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Analysis

Graphs calculated using newfound data: cylinder momentum/initial bob momentum vs length (left) acceleration vs length (right)

Total energy vs time graphs:

For each of the trials, we can see that the ratio between the momentum of the cylinder and the initial momentum of the pendulum bob decreases as the length of the string decreases. This information was used to make a graph of the momentum of the cylinder vs the length of the pendulum and gives a value that lets us find the linear velocity of the cylinder as the value shows us how much of the bob's momentum is transferred to the cylinder. This value lets us figure out the time of impulse using Ft=m(vf-vi) and substituting the change in momentum with a change in momentum in terms of energy. This information is key for simulating the impulse as the line of best fit was used in the computational model. The line of best fit for this graph was used in the subsequent physics analysis.

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For each of the trials, we can also see that the acceleration during the impulse varies depending on the length of the pendulum. As the length of the pendulum increases, the acceleration that the cylinder experiences during the impulse increases. The slopes of the velocity vs time graphs (section of the graphs before the impulse) were used to make a graph of the acceleration of the cylinder during the impulse vs the length of the pendulum and helps to vizualize how the force exerted on the cylinder changes as the length of the pendulum increases. The line of best fit for this graph was used in the subsequent physics analysis.

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The total energy vs time graphs were averaged and used to find the mean amount of energy that was conserved after the impulse. This is important for creating the mathematical representations of the velocity of the cylinder.

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In order to find the acceleration of the cylinder after the impulse, the average of the slopes of the velocity vs time graphs (section of the graph after the impulse) of the four trials was taken (X velocity (m/s) is the velocity of the cylinder). This information helps simulate an accurate representation of the cylinder slowing down after the impulse.

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