Energy Cons rev aug22

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William Rainey Harper College *

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201

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Mechanical Engineering

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Oct 30, 2023

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Conservation of Energy LAB Rev. 8/16/22 DLD 1 of 7 LAB Energy Conservation Objectives Examine energy transformation Determine if the mechanical energy of a ball shot straight up is conserved Equipment Computer with LoggerPro LabQuest Mini Motion Detector Projectile Launcher plastic ball Meter stick Long Rod Plumb bob Balance Ruler Table Clamp Medium rod Right angle clamp Theory The Work-Energy Theorem states that the sum of all work done by non-conservative forces (friction, tension, air resistance, etc.) is equal to the change in mechanical energy (here E is standing in for any mechanical energy). ∑ 𝑊 𝑁𝐶 = ∆𝐸 Mechanical energy is any type of energy that is dependent on the position or speed of an object. This lab features three types of mechanical energy, spring potential energy (𝑃𝐸 𝑠 = 1 2 𝑘 𝑠 ∆? 2 ) , gravitational potential energy (𝑃𝐸 ? = 𝑚𝑔?) and translational kinetic energy (𝐾𝐸 𝑇 = 1 2 𝑚𝑣 2 ) . Mechanical energy is conserved if there are no nonconservative forces doing work. ∑ 𝐸 𝑖 = ∑ 𝐸 ? To determine the total mechanical energy of a ball shot in the air at any given time, the position and speed of the ball must be measured. To find the energy stored in a spring, the compression or extension of the spring must also be measured. 1. Write out all of the terms in their entirety in the equation for the Work-Energy Theorem (the “Big Ugly”) for the kinds of mechanical energy that will be examined in this investigation (not just 𝑊 𝑁𝐶 = ∆𝐾𝐸 + ∆𝑃𝐸 , do the substitutions!). 2. What is the total energy of the ball has when the launcher is in the “ ready to launch ” position with the spring fully compressed? 3. What is the total energy of the ball at a random position in flight, not at the peak of its motion and not at the launch position?

Conservation of Energy LAB Rev. 8/16/22 DLD 2 of 7 LAB Procedure 1. Using a balance, measure the mass of the ball. Mass of ball (g) = (kg) 2. Place the launcher on the floor. Using the table clamp, attach the long rod vertically to the end of the table. Place a right angle clamp along the vertical rod and attach the medium rod so that it is horizontal and cantilevered over the launcher, as shown. Fig. 1 – Example of the launcher and detector orientation 3. Use the motion detector’s clamp to attach the motion detector to the medium rod so it is looking down at the launcher. 4. Do a test shot on short range (depress the spring one click. Hint: Look at the yellow indicator on the side of the launcher!) to ensure that the ball does not hit the motion detector! Adjust the height of the detector so that there are at least 15cm between the maximum height reached by the ball and the detector. 5. Measure the distance between the motion detector screen and the top of the launcher. Align the launcher with the motion detector screen using the plumb bob. This is a critical step to get appropriate data. You can tell that your launcher and detector are aligned if you have symmetric parabolas on your graphs when you collect data. 6. Open LoggerPro software. Open folders: Probes and Detectors , Motion Detector. Double click on Motion Detector.cmbl file and make sure that it displays graphs of position and velocity. 7. Measure the distance that you compress the spring using the ruler and record below. Spring compression cm = (m)

Conservation of Energy LAB Rev. 8/16/22 DLD 3 of 7 LAB 8. Reload the ball on short range and prepare for launch. Click Collect to start recording data. After several seconds (when you hear the detector clicking), launch the ball. 9. Choose Analyze - Examine from the menu bar. From the Position vs. Time graph, determine the distance between the motion detector and the top of launcher (Y L ). Record in Table 1. 10. Choose 2 random times along the linear section of the Velocity vs. Time graph when the ball was in the air. Determine the position and speed of the ball by using Analyze - Examine from the menu bar. Record in Table 1. ( The spike found in the position vs. time data is due to the motion detector recording the movement of an air pressure wave generated at the time of release. Do not use this data from this region!!! ) 11. Calculate the height of the ball above the launcher for each random time selected. Record in Table 1. Sketch it out if you are having trouble figuring out how to complete this calculation. 12. Calculate the KE and PE g at time 1 and time 2. Record in Table 2 using a minimum of 4 decimal places. 13. Find the percent difference between the total energy at time 1 and time 2. Record in Table 2. Save your data file to your storage device. Table 1 Distance between Motion detector and launcher = (Y L ) Time Position of Ball (Y b ) (m) Speed (m/s) Height of Ball (m) Table 2 KE 1 KE 2 KE 3 PE 1 PE 2 PE 3 Total Energy Total Energy Total Energy Percent difference Show your work below for % difference. Show all your work (equations, substitution with units, answer). If your value for percent difference is greater than 5%, go back to your graph, choose a time 3, and try again! Select the two closest energies and recalculate the percent difference, showing your work in a second calculation.

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Conservation of Energy LAB Rev. 8/16/22 DLD 4 of 7 LAB 14. Repeat the process for a second launch at short range to verify your results and record the data in Table 3 and 4. Save your data file to your storage device. Table 3 Distance between Motion detector and launcher = (Y L ) Time Position of Ball (Y b ) (m) Speed (m/s) Height of Ball (m) Table 4 KE 1 KE 2 KE 3 PE 1 PE 2 PE 3 Total Energy Total Energy Total Energy Percent difference Show all your work below for % Difference. Questions 1. For each of your two trials, is the calculated total energy identical for both times used in determining the percent difference? Did you expect it to be? Which time had the greater energy? Was that expected? Explain. 2. Did you have to select and analyze information from a third time on either of the two trials? If so, why do you think this happened? (If not, you may simply answer that it wasn’t necessary.)

Conservation of Energy LAB Rev. 8/16/22 DLD 5 of 7 LAB 3. Looking at Trial 1 versus Trial 2, did the two trials have approximately the same total energy? Should they? Why or why not? 4. What is the difference between the conservation of mechanical energy and the conservation of total energy? Explain your answer completely. 5. Is mechanical energy conserved in real-life situations? Why or why not? 6. How does friction/air resistance affect the calculation for the kinetic energy? Explain your answer. 7. How does friction/air resistance affect the calculation for the potential energy at any given location? Explain your answer.

Conservation of Energy LAB Rev. 8/16/22 DLD 6 of 7 LAB 8. In a conservative system, the energy that is in the ball after launch must have been stored somewhere before the ball was launched. In the system used in this lab, where was the energy stored? 9. Estimate the spring constant of the projectile launcher using the spring compression distance you measured as part of the lab procedure and the equations you developed at the beginning of the investigation. 10. As always, experimental errors influenced your data and results. Complete the table for the three errors that you feel had the greatest impact on the experiment. If your answers do not fit in the space provided, please expand the table or make your own. Complete Description of Error Type of Error (Systemic or Random) Influence on Data and/or Results Suggestion for Mitigation

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