lab report 6 - PHY2053L

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Dec 6, 2023

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Cristian Acuna Vasquez 02/24/2020 PHY2053L Title: Energy of a Tossed Ball Purpose: The purpose of this experiment was to measure the change in the kinetic energy and potential energies as a ball moves in free fall, and see how the total energy of a ball changes surging free fall. Background Information: The law of conservation of energy states that the total energy is constant in any process. It may change in form or be transferred from one system to another, but the total remains the same. In terms of energy, when a ball is dropped it has gravitational potential energy, PE to start. At it falls, this is converted into kinetic energy, KE because it speeds up. As it rises after bouncing it slows down, losing kinetic energy, and gaining gravitational potential energy. Materials: computer Vernier Motion Detector Vernier computer interface Basket ball Logger Pro Calculator Wired Basket Procedure: Measure and record the mass of a basketball. Connect the Motion Detector to the channel of the interface. Place the Motion Detector on the floor and protect it by placing a wire basket over it. Hold the ball directly above the Motion Detector. Have your partner click to begin data collection. Toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector catch the ball before it hits the detector. Click on the Examine button, and move the mouse across the position or velocity graphs of the motion of the ball to analyze the data Data:

Mass of the ball (kg) 0.484 Position Time (s) Height (m) Velocity (m/s) PE (J) KE (J) TE (J) After release 0.4995 0.575 3.2679 2.2728 2.584 5.312 Between release and top 0,6327 0.937 2.0484 4.445 1.015 5.460 Top of path 0.8325 1.153 0.1524 5.5469 0.006 5.5475 Between top and catch 0.999 1.041 -1.405 4.937 0.478 5.414 Before catch 1.1655 0.677 -2.8127 3.212 1.914 5.527 Formulas Used to obtain:

Potential Energy (PE) = Mass * Gravitational Acceleration * Change in Height Kinetic Energy (KE) = (0.5) * Mass * Velocity2 Total Energy (TE) = Kinetic Energy + Potential Energy Results/Calculations/ Analysis 1a. Position Time (s) Height (m) Velocity (m/s) After release 0.4995 0.575 3.2679 1b Position Time (s) Height (m) Velocity (m/s) Top of path 0.8325 1.153 0.1524 1c. Position Time (s) Height (m) Velocity (m/s) Before catch 1.1655 0.677 -2.8127 1d. Position Time (s) Height (m) Velocity (m/s) Between release and top 0.6327 0.937 2.0484

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Between top and catch 0.999 1.041 -1.405 1e. Position PE (J) KE (J) TE (J) After release 2.2728 2.584 5.312 Between release and top 4.445 1.015 5.460 Top of path 5.5469 0.006 5.5475 Between top and catch 4.937 0.478 5.414 Before catch 3.212 1.914 5.527 2. How well does this part of the experiment show conservation of energy? The law of conservation of energy states that energy is never created or destroyed, only transferred. Conservation of energy means that the total amount of energy in a closed system remains constant. This part of the experiment shows conservation of energy well because the in both the position and velocity vs time graphs energy is clearly only being used as the ball is being thrown up and the ball itself, pulls itself down. 3a. KE = ½ mv 2 Position KE (J) After release 2.584 Between release and top 1.015

Top of path 0.006 Between top and catch 0.478 Before catch 1.914 3b. PE= mgh Position PE (J) After release 2.2728 Between release and top 4.445 Top of path 5.5469 Between top and catch 4.937 Before catch 3.212 4. Inspect your kinetic energy vs time graph for the free-fall flight of the ball. Explain its shape and print or sketch the graph. The Kinetic Energy portion of the graph looks sort of like an "M" or, more accurately, an inverted parabola. This is because it starts out at zero J as I'm holding it still above the motion detector. Then, as I throw it in the air, it gains KE, therefore the graph goes in the positive y direction. As the ball loses its acceleration and then begins to decelerate and head towards the top of its path, it has more potential energy than kinetic energy, hence why the graph begins to move toward zero, in the negative y direction. As the ball approaches the top of its path it momentarily has no

velocity, meaning there is no KE, only PE, hence why the KE graph momentarily is at zero J. As the ball begins to gain velocity as it plummets back towards Earth, the KE rises again. Finally, the KE goes back to zero when I catch the ball, stopping all movement. 5. inspect your potential energy vs time graph for the free-fall flight of the ball. Explain its shape and print or sketch the graph. The PE starts above zero J and creates a parabolic pattern as it returns to its original position above zero. First, the reason it does not start at zero is because I'm holding the ball above the motion detector (above the Earth). The formula for PE is mgh, and since there is some height between the motion detector and the ball, there is some PE to start with. The graph creates a parabola because as the ball rises into the air, it gains more height. The higher the ball, the more the PE it has. At the top of its path is the most PE it will have because it's the highest it will travel.

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6. Compare your energy graph predictions ( from the preliminary Questions ) to the real data for the ball toss. During free fall, the shape of the kinetic energy vs time graph is a Parabola with a maximum at the end of the curve where the KE reach its higher value. 7 Logger pro will also calculate total Energy ( TE), the sun of KE and PE, for plotting, Record the graph by printing or sketching

8. What do you conclude from this graph about total energy of the ball as it moved up and down in free fall? Does the total energy remain constant ? Should the total energy remain constant? Why? If it does not., what sources of extra energy are there or where could the missing energy have gone? According to the graph, the total energy of the ball remained constant as it moved up and down in free fall. According to the data in our data table, however, the total energy does not remain constant, suggesting a small amount of air resistance that was insignificant enough to be hidden in the graph. The total energy should not remain exactly the same, as work is being done on the ball by air resistance (a non-conservative force). Error Analysis: The major sources of error in this experiment came from the uncertainty/random error that the technology and tools used to calculate the values in this experiment since there was not a lot of human manipulation that could influences the values measured. Performing more trials would help reduce random error in the experiment, though, and would have allowed use more data points to get more accurate results. There was some human error due to the change of trajectory of the ball when it was thrown in the air. Conclusion: In conclusion, this experiment exposed the concept of conservation of energy, meaning that the changes in PE and KE of a system will equal the TE at any given point in time (in the absence of friction/air resistance). There are some situations where the force due to friction over a distance will do negative work to the system, resulting in a decrease of TE. During the ball's path, there are two points when it has the most KE that it will ever have in the system. These two points are when the force tossing the ball is immediately taken away, and right before the ball is caught on its way back down. Also, the ball had its greatest amount of PE while it was at the top of its path. That it where the ball is at its maximum height, and a larger height contributes to a larger PE.

Finally, the amount of KE and PE at the start will be equal to the amount of KE and PE at the end. This happens because the ball begins with 100% KE and 0% PE. As the height of which the ball is at increase, and the ball reaches its maximum height, the KE drops to 0% and the PE rises to 100%. Then the ball drops back down to its starting point, which has the same height as before, so the KE% will be back at 100% and the PE will go back to 0%. so since there is the same amount of each type of energy at the end and start, and the TE remains constant, this is how energy is conserved in a system. Preliminary questions: 1. What form or forms of energy does the ball have while momentarily at rest at the top of the path? Potential energy 2. What form or forms of energy does the ball have while in motion near the bottom of its path? Kinetic energy 3. Sketch a graph of velocity vs. time for the ball. 4 Sketch a graph of kinetic energy vs time for the ball

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5 Sketch a graph of potential energy vs time for the ball 6 If there are no frictional forces acting on the ball, how is the change in the ball potential energy related to the change in kinetic energy? To start, I know that TE = PE + KE - Fnc, Fnc being non-conservative forces. Friction is the non- conservative force in this case, and if there is no friction that means, TE = PE + KE. This means that there is no change in total energy, the change in kinetic is inversely proportional to the change in potential.

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