PHY 101L Module Five Lab Report

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PHY 101L Module Five Lab Report Name: Dmitrius Washburn Date: 2/10/2024 Complete this lab report by replacing the bracketed text with the relevant information. Overview In this investigation, you’ll design an experiment to test the law of conservation of energy. Then you’ll perform that experiment. This is completely open-ended. This allows you to use whatever materials and data acquisition techniques that you would like! Safety Read all the instructions for this laboratory activity before beginning. Observe established laboratory safety practices. Safety goggles should be worn during this lab. Make sure the lab area is clear of pets, children, and breakable objects. Do not eat, drink, or chew gum while performing this activity. Wash your hands with soap and water before and after performing the activity. Clean up the work area with soap and water after completing the investigation. Keep pets and children away from lab materials and equipment. Time Requirements Preparation: 30 minutes Experiment: 30 minutes Materials Needed From the Lab Kit Tape measure Materials Needed but Not Supplied in the Lab Kit Stopwatch Calculator Pen and paper for notetaking Procedure 1. You’ll design an experiment to test the law of conservation of energy. This experiment should include the measurement of some kind of energy transformation. This could be energy transformations from gravitational or elastic potential energy to kinetic energy, from potential energy to kinetic energy, or from kinetic energy to potential energy. The possibilities are endless! You’re free to use materials from your Carolina Biological lab kit. Or you may use materials that you have around your home. In either case, always make sure that you are following safe laboratory practices. * If you are unsure whether the experiment you plan on designing includes the measurement of an energy transformation, consult with your instructor. a. Possible energy transformations include the following: i. Measuring the initial and final gravitational potential energies of a ball bounced

on a hard surface ii. Measuring the initial gravitational potential energy and final kinetic energy of a ball rolling down an inclined plane iii. Measuring the initial elastic potential energy and final gravitational potential energy of a rubber band or spring launched upward from the ground 2. Once you’ve identified all of the materials needed for your experiment, gather all of your needed materials, a timing device, a tape measure, and pen and paper for note-taking. 3. Next, perform your experiment. Take note of all the data that you collect and any calculations that you use. Some equations that might be helpful include the following: kinetic energy = ½ mass x velocity 2 gravitational potential energy = mass x gravitational acceleration x height elastic potential energy = ½ spring constant x displacement 2 total initial energy = total final energy 4. Using your calculations, determine whether or not energy was conserved in your experiment. If energy was not conserved, explain why you feel that it was not conserved. Lab Questions 1. Explain the procedures you used to perform your experiment. This should include all of the materials that you used, the procedure that you followed, as well as any calculations used in your experiment. Include sufficient detail so that a fellow student could follow your instructions and complete your experiment exactly as you did. Materials Used:  Steel sphere  Inclined plane  Modeling Clay  Protractor  Measuring tape  Stopwatch  Scale  Notebook and pen to record measurements  Calculator  Book to increase inclined plane (optional) Procedure: 1. Set up the inclined plane on a flat, stable surface. Make sure the incline is smooth and without any obstacles. Ensure the inclined plane is secured to the modeling clay to prevent any movement during the experiment. Adjust the angle of the inclined plane to

a measurable value using a protractor for accuracy, and take note of the angle in your notebook, for this experiment it will be set to 6° . 2. Use the scale to measure the mass of the steel sphere. Record the mass in grams in your notebook and denote as m for future equations. 3. Use the measuring tape to measure the vertical height from the base of the inclined plane to the top. Record this figure and denote as h for future equations. Record this height as the vertical displacement over which the steel sphere will roll. 4. Calculate the initial gravitational potential energy by using the equation PE = m × g × h , where m is the mass of the steel sphere, g is the accleration due to gravity ( 9.8 m/s 2 ), and h is the vertical height of the inclined plane at the start. Calculate the final gravitational potential energy by using the same equation but replacing h with the vertical height of the inclined plane at the end. 5. Place the steel sphere at the top of the inclined plane and ensure to release it from rest, and allow it to roll freely down the incline. 6. Start the stopwatch as you release the sphere and stop it as the sphere reaches the bottom of the incline. Record the time it takes the steel sphere to reach the bottom in your notebook. 7. Repeat steps 5 & 6 two additional times for a total of 3 tests and record the average time of the three trials in your notebook. 8. Calculate the acceleration of the sphere by using the formula a=g x sin(θ) where g is the acceleration due to gravity ( 9.8 m/s 2 ), and sin(θ) is the angle of inclination, in this case 6° . 9. Calculate the final velocity by using the formula v=u+at , where u is the initial velocity (which is zero because it started at rest), a is the acceleration of the steel sphere down the incline, and t is the time taken for the sphere to roll down the incline. 10. Calculate the kinetic energy by using the formula KE=½mv 2 , where m is the mass of the steel sphere and v is the final velocity of the sphere at the bottom of the incline. 2. What type(s) of energy did you measure in your experiment? Gravitational potential energy and kinetic energy. 3. Explain the transfer of energy. In your experiment, what was your initial form of energy? What form of energy was it converted to? If there were multiple transfers of energy occurring in your experiment, detail each of them below. In this experiment, the initial form of energy was the gravitational potential energy as the sphere sat at the top of the incline. This was converted to kinetic energy as the steel sphere rolled down the incline. 4. Include your data in both table and graph format below. Use proper titles and labels on your table and graph. Mass of steel sphere: 0.0674 kg Angle of inclined plane: 6° Vertical height of ramp at start: 0.12 m Vertical height of ramp at end: 0.048 m

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Accleration due to gravity: 9.8 m/s 2 Gravitational Potential Energy Initial: 0.079 J Gravitational Potential Energy Final: Acceleration of steel sphere: 1.02 m/s 2 Velocity of steel sphere: 1.90 m/s Kinetic energy of the steel sphere: 0.121 J Trial Time (s) Average Time (s) 1 1.88 1.86 2 1.85 3 1.86 5. Include any calculations that you used to analyze your data below. To find the average time I added the three totals I got and then divided the total by three to find the average time. 1.88 + 1.85 + 1.86 = 5.59  5.59/3 = 1.863 . To find the initial and final gravitational potential energy of the steel sphere at the top and bottom of the incline, I used the formula PE = mgh and multiplied the mass of the sphere by the acceleration due to gravity, and multiplied that by the height of the incline at the top of the incline, then at the bottom of the incline. PE = mgh  PE = 0.0674 x 9.8 x 0.12  PE = 0.079 J PE = mgh  PE = 0.0674 x 9.8 x 0.048  PE = 0.032 J To find the acceleration of the steel sphere as it was rolling down the ramp, I used the formula a=g x sin(θ) by multiplying the acceleration due to gravity by the sine of the angle of the ramp. a = g x sin(θ)  a = 9.8 x sin(6°)  a = 1.02 m/s 2 To find the velocity of the sphere as it rolls down the ramp, I used the formula v=u+at by multiplying the acceleration of the sphere by the average time and add that to the initial velocity (which is zero because it started at rest). V = u + at  v = 0 + (1.02 x 1.86)  v = 1.90 To find the kinetic energy of the sphere as it rolled down the incline, I used the formula

KE=1/2mv 2 by multiplying half the mass of the sphere by the squared amount of the velocity of the sphere. KE = ½mv 2  KE = ½ (0.0674) x (1.90 2 )  KE = 0.0337 x 3.61  KE = 0.121 J 6. Describe whether or not you think that energy was conserved. If energy was not conserved, explain your reasoning and what you think might account for the “missing energy.” Use evidence to support your reasoning. I don’t believe that energy was conserved in this experiment. The reason behind this is that these calculations don’t account for any forces acting upon the steel sphere such as wind resistance, friction or resistance while rolling. I can account for this by adding the initial kinetic energy with the initial potential energy and seeing if there is any difference between adding the final kinetic energy amd the final potential energy. The calculations would be as follows: 0.121 + 0.079 = 0.2 J Initial 0.121 + 0.032 = 0.153 J Final Here we can see that the total initial energy is greater than the toal final energy, and therefore the energy was not conserved.

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