions, and that the acceleration due to gravity, g, is -9.8 m/s2 . Record these values in Table 3. 9. Next, align the rocket with the first angle choice and fire it with the same force you used initially. Try to record launches where the rocket travels in a parabola and does not stall or flutter at the top. Measure the distance traveled with the tape measure. Repeat this for two additional trials, recording the actual range in Table 3. Results Data table for marble experiment (Procedure 1): Height = 0.610 meters Trial Number Distance (meters) Calculated velocity (m/s) 1 0.346 11.46 2 0.325 11.44 3 0.366 11.47 4 0.325 11.44 5 0.305 11.43 6 0.325 11.44 7 0.366 11.47 8 0.366 11.47 9 0.325 11.44 10 0.305 11.43 Average 0.336 11.449 Standard Deviation 0.0240 0.0116 Data table for marble experiment (Procedure 2): Height = 0.814 meters Trial Number Observed Distance (meters) Predicted Distance (meters) Difference between observed and predicted distances (meters) 1 0.432 0.466 -0.034 2 0.753 0.466 0.287 3 0.486 0.466 0.020 4 0.670 0.466 0.204 5 0.455 0.466 -0.011 6 0.714 0.466 0.248 7 0.512 0.466 0.046 8 0.714 0.466 0.248 9 0.455 0.466 -0.011 10 0.670 0.466 0.204 Average 0.586 0.466 0.120 Standard Deviation 0.1284 0.1284 Data table for rocket experiment - vertical launch Trial Number Flight time (sec) Calculated velocity (m/s) 1 1.25 6.13 2 1.32 6.47 3 1.59 7.80 4 1.12 5.49 5 1.28 6.28 6 1.64 8.04 7 1.54 7.55 8 1.22 5.98 9 1.38 6.77 10 1.49 7.31 Average 1.38 6.78 Standard Deviation 0.174 0.854 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? The total distance traveled would double because they had double the horizontal speed. At the same time both marbles would spend about the same amount of time in the air since vertical motion is not affected. ·  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 valueX100 Air resistance could cause a source of error as well as the movement of the marble across the table. If it doesn’t roll perfectly horizontally it will cause error. Rocket Experiment ·  Of the three angles that you tested, what angle gave the greatest range?  The least? The angle that gives the greatest range is the one at 45 degrees. ·  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? Air resistance always plays a role in these types of experiments. Air resistance will affect the rocket’s speed as gravity pulls down. All in all, air resistance will reduce the acceleration of the rocket.  ·  Discuss any additional sources of error, and suggest how these errors might be reduced if you were to redesign the experiment. Inconsistent launch speeds and movement of the rocket during the launch, since these rockets are so testy, could also be a source of error. The perfect experiment would be to use a vacuum with an automatic launcher.  This would reduce the air resistance source of error as well as the movement of the rocket during launch. ·  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. To make the maximum distance for the ball to be kicked, the ideal conditions are to kick the ball at a 45 degree angle. This would make the ball move the furthest horizontally and not vertically. If I am trying to put out a fire at work with a hose, I would also want to use the same angle to ensure that enough water is hitting the fire, a type of projectile motion. Conclusions References Lab 7: Projectile Motion. (2011). In Lab Manual Introductory Physics (Vol. 3.3). Sheridan, CO: Esciencelabs.com.

he ecological footprint is a tool for helping us to visualize the impacts we make on the environment. For a brief overview of the concept, please watch this one-minute video The Ecological Footprint Explained (Links to an external site.)Links to an external site. prior to beginning work on this discussion.In this week’s class discussion, you will have the opportunity to learn more about how connected you are to the ecosystems and biosphere that you inhabit. Everyday choices can impact our environment; through those choices, we can either add to our environmental impact, or reduce it.In a course-long project beginning this week, you will take on the challenge of lessening your impacts on the environment, through reducing the size of your ecological footprint. Specifically, you will identify possible lifestyle changes that would reduce the amount of resources you use and/or the amount of carbon dioxide emissions that you produce. In a course-long experiment, you will determine whether or not it is possible to make a measurable difference in your environmental impact through a few simple actions in your daily life. The first step, of course, is to determine your ecological footprint right now. To do that, you will calculate three footprints: an overall ecological footprint that takes most of our daily behaviors into consideration; a carbon footprint that focuses on our daily carbon emissions that are contributing to global climate change; and a water footprint that assesses daily water use.Part A: Ecological FootprintUse the footprint tool from the web page What Is Your Ecological Footprint? (Links to an external site.)Links to an external site. to calculate your ecological footprint. At every opportunity, please select the “add details to improve accuracy” option. At the end of the footprint activity, make a note of how many earths would be required if everyone lived like you. Then click on “see details” to obtain the following information:Your ecological footprint, in global hectares (a hectare is about two and a half acres).Your top three consumption categories.Finally, research some ways you might reduce your footprint, identifying a few specific ones that you might put into practice throughout the course.Part B: Household Carbon Emissions FootprintNext, use the Carbon Footprint Calculator (Links to an external site.)Links to an external site. to calculate your household carbon emissions footprint. After answering all the questions:Make a note of your carbon emissions footprint in pounds. Is that above or below the average household carbon footprint in the US?Also, explore specific actions you might take to reduce your footprint. Which of them might be practical to undertake in the next five weeks?Part C: Water FootprintFinally, use Water Footprint Calculator (Links to an external site.)Links to an external site. to calculate your daily water footprint. After answering all the questions:Make a note of your gallons per day water footprint.Record the top three contributors to it.Scroll down the page to access a series of “Tips” buttons you can click on for advice on reducing your footprint. Again, make a note of some specific ideas you see that might be practical to implement over the next five weeks.