Question Description
LabAssignment 2: Projectile Motion
Instructor’s Overview
Projectile motion is a part of oureveryday experience. When you strike abaseball or softball, you are creating a projectile motion scenario. Similarly, you yourself are a projectile whenyou jump into a pool to cool off on a sweltering summer day. In this lab you will get some hands-onexperience with projectile motion and apply the two-dimensional kinematicequations that we have developed. Youwill perform experiments and compare your results to theory.
This activity is based on Lab 7 of theeScience Lab kit. Although you shouldread all of the content in Lab 7, we will be performing a targeted subset ofthe eScience experiments.
Our lab consists of two main components. These components are described in detail inthe eScience manual (pages 83-88). Hereis a quick overview:
- In the first part of the lab, you will launch amarble off of a table or other elevated surface and measuring thehorizontal distance that the marble travels. From this distance, you will calculatethe launch velocity of the marble. You’ll then repeat the experiment using a different launch heightand try to predict the new horizontal distance using the velocity that youderived from the first part of the experiment.
- In the second part of the lab, you will launchsmall foam rockets. The first partof this experiment involves measuring the flight time of the rocket andderiving launch speed. In thesecond part of the experiment, you will explore the dependence of range onlaunch angle.
Note: In the rocket experiment, perform and document steps 1-7. Then launch your rocket at three angles: 30degrees, 45 degrees, and 60 degrees. Record all of your data in the tables that are provided in thisdocument. Don’t use the tables in theeScience manual.
Take detailednotes as you perform the experiment and fill out the sections below. This document serves as your lab report. Please include detailed descriptions of yourexperimental methods and observations.
Experiment Tips:
Marble ona ramp
- Although you are welcome to use the water and cornstarch technique outlined in the eScience lab manual, I used a slightlyless messy technique. Take a toweland fold it into several layers. Place the towel in the marble landing area and smooth the surfacewith your hand. When the marblehits the towel, its landing is deadened and you will see a slightimpression of where it landed. Measure to this impression to determine the range of the marble.
- Make sure that you place your marble at the sameposition on your ramp. This helpsinsure the repeatability of launch speed.
Rocketexperiment
· Ihad the best results when I didn’t squeeze the launch bulb excessively. The rocket flies more consistently andtravels a manageable distance from a measurement perspective.
· Beforecollecting data, make sure you practice you launch technique. Try to squeeze the launch bulb in aconsistent manner to minimize experimental variation.
· Launchthe 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 motionand use kinematics to predict how far a projectile will travel. This isperformed by launching a marble off of a table or otherelevated surface and measuring the horizontal distance that the marble travels.The second part will look at a rocket being launched at different angles andthe influence of gravity. I will determine the relationship between the angle at whicha projectile was launched and the time of flight of the rocket.
Introduction
Background: A projectileis an object acted on by gravity alone. A projectile is any object which, once projected, continues in motion byits own inertia and is influenced only by the downward force of gravity. Inthis lab, it can be assumed that projectiles are fired either vertically orhorizontally.
Objective:Theobjective of this experiment is to predict the range of a projectile set inmotion. Learnhow to solve projectile motion problems. Understand that the acceleration due togravity 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 hypothesisfor the marble experiment is that as the initial height of the marble increasesthe horizontal distance will also increase. For the rocket launch experiment,my hypothesis is that as the angle of the projectile decreases the time offlight will also decrease.
Material and Methods
The materialsneeded for this lab are provided below:
Experiment1:
Ramp
Marble
Corn starch
4 sheets ofblack construction paper
Tape measure
Monofilamentline
Fishingsinker
Paper towel*
Water*
*You mustprovide
Procedure:
1. Place theramp 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 aplumb line by launching the fishing sinker to the monofilament line.
3. Hold thestring to the edge of the ramp, and mark the spot at which the weight touchesthe ground. Note: The plumb line helps to measure the exact distance from theedge of the ramp to the position where the marble “lands.”
4. Lay down arunway of black construct on paper.
5. Wet themarble all over with water, and drop into the cornstarch bag to coat. Roll on apaper 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 themarble hits the construction paper, the force will cause some of the cornstarch to come off, and leave a mark on the construction paper so you can seethe point of first contact!
6. Begin theexperiment by releasing the marble at the marked point on the ramp.
7. Measurethe distance traveled to the first mark made on the carbon paper using the tapemeasure. Record this value in Table 1 on the following page.
8. Repeatsteps 5-7 nine more times and record your data in Table 1.
9. Next, useyour data to calculate the velocity of the marble for each t
Experiment2:
4 SqueezeRockets™
1 SqueezeRocket™ Bulb
Protractor
Tape measure
Stopwatch
Procedure:
1. Mark thespot from which the rockets will be launched.
2. Load aSqueeze Rocket™ onto the bulb.
Note:The Squeeze Rocket™ is a trademark product name. The “rocket” itself does notuse a self-propelled mechanism. ACer a rocket is launched, gravity is the onlymajor force which acts upon the “rocket”.
3. Using aprotractor, align the rocket to an angle of 90° (vertical).
4. Squeezethe bulb (you will need to replicate the same pressure for each trial), andsimultaneously start the stopwatch upon launch (alternatively, have a partnerhelp you keep time). Measure and record the total time the rocket is in theair. Repeat this step three or more times, and average your results. Recordyour results in Table 3.
tavg=_1.38sec_
5. Calculatethe initial velocity of the rocket (vinitial = voy) usingthe kinematics equations.
6. Recordyour 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 equalto t/2.)
7. Repeatthis trial two more times, and record the values in Table 3.
8. Choosefour additional angles to fire the rocket from. Before launching the rocket,calculate the expected range using the vertical velocity and the angle fromwhich the rockets will be fired. Remember that you can use zero for any initialpositions, and that the acceleration due to gravity, g, is -9.8 m/s2 . Recordthese values in Table 3.
9. Next,align the rocket with the first angle choice and fire it with the same forceyou used initially. Try to record launches where the rocket travels in a parabolaand does not stall or flutter at the top. Measure the distance traveled withthe tape measure. Repeat this for two additional trials, recording the actualrange 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 andpredicted 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 – angleexperiments
Angle = 30 degrees |
|||
Trial Number |
Predicted range (meters) |
Measured range (meters) |
Difference (meters) |
1 |
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2 |
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3 |
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4 |
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5 |
|||
Average |
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Standard Deviation |
Angle = 45 degrees |
|||
Trial Number |
Predicted range (meters) |
Measured range (meters) |
Difference (meters) |
1 |
|||
2 |
|||
3 |
|||
4 |
|||
5 |
|||
Average |
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Standard Deviation |
Angle = 60 degrees |
|||
Trial Number |
Predicted range (meters) |
Measured range (meters) |
Difference (meters) |
1 |
|||
2 |
|||
3 |
|||
4 |
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5 |
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Average |
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Standard Deviation |
Analysis and Discussion
Marble experiment calculations
Show yourcalculation of the launch velocity of the marble as a function of height anddistance travelled (needed for Procedure 1 in the eScience manual):
Use yourequation above to solve for the range as a function of launch velocity andheight (needed for Procedure 2 in the eScience manual):
Rocket calculations
Show yourcalculation of the launch velocity of the rocket as a function of flight time.
Describe howyou came up with your predicted ranges. What relation did you use?
Based on your experimental results,please answer the following questions:
Marble Experiment
· Supposeyou altered your existing ramp so that the marbles had twice their initialvelocity right before leaving the ramp. How would this change the totaldistance traveled and the time that the marbles were in the air?
The totaldistance traveled would double because they had double the horizontal speed. Atthe same time both marbles would spend about the same amount of time in the airsince vertical motion is not affected.
· Didyour prediction in Procedure 2 come close to the actual spot? Find the percenterror of your predicted distance (expected) compared to the actual averagedistance (observed). What are somesources of error in this experiment?
% error = [ (observed value ‐ expected value)]/ expected valueX100
Air resistance could cause a source oferror as well as the movement of the marble across the table. If it doesn’troll perfectly horizontally it will cause error.
Rocket Experiment
· Ofthe three angles that you tested, what angle gave the greatest range? The least?
The anglethat gives the greatest range is the one at 45 degrees.
· Drawa FBD for a rocket launched at an arbitrary angle (assume the rocket has justonly barely left the launch tube, and neglect air resistance).
· Whatrole does air resistance play in affecting your data?
Airresistance always plays a role in these types of experiments. Air resistancewill affect the rocket’s speed as gravity pulls down. All in all, airresistance will reduce the acceleration of the rocket.
· Discussany additional sources of error, and suggest how these errors might be reducedif you were to redesign the experiment.
Inconsistentlaunch speeds and movement of the rocket during the launch, since these rocketsare so testy, could also be a source of error. The perfect experiment would beto use a vacuum with an automatic launcher. This would reduce the air resistance source of error as well as themovement of the rocket during launch.
· Howwould a kicker on a football team use his knowledge of physics to better hisgame? List some other examples in sports or other applications where thisinformation would be important or useful.
To make themaximum distance for the ball to be kicked, the ideal conditions are to kickthe ball at a 45 degree angle. This would make the ball move the furthesthorizontally and not vertically. If I am trying to put out a fire at work witha hose, I would also want to use the same angle to ensure that enough water ishitting the fire, a type of projectile motion.
Conclusions
References
Lab 7: ProjectileMotion. (2011). In Lab Manual Introductory Physics (Vol. 3.3). Sheridan, CO:Esciencelabs.com.