Lab 1_ Springs and Elastic Potential Energy
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Lab 1: Springs and Elastic Potential Energy
Group #3
Ann McGinty
Olivia Kawalec
Lysa Korusenge
Monday, January 22, 2024
iOLab Unit #4
Introduction:
The purpose of this lab was to use Excel to calculate the kinetic and potential energies of a
small spring, knowing the mass of the iOLab, to better understand the Law of Conservation of
Energy and Hooke’s Law. This is done by experimentally measuring the mass of the iOLab in
Exercise 1, graphing a parametric plot of the iOLab’s Force and Wheel position, velocity, and
acceleration when a small spring is attached to it in Exercise 2, and using this data to determine
how efficient the system is in Exercise 3.
Exercise 1: Measure the Mass of the iOLab Remote: Data Collection
In this exercise, we calibrated the iOLab, inserted the eye hook, and then selected the
accelerometer and force sensors on the iOLab software. We began measuring the data, picked
up the iOLab device by its toggle for a few seconds, then set it down and stopped the collection.
Afterwards, we highlighted the section of the graph on the force sensor that indicated the iOLab
was being held in the air. This represents the force of gravity on the iOLab. The experimental
quantity for acceleration was also indicated in the accelerometer sensor’s graph. This allowed
us to solve for the mass using the formula:
𝐹
𝑔
= 𝑚𝑔.
Figure 1.1 - Image of iOLab being held in the air to calculate the force due to gravity
Exercise 1: Measure the Mass of the iOLab Remote: Data Analysis
Figure 1.2 - Highlighted region is showing acceleration due to gravity while iOLab is stationary
on table
Based on the first graph, we found that Ay = -9.824 m/s^2 +/- 0.0360 m/s^2
This is our value of g (acceleration due to gravity).
Figure 1.3 - Highlighted region is showing the force of gravity when the iOLab is being held
stationary in the air
Based on the second graph, we found Fy = -1.992 N +/- 0.0310 N
This was our value of the force due to the Earth’s gravitational pull.
𝑚 = 𝐹
𝑔?𝑎𝑣 /𝑔
𝑚 = − 1. 992 𝑁 / − 9. 824 𝑚/?
2
𝑚 = 0. 203 𝑘𝑔
𝑚 = 203 𝑔
σ
𝑚
=
𝑚
(σ
𝐹
𝑔?𝑎𝑣
/𝐹
𝑔?𝑎𝑣
)
2
+ (σ
𝑔
/𝑔)
2
σ
𝑚
=
0. 203 𝑘𝑔
(0. 0310 𝑁 / − 1. 992 𝑁)
2
+
(0. 0360 𝑚/?
2
/
−
9. 824 𝑚/?
2
)
2
σ
𝑚
=
0. 00325 𝑘𝑔
Therefore, the mass we obtained is m = 0.203 kg +/- 0.00325 kg.
Figure 1.4 - Image of iOLab on triple beam balance
The mass value obtained from the triple beam balance is approximately 195 grams + 4.8 grams
(199.8 grams, or 0.1998 kg). The uncertainty associated with this value is +/- 0.05 grams (half
the smallest value that can be detected on the scale, which is 1 gram). The value calculated from
the triple beam balance scale and our calculations are very similar, and also very close to the
expected value of 200 grams.
Exercise 1: Measure the Mass of the iOLab Remote: Conclusion
The mass of the iOLab was 0.203 kg +/- 0.00325 kg, as calculated from the equation: Fg = mg.
We took the force of gravity and the acceleration due to gravity from the force and the
accelerometer graphs, respectively. This agrees with the expected value of 200 g for the iOLab.
The mass we obtained from the triple beam balance was 199.8 g +/- 0.05 g. One potential
source of error includes holding the iOLab unsteadily in the air, causing the force of gravity
measurements to be off. To minimize this error, we can keep our elbow on the table to assure
that the iOLab is wobbling as little as possible.
Exercise 2: Measure the Spring Constant, k, of the Short Spring: Data Collection
In this exercise, we added the small spring onto the force sensor of the iOLab. The iOLab data
was reset, and the force and wheel sensors (including position, velocity, and acceleration) were
selected. The iOLab was pushed back and forth relative to a vertical barrier (the wall). Next, a
parametric plot, plotting Force on the x-axis versus Wheel Position on the y-axis. Afterwards,
two points were selected at opposite ends of the plot, and the slope of the line was obtained.
This was done five times. Finally, the five values of the slope were averaged to determine the
mean and corresponding standard deviation.
Figure 2.1 - Image of spring being pushed against the vertical barrier (wall)
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