Exp 07 - KineticPotentialEnergy Redux

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Ocean County College *

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281

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Physics

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Apr 3, 2024

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Uploaded by cnw124

Physics 281 Experiment 7 Name: Cassidy Wojcik Kinetic and Potential Energy 1 INTRODUCTION: When a juggler tosses a ball straight upward, the ball slows down until it reaches the top of its path and then speeds up on its way back down. In terms of energy, when the ball is released it has kinetic energy, K = ½ mv 2 . As it rises during its free-fall phase it slows down, loses kinetic energy, and gains gravitational potential energy, U g = mgy. As it starts down, still in free fall, the stored gravitational potential energy is converted back into kinetic energy as the object falls. If no work is done by frictional forces, the total energy will remain constant. In this experiment, we will see if this works out for the toss of a ball. Motion Detector In this experiment, we will study these energy changes using a Motion Detector. LAB REPORT: Laboratory Cover Sheet This paper with Data Tables and answers to questions Printouts of any requested graphs OBJECTIVES: • Measure the change in the kinetic and potential energies as a ball moves in free fall. • See how the total energy of the ball changes during free fall. MATERIALS: Laptop with Logger Pro software No. 3 soccer ball Vernier Lab Pro interface wire basket Vernier Motion Detector & cable meter stick, lab balance PRELIMINARY QUESTIONS: For each question, consider the free-fall portion of the motion of a ball tossed straight upward, from just as the ball is released to just before it is caught. Assume neglgible air resistance. 1. What form of energy does the ball have while momentarily at rest at the top of the path? For the moment, the ball is at rest at the top of the path, the ball has potential energy. 2. What form of energy does the ball have while in motion near the bottom of the path? While the ball is reaching the bottom of the path, but did not hit the bottom yet, the ball has kinetic and potential energy.

Physics 281 Exp 7 2 3. Sketch a graph of velocity vs . time for the ball. 4. Sketch a graph of kinetic energy vs . time for the ball. 5. Sketch a graph of potential energy vs . time for the ball. 6. If there are no frictional for ces acting on the ball, how is the change in the ball’s potential energy related to the change in kinetic energy? When there are no frictional forces the change in the potential energy is the same as the change in the kinetic energy. This allows the energy to be conserved as the ball travels.

Physics 281 Exp 7 3 PROCEDURE: 1. Measure and record the mass of the ball in Data Table 1.. 2. Connect the Motion Detector to the DIG/SONIC 1 channel of the interface. Set the Motion Detector switch to Normal. Place the Motion Detector on the lab table and protect it by placing a wire basket over it. 3. Open the file “16 Energy of a Tossed Ball” from the Physics with Vernier folder. 4. Hold the ball directly above and about 0.3 m from the Motion Detector. In this step, you will toss the ball straight upward above the Motion Detector and let it fall back toward the Motion Detector. Have a partner click to begin data collection. Toss the ball straight up after you hear the Motion Detector begin to click. Use two hands. Be sure to pull your hands away from the ball after it starts moving so they are not picked up by the Motion Detector. Throw the ball so it reaches maximum height of about 1.0 m above the Motion Detector. 5. Verify that the position vs . time graph corresponding to the free-fall motion is parabolic in shape, without spikes or flat regions, before you continue. This step may require some practice. If necessary, repeat the toss, until you get a good graph. 6. Find the slope of the linear part of the velocity graph. Slope = _____________. Print the position and velocity graphs with the fit box in the velocity graph. When you have good data on the screen, proceed to the Analysis section. DATA TABLE 1 Mass of the ball (kg) 0.411 Position Time Height Velocity Potential Energy Kinetic Energy Total Energy (s) (m) (m/s) (J) (J) (J) After release 0.522 0.198 2.77 797.504 1576.781 2374.285 Top of path 0.801 0.587 0.05 2364.319 0.512 2364.830 Before catch 1.122 0.108 -3.02 435.002 1874.242 2309.245 ANALYSIS: 1. Click on the Examine button, , and move the mouse across the position or velocity graphs of the motion of the ball to answer these questions. a. Identify the portion of each graph where the ball had just left your hands and was in free fall. Determine the height and velocity of the ball at this time. Enter your values in your data table. b. Identify the point on each graph where the ball was at the top of its path. Determine the time, height, and velocity of the ball at this point. Enter your values in your data table. c. Find a time where the ball was moving downward, but a short time before it was caught. Measure and record the height and velocity of the ball at that time.

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Physics 281 Exp 7 4 d. For each of the three points in your data table, calculate the Potential Energy (PE), Kinetic Energy (KE), and Total Energy (TE) and enter in the table. Use the position of the Motion Detector as the zero point of your gravitational potential energy. 2. Analyze how well does this part of the experiment show conservation of energy: Compute the average TE for the three points, and then the per cent error of each point from the average: Average TE (w/uncertainty): 2349.453 J δ 32.5 % error: After release: 1.057% Top of path: 0.65% Before catch: 1.711% 3. Now analyze the ball's kinetic and potential energy during its flight. a. Logger Pro can graph the ba ll’s kinetic energy according to K = ½ mv 2 if you supply the ball’s mass. To do this, adjust the mass parameter. b. Logger Pro can also graph the ball’s potential energy according to U g = mgh . Here m is the mass of the ball, g the free-fall acceleration, and h is the vertical height of the ball measured from the position of the Motion Detector. c. Go to the next page by clicking on the Next Page button, . 4. Inspect the kinetic energy vs . time graph for the free-fall flight of the ball. What is the shape of the curve? ____________________. Print this graph. 5. Inspect your potential energy vs. time graph for the free-fall flight of the ball. What is the shape of the curve? __________________. Print this graph. 6. Logger Pro will also calculate and graph Total Energy, the sum of K and U g , versus time. Do Statistics for the free-fall part (using the three instants): Mean: 2349.453 Maximum: 2374.285 Minimum: 2309.245 Do a linear fit to the part of the graph of the ball in flight. What is the slope? Slope -32.52 Print this graph with the fit box. See the last page for both plots. 7. What do you conclude from this graph about the total energy of the ball as it moved up and down in free fall? From the graph you can conclude that the total energy had very little change as the ball moved up and down in free fall. This makes sense because of the law of conservation. The change could have due to another type of energy impacting the ball or the motion dector not being completely accurate. What should the slope be if the total energy is constant? The slope should be zero if the total energy is constant.

Physics 281 Exp 7 5 9. Why should the total energy remain constant (the answer is not “ because it ’ s conserved ” or any similar statement; this is tautological)? The total energy should remain constant because the mass of the ball of the does not change, only the height and velocity changes. The only forces acting on the ball as it moves up and down are conservative forces. If the forces were not conservative the total energy would not be expected to remain constant. If it does not, what sources of extra energy are there or where could the missing energy have gone? The missing energy could have gone into air resistance that was not taken into consideration in the lab. The air resistance impact would be minimal, but it would still have an impact on the change in the total energy. I think the residual plot refutes the idea that mechanical energy is conserved. The plot shows a huge change in mechanical energy from after release to before the catch. If the dots were closer together on the y-axis, then the plot would support the idea of mechanical energy being conserved.

Physics 281 Exp 7 6

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