Lab+5+-+Acceleration+of+gravity(2)
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CUNY Queens College *
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Subject
Aerospace Engineering
Date
Apr 3, 2024
Type
docx
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Uploaded by DoctorStrawFish65
LAB 5: Acceleration of gravity
Objectives:
1) In this lab we will analyze constant acceleration motion.
2) We will find experimentally the magnitude of the acceleration due to gravitational force (acceleration of free fall).
Introduction
When on object moves under the influence of gravity only, its motion is called free
fall. Near the Earth’s surface acceleration of free fall is about g = 9.80 m/s
2
. Its
direction is downward.
A ball dropped from small heights can be considered as being in free fall since the air drag force is much smaller than its weight at small speeds. In today’s experiment we will examine how a ball moves in a free fall and determine from the analysis the experimental value of g
.
Calculation of g
For an object starts from rest and speeds up at a constant rate (constant acceleration),
the distance covered (
d
) the object covers depends on time (
t
) as a quadratic function:
One way to find acceleration of an object in such case is to consider the dependence of distance d
on t
2
. That dependence becomes proportional and the formula for distance takes y = mx
form, which, as you might recall from algebra, is a linear graph with m
being the slope of the line (in the y
versus x
graph). d
plays the role of the dependent variable y
, t
2
plays the role of the independent variable x and a/2
becomes the slope of
the d
versus t
2
graph.
This method of looking at the above equation is called
linearization
.
Procedure
•
Watch the following video (showing a ball released from rest):
https://www.youtube.com/watch?v=OEcyVzwciCs HYPERLINK "https://www.youtube.com/watch?v=OEcyVzwciCs&feature=emb_logo"& HYPERLINK "https://www.youtube.com/watch? v=OEcyVzwciCs&feature=emb_logo"feature=emb_logo
•
Take data frame by frame, recording the position of the ball (e.g., track the bottom of the ball) and the time elapsed from the rest position and fill in Table 1
on page 3. YouTube movies can be stepped frame by frame using the , and .
keys on your keyboard. Note that the ruler markings in the video are in cm-s.
•
In this lab you will use an online graphing calculator to plot the distance (
d
) versus time squared (
t
2
) graph, to find the best fitting line and to find its slope.
Go to the following website:
https://www.nctm.org/Classroom-Resources/Illuminations/Interactives/Line-
of-Best-Fit/
Insert t
2
values for x
and d
values for y on that website. Make sure that “Show
line of best fit” box is checked.
•
After all the data points are entered, the website will show you the plot of the best
fit line and give you formula for the best fitting line (an equation in green on the left side of the screen). The number in front of x
will be the slope. Take a picture of the graph and include it in your lab report.
•
Multiple the slope by two to find the experimental value of acceleration.
g
experimental
= _______________________
m/s
2
•
Compare your value to the actual value for acceleration of free fall, g = 9.80 m/s
2
and calculate % error.
Discussion & Conclusions
Discuss whether the objectives of the lab have been achieved. How close was the
experimental value of g to the theoretical value?
What were the main sources of errors in this experiment?
Air Resistance:
The experiment assumes negligible air resistance. However, in real-world scenarios, especially with a small ball dropped from a height, air resistance could affect the motion. This might lead to discrepancies between the theoretical and experimental values.
Distance
time t
Time squared
(t
2
)
(m)
(s)
(s
2
)
0
0
0
0.0005
0.033
0.001
0.0105
0.067
0.004
0.0405
0.100
0.01
0.0805
0.133
0.017
0.1405
0.167
0.027
0.1905
0.200
0.04
0.2705
0.233
0.054
0.3605
0.267
0.071
0.4605
0.300
0.09
0.5705
0.333
0.110
0.6705
0.367
0.134
0.8105
0.400
0.16
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0.9505
0.433
0.187
1.1005
0.467
0.218
1.2705
0.500
0.25
Table 1