1D Kinematics-1
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School
Indiana University, Purdue University, Indianapolis *
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Course
201
Subject
Aerospace Engineering
Date
Dec 6, 2023
Type
docx
Pages
4
Uploaded by ColonelFreedomDolphin37
1D Kinematics
Notes:
1.
This is a one-week lab. This lab will be done on campus with your lab part-
ner, in the Lab Room LD011 (basement).
2.
Turning in your report:
a.
A
full report
must be submitted.
b.
Collaborate with your partner on data collection, analysis and report.
c.
If you work in a group, please turn in only one report, but be sure it lists all
group members as authors.
d.
Lab reports should be uploaded to Canvas by the deadline in the course cal-
endar.
e.
Do not include your raw spreadsheets in the final report.
You may want to
use figures in your report that can contain snapshots of spreadsheet(s).
3.
Getting help:
a.
Your lab TA can answer questions during the lab or after the lab by email or
at their office hour (listed in the syllabus).
b.
You can also ask advice from lab partner(s) and/or other students.
Objective of this lab:
For this lab, you will refine/design and implement an experiment in which you use two different
methods (physical arrangements) to determine the (local) acceleration of gravity,
g
. You will then
compare your measured values of
g
with the standard value of 9.8 m/s
2
.
These are things you will do:
1.
Using the Vernier Go Direct® Motion Detector, measure the velocity versus time for two dif-
ferent objects/configurations: cart on a ramp and a dropped ball.
Perform multiple runs.
2.
Using the Vernier Graphical Analysis™ Software Package, perform a linear regression (for
each configuration) to obtain the slope of the velocity data.
3.
Using your knowledge of 1-dimensional kinematics, and the slope value from the velocity
data, determine the acceleration due to gravity,
g
, for each configuration.
Compare this mea-
sured value to the “theoretical” value.
4.
Investigate if other pertinent data are buried or hidden in your velocity versus time data. Dis-
cuss those that you identify.
5.
Identify errors that can occur in your experiment.
Minimize those errors.
What you will learn:
Please review the learning goals for the semester in lab in the handout from the first
week. In addition, this lab has several specific goals:
1.
You will practice keeping lab notes in a paper notebook, computer file, or other format.
1.
You will enhance the data analysis skills you learned previously, by applying them to real
data.
2.
You will learn to distinguish between two types of errors that occur in data: systematic errors
and random errors.
3.
You will enhance your understanding of how noise arises in data, and how to account for that
noise when interpreting experimental results.
4.
You will practice scientific communication skills by preparing graphs and writing a formal
lab report.
What goes in my lab notes, and what about my report?
The purpose of lab notes is to enable you or a colleague to reconstruct what was done and why.
They don’t have to be neat, in complete sentences, etc., but they do have to be useful.
In a case like this, they should include things like what were the two setups for measuring the
gravitational acceleration and what you did while recording data in those setups.
Did you try other setups or take multiple data sets for same setup?
If you store multiple files, record what filenames correspond to what conditions.
The purpose of a
report
is to explain what you learned and how you learned it. The sorts of things
that belong here are
A description of each step you did as part of Activity 1 and Activity 2.
Any graphs to show to your results.
Explain how you determined your results.
Explain differences between theory (standard value) and your actual (measured) acceleration
due to gravity.
Your conclusions about any relevant and useful information you were able to extract from the
data.
An analysis of the errors of the in your experiment including an explanation of how calculated
average acceleration, found the standard deviation, and determined the standard error.
Equipment:
For this lab, the following are available for use: dynamics cart, ramp/incline, stacking blocks (or
books), rubber ball, ring stand with crossbar, clamps, meter stick, computer, Vernier Go Direct® Mo-
tion Detector, and Vernier Graphical Analysis™ Software Package.
Dos & Don’ts:
Don’t
break the equipment -- Make sure the cart does not go too fast.
Make sure your
ramp is not too high.
Do
consult with your Lab TA about the various techniques you want to consider as you
design your particular experiment.
Don’t
forget to record your data for each run.
Do
use your imagination and have fun.
Background:
Please note that the acceleration you will be measuring in this experiment (
a
) is equal
to g cos(
θ
). The details of this equation will be clear in the ‘Force’ chapter.
Sample Set-Ups:
For Activity:
Cart on Ramp
, consider using the blocks (books) stacked to height
h
, measure the dis-
tance
x
(the underside of the ramp), then you know the angle.
ACTIVITY:
Cart on Ramp
Spend time properly setting up the Vernier Go Direct® Motion Detector and Vernier Graphi-
cal Analysis™ Software Package.
You will likely have to adjust the position and aim of the
Motion Detector several times to get it right (this is not trivial and will take time).
Practice releasing the cart and making additional adjustments so that you have good data, dis-
tance
x
should be around 2 meters and the cart should never be closer than 40 cm to Motion
Detector.
Do practice runs until you obtain good data showing an approximately
constant slope
on the
velocity
vs
.
time graph during the motion of the cart.
You can use the Graphical Analysis™ Software Package can fit a straight line to a portion of
your data -- use the Linear Fit button,
to perform a linear regression of selected data, this will
give you the slope.
Make sure to do multiple runs. How many?
You choose -- the more you do, the better your
data and thus the experiment.
Save your data for each run.
Use Excel (or similar) to make graphs, do analysis, etc.
Using what you have learned in lecture about 1D kinematics, fully analyze your experiment.
For example, the slope of velocity yields the acceleration
a
(along the incline). Use that to
then find the acceleration due to gravity,
g
.
Recall, you will have the data for multiple runs, compute an average value. Compare your
“measured” acceleration due to gravity to the “theoretical” value for
g
of 9.8 m/s
2
.
Discuss
and calculate the Percent Error. Explain.
Repeat the experiment for different values of ‘
h
’ (Please note that ‘
h’
is shown in the dia-
gram).
What other unknowns are possibly buried in your data?
Discuss those, as well.
x
h
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