PHY 211 Lab 3 Report

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University of Kentucky *

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211

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Aerospace Engineering

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Oct 30, 2023

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Lab #3: Acceleration on an Incline and Flat Track PI: Laney Pollina DA: Brendon Thomas Researcher: Cassidy Rowe Introduction (DA) The research question answered by this experiment is how does changing the incline of a track impact the relationship between position, velocity, and acceleration. Also, the impact of friction between the car and track is also examined in this lab. The main findings from this experiment were that increasing the incline of the track causes the car to accelerate faster, and that friction causes the car to not accelerate as fast as it should theoretically. Procedure (Researcher) Trigonometry is the primary function used in this experiment. The equation shown below represents the relationship between the angle of the track ( θ ), the height of the block (H), and the distance between the two legs of the track (L) accompanied by the trigonometric function sin. sin = ? H L It is important to use trigonometry rather than only a protractor because trig is very accurate if there are no errors in the calculations. The drawing above represents the hidden acceleration triangle. The “g” can be defined as gravity, which is equal to 9.8m/s^2. The acceleration is represented by the a ❑ 1 ❑ component which is perpendicular to the track, and the a ❑ 11 ❑ component that is parallel to the track. By examining the data from the photogate, an equation can be formulated to determine the time that the car spent in the first gate. This equation subtracts the time spent “blocked” from the time spent “unblocked” in the gate. Analysis (DA)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 -0.2 -0.1 0 0.1 0.2 0.3 0.4 Graph 1: Comparing Accelerations Between Theoretical, Control, Push, and Friction atheory(m/s^2) aControl ave (m/s^2) aPush ave (m/s^2) aFriction ave (m/s^2) Trial/Group Acceleration (m/s^2) Graph 1: Graph 1 shows a comparison between the acceleration of the theoretical, control, push, and friction. The error bars of each group, except for aFriction, overlap which shows that there is not a significant difference in the changing accelerations between the three groups. aTheory should hypothetically be higher than the control and push group because the theoretical calculation of the acceleration does not consider the friction as the car travels down the track. Therefore, aTheory should be higher than the acceleration observed in the control and push groups. It is useful to include the friction in the graph to show a visual representation as to how friction impacts the acceleration of the control and push groups. 0.5 1 1.5 2 2.5 3 3.5 -0.16 -0.14 -0.12 -0.1 -0.08 -0.06 -0.04 -0.02 0 0.02 Graph 2: Comparing Accelations Between Forward, Opposite, and Friction aForward ave (m/s^2) aOpposite ave (m/s^2) aFriction ave (m/s^2) Trial/Group Acceleration (m/s^2) Graph 2: Graph 2 shows a comparison between the acceleration of the car in the forward and opposite directions as well as the friction. The error bars of each group do not overlap which shows that there is a significant difference in the changing accelerations between the three groups. These differences can be accounted for due to the direction the car was traveling along the track. It makes sense that the forward direction would have a positive acceleration because

it is moving down the track compared to the car moving in the opposite direction is traveling up the track through the photogates in the opposite direction. Table 1: Comparing Accelerations aTheory (m/s^2) 0.3259 ± 0.0033 aControl (m/s^2) 0.3393 ± 0.09 aPush (m/s^2) 0.3432 ± 0.0836 aFriction (m/s^2) -0.0624 ± 0.0047 aForward (m/s^2) 0.0092 ± 0.0105 aOpposite (m/s^2) -0.134 ± 0.01996 Conclusion (PI) The purpose of this experiment was to find the experimental relationship between acceleration, position, and velocity of a car on an incline as well as a flat track. Our group was able to determine values of acceleration for 6 different values, including aTheory, aControl, aPush, aFriction, aForward, and aOpposite. We determined the angle of the track to be ? = 1.903995076 ±0.019293852. The first graph shows the relationship between aTheory, aControl, aPush, and aFriction. For this graph, our car was let go on the top of an incline. Our aTheory was unexpectedly smaller than expected, as hypothetically it should be the largest value. Because of this, we believe there was a systemic error, in this case we think we pushed the car a little too hard down the track. The values for aControl and aPush were extremely close in value, which was expected as they were both sent down the track the same way other than for aPush we gave pushed a little harder. Our aFriction value was in the negatives, which makes sense because this force opposes the force given by the car, ultimately causing the car to decelerate. The second graph shows the relationship between aForward, aOpposite, aFriction. For this graph, we pushed a car across a flat track. The value of aForward was found to be 0.009223734±0.010540081, while the value of aOpposite was found to be -0.13403662±-0.019964307. The difference in values between aForward and aOpposite displays that there is a difference in accelerations when moving a car back and forth. This could be due to many different factors, including on our part how we pushed the car, if the wheels move differently one way or another, or if the car potentially had uneven weight distribution. To conclude, this lab taught us the relationship between acceleration, position and velocity, and ultimately how they are related. We also discovered what friction is and what it does, and how it is important in instances like this to take account of.

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