PHYS 200 Lab Report #5
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Athabasca University, Athabasca *
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200
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Mathematics
Date
Feb 20, 2024
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docx
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Uploaded by CoachBravery11850
Sherlow | ID 3309093 | PHYS 200 | Lab #5
Athabasca University PHYS 200 Lab Report #5
Collision in Two Dimensions
Ashley Sherlow
February 11, 2024
Student Number: 3309093
Introduction
This experiment is intended to study the theory of a two-dimensional collision involving two bodies. The collision scenario includes a body (Sphere 1) moving with an initial velocity v
1
in the positive x-direction that collides with a second, identical body (Sphere 2) (therefore assuming identical masses), which was initially at rest. The result of the collision leads to Sphere 1 deviating from its original path by an angle θ, while Sphere 2 scatters with a final velocity v
2f
at an angle ɸ.
Conservation of total momentum in each direction is a foundational rule in these scenarios. This conservation is expressed by Equations L5.1 and L5.2, regardless of whether the collision is elastic or inelastic. Since these are two identical objects, we can cancel the mass in these equations, simplifying the expressions. In the case of an elastic collision, Equation L5.3 introduces the conservation of total kinetic energy. By solving Equations L5.1, L5.2, and L5.3, additional relationships are
illustrated (L5.4, L5.5, L5.6), however they are relevant only to perfectly elastic collisions. Procedure
To conduct this experiment on two-dimensional collisions, I gathered two identical spherical objects – tennis balls – and a measuring tape to establish a length scale (unfortunately the measuring tape was in inches only so I did the conversion and adjusted this in Tracker accordingly). To record the video, I used a smartphone, and I selected the hardwood floor as the flat surface. To begin, I placed one tennis ball (Sphere 2) on the hard surface about 20cm from Sphere 1, and I then positioned the measuring tape to establish a length scale. My assisting partner then propelled Sphere 1 towards Sphere 2 using his hand while I recorded the video. I then uploaded the video to Tracker for analysis.
Pictures
Data
Data collected during the experiment: Spreadsheet with Data, Graphs, Linear Fit: Collision in 2D
1
^ Sphere 1 Time Graph Overview 2
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^ Sphere 1 Time Graph X direction
^ Sphere 1 Time Graph Y direction
3
^ Sphere 2 Time Graph Overview
4
^ Sphere 2 Time Graph X direction
^ Sphere 2 Time Graph Y direction
Analysis & Discussion
To analyze the collision data, I used Tracker software. The position of Sphere 1 (x coordinate) was examined as a function of time just before the collision, and the positions (x and y coordinates) of each sphere were defined as a function of time just after the collision. 5
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Position vs. Time Graphs:
6
7
Linear Fits were first calculated. Using the slopes obtained from the linear fits, velocities were calculated.
8
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9
10
Scattering Angles
The scattering angles were estimated based on the calculated velocities.
11
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Conservation of Linear Momentum:
Equations L5.1 and L5.2 were analyzed using experimental and calculated data. Results indicated that the values were close to but exact to those I found in previous calculations from the data. The discrepancies are likely due to a number of
measurement inaccuracies combined with the likelihood that this is an inelastic collision.
Elasticity of the Collision:
As seen above, I tested the validity of Equations L5.3, L5.5, L5.6, and L5.4. Calculations showed that the collision is likely inelastic in nature. Kinetic energy wasn’t conserved and the angle condition also did not hold true. These findings suggest that the collision was not perfectly elastic.
12
Limitations and Measurement Uncertainty:
Factors such as: ●
air resistance
●
imperfections in the tennis balls (weight discrepancies, shape, etc.)
●
measuring tape accuracy
●
my own subjective evaluation of measurements
●
tracker software limitations and user error
●
environmental factors - uneven flooring
Finally, the assumption of perfect elasticity is likely not valid in this instance.
Conclusion
This two-dimensional collision experiment illustrated the complex nature of collision dynamics and the behaviour of interacting bodies, as well as the unlikelihood for perfectly elastic collisions to occur in the real world. F
The analysis of my experimental data revealed that while there were discrepancies between the theoretical predictions of linear momentum conservation (Equations L5.1 and L5.2) and the values obtained. The collision seemed to be inelastic in nature, as evidenced by the discrepancy between calculated and expected values for kinetic energy conservation (Equation L5.3). Additionally, the lack of alignment between final velocities with theoretical expectations plus the failure of the angle condition (Equation L5.4) further supported my conclusion that this was an inelastic collision.
Finally, several sources of measurement uncertainty were identified, including inaccuracies in the measuring tape calibration, my own error in measurement, the limitations of Tracker software (level of detail), and potential environmental factors such as uneven flooring. These factors all contribute to the overall uncertainty in the experimental results and highlight the importance of meticulous experimental design and analysis.
Overall, my experimental findings highlight the improbability of real-world collision scenarios to exhibit perfectly elastic outcomes, and the importance of precision in experiments.
Questions
Provide detailed answers to the questions at the end of the lab.
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14
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