PHY111L Lab 3 Uniformly accelerated motion3 (1)
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School
Grand Canyon University *
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Course
111L
Subject
Mathematics
Date
Apr 3, 2024
Type
docx
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4
Uploaded by SuperGalaxy9213
Lab 3:
Uniformly Accelerated Motion
Your report will consist of the typical 10 parts starting with a testable question. Learning Objectives
●
Demonstrate the uniform increase in the instantaneous velocity with time for a cart on an inclined plane and determine the acceleration by using a best-fit trend line to an appropriate graph. ●
Determine an experimental value for g
(the acceleration due to gravity) by interpretation of the cart’s acceleration as a component of g
.
1.
Testable Question:
How is velocity (v) related to distance (x).
2.
Hypothesis:
As the distance increase then velocity will also increase because gravity is acting on the car.
3.
Variables:
Control(s): gravity(g=9.81m/s^2), angle of the track=(5 or 8 degrees), Flag size (s=0.0254m)
Independent: Distance (x) m
Dependent: Velocity (v) m/s
4.
Experimental Design:
i
Xm
sqrt x (m
t(ser)
V(m/s
1–8
1–8
5.
Materials: ●
GLX
●
Pas Car ●
Phone angle measuring ●
Photogate
●
Ramp
6.
Procedure:
1.
For this we started with the angle at 5 degrees first and put the car 10 cm away then started increasing the distance by 10 cm each trial until the distance was 80 cm. 2.
We then recorded the data that was present on the GLX and transferred that to a graph. 3.
After the experiment was done at 5 degrees we then repeated the same thing for 8 degrees. average speed ,
v
=
flag
¿
∆ x
time
∈
gate ,∆t
∨
v
=
∆ x
∆t
o
θ
=
sin
−
1
(
∆ y
122.0
cm
)
a
= g
∙sin
θ
= g
∙
∆ y
122.0
cm
.
7.
Data:
i
X(m)
sqrt X (m
t(sec)
V(m/s)
1
0.1
0.316
0.425
2
0.2
0.447
0.598
3
0.3
0.548
0.734
4
0.4
0.632
0.855
5
0.5
0.707
0.958
6
0.6
0.775
1.050
7
0.7
0.837
1.139
8
0.8
0.894
1.204
8.
Analysis:
9.
Conclusion:
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Because distance and velocity showed no direct linear association, we had to employ graphical analysis to express our data linearly. The slopes between the two lines differed because we did two trials at varied track angles, resulting in varying cart accelerations. The graph shows that the track slanted at 8º increased its velocity faster than the track angled at 5º due to higher acceleration. The graph's equations indicate this increased acceleration. The equations for the tracks oriented at 8º and 5º were y=1.63x and y=1.36x, respectively, where slope denotes acceleration.
10. Evaluation:
During our experiment, we determined that the results supported our hypothesis. The theory was supported, although not in a linear sense. While calculating theoretical slope, we discovered that velocity is exactly proportional to the square root of the distance traveled, thus we had to apply graphical analysis to portray our findings in a linear manner. The R2 score for both trials was 0.999, which is considered high accuracy. An inaccuracy in photogate setup might have had an impact on our precision. If the photogate is not correctly tightened, it may continue to slide down and read a different flag for each trial, yielding results that do not agree with the theoretical findings or the calculated equations.