Lab 2physics

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Berkeley City College *

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Physics

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Jan 9, 2024

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Subash Thapa Subash Thapa Professor Francisco September 6 Lab 3 Cart on a Ramp Motion Detector Analysis: Part 1 Position vs Time graph: Velocity vs. Time Graph:
Subash Thapa Acceleration vs. Time Graph: Mark these regions on the graph: a. From about 0.75 to 1 seconds the cart was being pushed by hand. b. From about 1 to 2.5 seconds the cart was rolling freely. It was rolling up the incline from 1 to ~1.6 seconds, and down the incline from 1.6 to 2.5 seconds or so. c. On the velocity vs time graph, the cart had its maximum velocity at: -0.81m/s i. On the position vs time graph, the highest post of the cart was at (1.6,0.354) ii. The velocity of the cart at the top of its motion was: 0m/s iii. The acceleration of the cart at the top of its motion was: 1.311m/s^2 2. a. The parabolic region of the position graph is from about 0.5 to 2.5 seconds.
Subash Thapa . bThe equation is y = 0.4071x^2 - 1.235x + 1.3686 c The cart’s acceleration is constant during the free-rolling segment because the graph forms a parabola as shown. 3.
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Subash Thapa The slope of the fitted line is 1.2701, this corresponds to the acceleration we saw in the previous step. 4. a. b. The calculated mean acceleration from 1 second to 2.5 seconds = 1.3364, which is very close to our estimated acceleration of 1.2701m/s^2 found from the slope of the velocity graph. Conclusion: In this experiment, we investigated the motion of a cart rolling up and down an incline and analyzed the resulting position, velocity, and acceleration graphs. Our observations and analysis provided valuable insights into the cart's behavior during different phases of its motion. Position vs. Time Graph: We observed that the position vs. time graph exhibited distinct regions. Initially, the cart remained stationary (position did not change). As we gently pushed the cart up the incline, the graph showed a linearly increasing segment, indicating the cart's upward motion. At the highest point, the position remained constant as the cart momentarily stopped. Finally, the position vs. time graph displayed a linearly decreasing segment as the cart rolled back down the incline. Velocity vs. Time Graph:
Subash Thapa The velocity vs. time graph correlated with the position graph. When the cart was at rest, the velocity was zero. During the upward motion, the graph showed a linearly increasing velocity, and at the highest point, it briefly reached zero again. As the cart rolled down the incline, the graph displayed a linearly decreasing velocity. Acceleration vs. Time Graph: Our analysis of the acceleration vs. time graph revealed crucial information about the cart's motion. The acceleration was zero when the cart was at rest, became positive when it rolled up the incline, returned to zero at the highest point, and turned negative as the cart descended. Constant Acceleration and Quadratic Position: We noted that the cart's motion during the free-rolling segment demonstrated characteristics of constant acceleration. This was evident in the linear regions of the velocity vs. time and acceleration vs. time graphs. Furthermore, we fitted a quadratic equation to the position vs. time graph during this segment, confirming the parabolic nature of the motion consistent with constant acceleration. Comparison of Acceleration Values: We compared the calculated mean acceleration values obtained from the velocity graph and the acceleration graph during the free-rolling segments. Remarkably, these values were very close, indicating the consistency and accuracy of our measurements and analysis. Overall, our experiment yielded valuable insights into the kinematics of the cart's motion on the incline. We observed how the position, velocity, and acceleration graphs provided complementary information about the cart's behavior. Additionally, our findings supported the notion of constant acceleration during the free-rolling segments. The
Subash Thapa agreement between the acceleration values derived from different graphs strengthened the reliability of our experiment and analysis.
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