Lab #2

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Florida International University *

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2049L

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English

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Feb 20, 2024

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Tyler Herrick 6252039 Carol Reigosa 6248100 Juan Espitia 6320600 Lab Report #2 Preliminary Questions: 1. The position versus time graph for a ball in free fall depicts a parabolic shape. Initially, as the ball is thrown upward, the graph shows a positive slope, signifying its ascent. At the peak, the slope becomes zero, marking the momentary pause before the ball starts descending. During the downward motion, the graph displays a negative slope as the ball returns to the ground. The impact with the ground is represented by a sharp drop in the graph, which then remains at a constant position. This graph visually encapsulates the changing position of the ball over time, reflecting its upward motion, the pause at the peak, the descent, and the eventual impact with the ground. 2. The velocity vs. time graph for a ball in free fall would resemble a symmetrical V- shape. At the start, when the ball is launched upwards, the velocity would be positive and decrease as gravity acts against its motion. At the peak of its trajectory, the velocity becomes zero, marking the point where the ball starts descending. As it falls back down, the velocity becomes increasingly negative, reaching a maximum magnitude equal to the initial launch velocity. This graph visually represents the ball's

changing speed over time during free fall. The upward portion of the graph corresponds to the ascent phase, while the downward part illustrates the descent phase, with the slope reflecting the acceleration due to gravity. 3. In free fall, the acceleration vs. time graph for a ball thrown straight up and down would be a piecewise function. Initially, the graph would show a constant positive acceleration equal to the magnitude of acceleration due to gravity (approximately 9.8 m/s² on Earth) during the upward motion. This portion of the graph signifies the ball's acceleration against the gravitational force as it ascends. As the ball reaches its peak and begins to fall back down, the acceleration vs. time graph would then display a constant negative acceleration with the same magnitude, indicating the ball's descent under the influence of gravity. In summary, the graph represents a positive acceleration during ascent, reflecting the opposing force of gravity, followed by a negative acceleration during descent as the gravitational force aids the motion downward. Analysis: 1. Velocity vs Time Graph and Acceleration vs Time Graph A) Ball Being Tossed but Still in Your Hand (i) Examine the velocity vs time graph and identify this region.

This region should show a gradual increase in velocity from zero to a certain value, representing the ball being accelerated upwards in your hand before release. (ii) Examine the acceleration vs time graph and identify the same region. The acceleration should be positive during this time, indicating a force applied to the ball in the upward direction. B) Ball in Free Fall (i) Label the region on each graph where the ball was in free fall and moving upward. On the velocity vs time graph, this would be a downward linear slope. On the acceleration vs time graph, this would be a constant negative value. (ii) Label the region on each graph where the ball was in free fall and moving downward. On the velocity vs time graph, this would be an upward linear slope. On the acceleration vs time graph, this would still be a constant negative value. C) Position, Velocity, and Acceleration at Specific Points (i) On the velocity vs time graph, decide where the ball had its maximum velocity, just as the ball was released. This would be at the point where the velocity graph starts to become linear and before it starts to decrease. (ii) On the position vs time graph, locate the maximum height of the ball during free fall.

This would be the point where the position graph reaches its maximum value during the upward motion. (iii) What was the velocity of the ball at the top of its motion? The velocity at the top of its motion should be zero. (iv) What was the acceleration of the ball at the top of its motion? The acceleration at the top of its motion should be equal to the acceleration due to gravity (g), but in the opposite direction (negative). 2. Linear Segment of a Velocity vs Time Graph A linear segment of a velocity vs time graph indicates constant acceleration. The significance of the slope of that linear segment is the acceleration value. In the case of free fall, this slope represents the acceleration due to gravity (g). 3. Coefficient of the t Term in the Fit The coefficient of the t term in the fit of the velocity vs time graph should be close to the accepted value for g. This is because the velocity-time relationship in free fall is given by v = gt, where g is the acceleration due to gravity. 4. Acceleration vs Time Graph The acceleration vs time graph should appear to be more or less constant, and this means the acceleration is constant throughout the free fall. This constant acceleration should be close to the value of g determined in question 3.

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