Back and Forth Motion

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Miami Dade College, Miami *

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2048

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Physics

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Jan 9, 2024

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Back and Forth Motion Lab #2 Report Dania Espinosa Miami Dade College (5116) PHY2048-L-Physics w/ Calculus Dr. Eduardo Araujo Pradere September 19, 2021
Back and Forth Motion: Lab #2 Purpose: Everywhere we look we find objects in motion. When we talk about motion in physics, we talk about Kinematics, which is defined as the study of motion without considering its causes (no consideration of the masses of the objects nor forces that may have caused the motion). The purpose of this lab is to observe and analyze different objects in kinematic motion by comparing the positions and velocities with respect to time. When observing the data on how different objects move along a path from one position to another, we can further expand our description of motion by understanding how it related to position, displacement, velocity, and time. Apparatus &Procedure: For this experiment, the student will conduct five different variations of motion: (1) an oscillating pendulum, (2) a Dynamics Cart on an incline, (3) a student jumping in the air, (4) a mass oscillating at the end of a spring, and (5) a ball tossed into the air. A motion detector will be used in order to record the motion. This motion detector serves as the origins of a coordinate system which will then plot position vs. time points into a graph. Each variation trial will be performed independently by placing the motion detector in frame with the object at motion. It’s important to make sure that the motion detector is aligned and correctly positioned for accuracy. The student will then start the motion of the object along with the recording simultaneously. Once the motion is complete, the student will then open the Graphical Analysis application which will have generated the motions in graphs of position, velocity and acceleration as functions of time. Last step requires the student to analyze the information and the relationship between the physical quantities and answer the given questions. 2
Back and Forth Motion: Lab #2 Data: The data is generated for each motion variations with respect to time. Part I: Oscillating Pendulum Figure 6 3 Figure 4 Mass oscillating at end of a spring Figure 5 Ball Tossed in the Air Acceleration vs. Time Velocity vs. Time Position vs. Time
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Back and Forth Motion: Lab #2 Part II: Dynamics cart on an Incline Figure 7 Part III: Student Jumping in the Air Figure 8 4 Position vs. Time Acceleration vs. Time Velocity vs. Time Acceleration vs. Time Velocity vs. Time Position vs. Time
Back and Forth Motion: Lab #2 Part IV: Mass Oscillating at the End of a Spring Figure 9 Part V: Ball Tossed into the Air Figure 10 5 Acceleration vs. Time Velocity vs. Time Position vs. Time Acceleration vs. Time Velocity vs. Time Position vs. Time
Back and Forth Motion: Lab #2 Evaluation of Data: Part I- Oscillating Pendulum : From the graph, it’s clear that the acceleration for the pendulum was changing; it would increase as it came down and decrease when it was going up. On the velocity graph, the slope is changing, so therefore we can infer beforehand that the acceleration graph will also change. The velocity was zero when the pendulum was at the highest position on each end and as soon as it was reaching the lowest point. If you notice on the velocity graph where the slope is close to zero, the pendulum meets at the highest and lowest points of the position graph. The acceleration was zero at midpoint of the slope in the position chart but at the highest point of the velocity chart. In relation to the pendulum, the acceleration was zero (at mid-point) as it approached or dropped from close from highest point. The pendulum bob would reach the highest acceleration in at the lowest point in the motion; graphically right in between opposite ends of each slope. Part II- Dynamics Cart on an Incline : From the position graph, we can see that the cart’s acceleration jumped once the cart was pushed by the tester up the inclined ramp and stayed relatively close to zero even as it went back down the ramp. The velocity was zero when the cart reached the highest part of the inclined ramp. There was no acceleration when the cart was rolling. Part III- Student Jumping in the Air : The motion detected was above the jumper, therefore graphically, the highest point on the position graph is the when the jumper is bending his knees to jump and is farther away from the motion detector. When the jumper is up in the air and closer to the motion detector, the point on the graph will be the lowest point closer to zero. Acceleration is constant when the jumper is in airborne motion due to gravity. Velocity is zero when the jumper is at the highest point. The 6
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Back and Forth Motion: Lab #2 acceleration was briefly zero when the jumper was preparing to jump and midway the high and low points between the jump. Part IV- A Mass Oscillating at the End of a Spring : The slope of the velocity graph is constantly changing as the spring moves up and down, therefore so is the acceleration of the spring. The velocity of the spring was zero when it was at the highest end and zero at the lowest end. The acceleration graphically aligns with the midpoint of the oscillation of the spring going up and down and its where the acceleration is zero. It is moving the fastest in the middle when there was zero acceleration but the velocity was at its highest. The motion of this spring resembled that of the pendulum because they’re both sinusoidal, where its moving in a smooth and continuous wave. Part V- Ball Tossed into the Air : The acceleration is constant because graphically, you can see where the ball is released at the highest point of the velocity chart and then there’s a constant force of gravity acting on the ball represented by the slope going straight down. The velocity is zero when the ball is at the highest point right after it left the testers hands and returns to zero as soon as the tester catches it on its way down. The acceleration was briefly zero as it approached the highest point in the air, but the acceleration was -9.8 due to gravity as its going down. Analysis of all parts: Two features that the five position graphs had in common was that they all had slopes and magnitudes regardless of direction, up or down. Mathematically, position, velocity, and acceleration are all derivatives of one another. When you start with the position curve, you can find velocity by looking at the slope of that curve and then acceleration can be written as the slope of the velocity curve. The velocity curves of the motions related to one another because 7
Back and Forth Motion: Lab #2 they all had common maximum and minimum position values when the velocity was zero. The velocity graphs appeared different when some motions repeated and others didn’t. It also changed when there was a constant acceleration, in the case of the ball tossed in the air and student jumping due to gravity. You can also observe from the dynamics cart on an incline graph how the velocity depicts the incline and direction in which the cart was moving compared to the other motions where it was mostly up going up and down in a parabolic form. Conclusion: Based on observed data, one can conclude that the motion of an object moving back and forth is dependent on its position and how it changes with respect to time, giving us velocity. Once observing its velocity, one can also observe how it changes with respect to time giving us acceleration; an object with an acceleration of zero will have a maximum or minimum velocity. 8

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