Need help finishing projectile motion lab

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.