Conservation of Energy Lab (1)
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School
Stony Brook University**We aren't endorsed by this school
Course
PHY 133
Subject
Physics
Date
Dec 21, 2024
Pages
5
Uploaded by BaronAntelopePerson2021
Conservation of Energy LabName: Darrell Whiten-BooneTA: Shangke ZhouExperiment Date: 25 November 2024Report Date: 26 November 2024
IntroductionIn this lab, we will be studying the principles of conservation of energy as gravitational potentialenergy is converted into kinetic energy. The Conservation of Energy in a closed system statesthat energy is neither created nor destroyed, but rather transferred in different forms. Potentialenergy is dependent upon an object's position, while kinetic energy is associated with motion. Inmost real world energy transfers, energy is transferred due to friction as thermal energy.However, in this lab in particular, we’re focused on total mechanical energy, which is thecombination of kinetic and potential energy in different stages of motion. Through calculationsand observations, we aim to observe the law of conservation of energy and explore its practicalapplications in real world systems.TheoryThe equations explain the rules of energy conservation in a system that includes bothgravitational and kinetic energy. Potential energy is influenced by the mass of an object, theforce of gravity acting on it, and its vertical position, and alterations in potential energy are inaccordance with shifts in location. By setting the zero point for potential energy in a subjectivemanner, the potential energy becomes solely reliant on the object's position. On the flip side,kinetic energy is determined by adding up the energies of every moving component, such as thehanging mass and the glider. In conclusion, the principle of conservation of energy asserts thatthe overall energy of the system stays unchanged as long as no external forces or energylosses like friction are added.ProcedureIn Part I, we merely set up the experiment and our measurements. Firstly, we level the airtrackand place the cart in a stable position. We then set a scale for the photogate by measuring thelength of some black-clear segments as D. We then divide by the amount of segments as d. Wealso open the file, and obtain the mass of the glider, M.In Part II, we use a 20g mass in order to record the carts time, position, and velocity. We hook astring from the glider over the pulley at the end of the air track and down, ensuring that the carthas space before the mass hits the floor. We then attach the 20g mass to the end of the string,and pull the cart to the end of the track opposite of the pulley. We use the computer andphotogates to obtain the values we need, catching the cart before it reaches the other side.In Part III, we do everything the same as we did in Part II, except using two 20g masses (40g intotal) instead of one.
ResultsAnalysis
This is a graphical representation of the total energy (kinetic + potential) vs. time for the 20gmass. According to the law of conservation of energy, our slope should be relatively close tozero as the kinetic and potential energy forces should balance each other out. However, ourslope of 6.97 indicates that energy is being gained or lost over time. Therefore, our results forPart II can’t be applied to the laws of conservation of energy.This is a graphical representation of the total energy (kinetic + potential) vs. time for the 40gmass. According to the law of conservation of energy, our slope should be relatively close tozero as the kinetic and potential energy forces should balance each other out. However, ourslope of 2.30 indicates that energy is being gained or lost over time. Therefore, our results forPart II can’t be applied to the laws of conservation of energy.DiscussionAssuming we have a single particle moving in one dimension whose potential energy as afunction of x is U(x), we will use the chain rule and the relationship between F(x) and -U’(x). Thetotal energy of the system, E_total, is the sum of kinetic energy (KE) and potential energy (PE)meaning E_total = KE + U(x) = 1/2mv^2 + U(x). If we differentiate this with respect to time weattain. dE_total/dt = (d/dt)(1/2mv^2) + d/dt(U(x)). Differentiating the kinetic energy term(1/2mv^2) leads us to d/dt(1/2mv^2) = mv(dv/dt). We’re able to relate dv/dt to force using
Newton’s Second Law, which states that F = m(dv/dt). d/dt(1/2mv^2) = Fv. The potential energydepends on x, so d/dt(U(x)) = dU/dx(dx/dt). Given dx/dt = v, we get d/dt(U(x)) = U’(x)v. Given therelationship between F(x) and -U’(x), d/dt(U(x)) = -Fv. dE_total/dt = Fv - Fv = 0, proving the lawof conservation of energy.We assumed the pulley was frictionless, and if it weren’t, the slope of our total energy vs timegraph would have a negative slope as energy would be lost to heat. We assumed the pulley ismassless. Although negligible, the pulley does contain some mass which creates rotationalkinetic energy. Regarding our total energy vs. time plots, it could result in a positive or negativeslope depending on whether the system gains or loses energy due to the pulley. Moreimportantly though, the measured total energy would be less than the actual total energy. If weused the inverse process, friction would cause more energy to be lost to heat, but regarding themass of the pulley, rotational energy would decrease causing the slope to deviate less.In a PE vs. KE plot, conservation of energy predicts a slope of -1 as when potential energyincreases, kinetic energy decreases proportionally. The y-intercept is representative of the totalenergy of the system. A massive pulley would cause the y-intercept as well as the slope todeviate while friction would cause energy dissipation, leading to a downward shift in the line.Comparing this to an Energy vs. Time plot, the latter is more effective at visualizing the rate ofenergy loss due to friction but requires time-dependent data and experiment-specific details tointerpret systemic errors. In contrast, the PE vs. KE plot better highlights deviations from idealenergy conservation and is useful for identifying energy dissipation or hidden energies withoutrequiring time-based measurements. If the inverse process (mass moving upward) were used,friction would cause faster energy loss in both plots, and the massive pulley's rotational energywould slightly alter the slope in the PE vs. KE plot, potentially introducing nonlinearities.ConclusionWithin uncertainty, neither of our results can be accepted to the experimental expectations ofthe law of conservation of energy. Our results indicate that energy can be created and/ordestroyed, which directly violates the laws of physics. We must review our methodology anddata collection in order to mitigate errors for the future. Our results were meant to be asindependent to other forms of energy such as thermal energy and other types as possible. Weattempted to accomplish this by implementing a frictionless airtrack, as well as mitigating theeffects of air resistance. However, it seems we faltered in some areas of our experiment. Ihypothesize that we may have attained incorrect mass and/or velocity measurements, or ourphotogate was incorrectly calibrated. Nonetheless, by looking back at our errors, we canperform this experiment in the future to produce acceptable results.