Lab06_Conservation of Energy 2

Penn State University Physics 211R: Lab – NA II: Conservation of Energy 3 Physics 211R: Lab Report Template Nittany Adventure – The Conservation of Energy (Type in this document and print these pages at the end of the laboratory) Notes: • A maximum of three students will be allowed per group. o In the event that a group of four students must be formed, you need to check with your laboratory instructor before starting to work on the activity. • All the members of the group must participate in the activity. If a student is not participating (even when present) s/he may receive a score of zero in the activity. • Students arriving 10 minutes or more past start will not be admitted. • This activity must be returned at the end of the lab period. All the students completing the activity must be present when handing this to the laboratory instructor; a student not present at this time may not get credit for the activity. o Writing the name of a person not present is not permissible and may result in a potential academic integrity violation being processed. • After you receive the graded report back, you should make a copy of the front page (this page) and keep it for you records. This will serve as evidence of your grade for this activity. • You are responsible for checking your grade (in the course website) and report any mistakes to your laboratory instructor within two weeks after the activity. Date: __10/24/23______________ Enter your name as it appears in your PSU registration, no nicknames please. Name: Aparna Raghu Section # 033R Name: Amanda Haft Section # 033R Name: Olivia Cichocki Section # 033R Clean Up Check: After you finish working and completing the lab report, you need to clean and organize your working area. Then call one of your laboratory instructors who will check your area, initialize below and take the lab report. All the members of the group must be present at that time. If you leave the lab before your laboratory instructor performs the check up, you will be deducted 5 points from your score for this lab report. Laboratory Instructor Initials: ____YL___ Score: _______

Penn State University Physics 211R: Lab – NA II: Conservation of Energy 6 Q4. Looking at the two above graphs, what aspects ( note: plural ) of these graphs tell you that there is dissipation in your system? Be clear on which aspects are from which graph. In the second graph, you can see that the kinetic energy is decreasing with each oscillation, as it slopes downwards. In the first graph, you can see a similar thing where the position that the cart travels decreases more and more because the dissipative forces. Q5. Now look specifically at the K vs Position graph. Where along the car’s path is the kinetic energy zero? Where is K a maximum? If you let the cart come to rest on the track at the “equilibrium point,” what was true of the kinetic energy at this location ( x eq ) while the ride was running? Kinetic energy is zero at the starting position and the ending position when the cart comes to a rest. K is at maximum at equilibrium point. At the equilibrium point, the kinetic energy is at its maximum value (0.22-0.24 joules) Next look specifically at the K vs Time graph. This is what we typically use to characterize the impact of dissipation. In particular, we often discuss the “Q factor” for oscillators. In this questions you will measure Q for your ride. If you look at just the peak of the kinetic energy as a function of time you’ll see that it decays exponentially (the amplitude could be fit by a function Ae -t/  ). Measure the amplitude of a K peak near the beginning of the motion, then find a subsequent peak which has about 1/e of that amplitude (i.e. an amplitude of as close to 0.37 of the first amplitude as possible). How many periods (intervals between peaks) do you need to get to that peak? Q is that number times 2  . A cool thing about exponential decay is that it doesn’t matter which peak you start with – you should always find the time to decay to 1/e of that amplitude (one “time constan t”) is the same. Q6. What is Q for your oscillator? 12 * 2pi = 24pi = 75.4 = Q Q7. If the friction got much smaller in your system, what would happen to Q? If you wanted the ride to last a really long time, would you want it to be a “high Q” or “low Q” oscillator? If the friction got much smaller in our system, the cart would be oscillating for longer because less energy is lost due to dissipative forces. This means there would be more oscillations which means a higher Q value.

Penn State University Physics 211R: Lab – NA II: Conservation of Energy 9 to eliminate this in the y-intercept (that is, write the y-intercept in terms of the slope and other constants, not including sin  ). 0 = k ( x 0 - x ) – (M+ m added ) g sin(  ) 𝑘𝑥 = −𝑔 𝑠𝑖? 𝜃 𝑘 ? 𝑎 ⅆⅆ + (𝑥 0 + ? 𝑠𝑙??𝑒 ) Q14. In order to do this quickly you will make the measurement for just 4 values of m added (including 0). Make the measurement (using the position sensor to determine the equilibrium position of the car for each of the added masses), fill in the below table, then plot and do a linear fit of the data in excel (include the plot, showing the linear fit parameters, below). m added (kg) x (m) 0 0.571 0.050 0.541 .1 0.500 0.150 0.464 Q15. Using your expressions in Q13 and your fit parameters from Q14, calculate x 0 . 𝑘𝑥 = −𝑔 𝑠𝑖? 𝜃 𝑘 ? 𝑎 ⅆⅆ + (𝑥 0 + ? 𝑠𝑙??𝑒 ) X0=.92 Check with an instructor at this point to make sure that your values of k and x 0 are reasonable Lab Activity 3: Analyzing the Potential Energy of The Nittany Bouncer In this section, you analyze the potential energy of your Nittany Bouncer ride. Again : Use the motion sensor as the zero point of gravitational potential energy and the spring at its relaxed length (x = x o ) as the zero point of elastic potential energy. y = -0.724x + 0.5733 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 x (m) mass added (kg) Mass added (kg) vs. Position (m)