5AL Lab 6 Assignment Submission Template - W23

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Physics

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Jan 9, 2024

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5±!%& !%&aIJFb 6 ±ssignment [ $%aylana and ²assidy], [03/07/2023], [!%&aIJFb 451SeJKGction °6], [³enJKGch #5] >WRhPK]n UPfXSi]nXSisWRhPKNI CNINIXSi]nVQg your rPKspo]nsPKs o]n PKCLGWRh s[lXSiNIPK, sCvPK tWRhXSis Cs C +±" UPfXSi[lPK C]nNI up[loCNI XSit to your #rCNIPKsLGopPK CssXSiVQg]n\mPK]nt.

451Slide 2: +QcGuaub betYec ´or the mass initially at rest released from an angular displaJKGcement near 30°, paste a sJKGcreenshot of the 562TraJKGcker window showing the IJFball and some of the experimental data extraJKGcted. '($ote here the mass of your IJFball and the length of your pendulum (the length IJFbetween the pivot and the JKGcenter of mass of the hanging oIJFbjeJKGct.) string length: 71 JKGcm IJFball: 45 g

451Slide 3: 01-aste here your plots of the y position and veloJKGcity magnitude v of the IJFball versus time. ±lign and adjust the two plots so the time axes matJKGch. ´rom a maximum value of the y position, JKGcompute the theoretiJKGcal expeJKGctation for the next maximum in the veloJKGcity magnitude, and JKGcompare it with the aJKGctual value of the maximum veloJKGcity. ²ompute also from the maximum y value the tension in the thread at the maximum veloJKGcity point. )*&ur theoretiJKGcal/JKGcalJKGculated v value was 1.508 m/s, and the aJKGctual v value (max) was 1.387 m/s. 562This makes sense IJFbeJKGcause in our theoretiJKGcal JKGcalJKGculations we disregard faJKGctors like air resistanJKGce and rotation of the IJFball itself, whiJKGch would slow the veloJKGcity of the IJFball as it swings. ±lso this value is relatively similar to the theoretiJKGcal value.

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451Slide 4: 01-aste here the plots of kinetiJKGc energy and potential energy versus time, aligning and adjusting the time axes to matJKGch. &'ake sure you indiJKGcate 451Sµ units in the plots. µs this variation what you expeJKGct? 562This graph demonstrates the kinetiJKGc, potential, and total energy of the pendulum as it swings through roughly 2 JKGcyJKGcles. 562The pattern of the graph is slightly jagged IJFbeJKGcause we had issues with the 562TraJKGcker program on traJKGcking the veloJKGcity. 562This made our kinetiJKGc energy appear off, whiJKGch also affeJKGcted our total energy levels. ¶owever disregarding these, this variation is similar to what we would expeJKGct. ±s 01-· inJKGcreases, $%· deJKGcreases and viJKGce versa. 562This is to IJFbe expeJKGcted IJFbeJKGcause in theory total energy, whiJKGch is equal to $%· + 01-·, should remain JKGconstant.

451Slide 5: 01-aste here your plot of the total meJKGchaniJKGcal energy of the pendulum versus time. ²omment on the plot: is energy JKGconserved during the motion? What fraJKGction of the initial energy is lost to friJKGction after 2 JKGcyJKGcles? ±lthough the graph appears jagged at some points, there is a generally deJKGcreasing trend of data when it JKGcomes to total energy. 562This would indiJKGcate that the energy was not totally JKGconserved during motion. !%&ooking at the graph, after 2 JKGcyJKGcles of motion, approx 22% of the energy was lost to air friJKGction/resistanJKGce during these JKGcyJKGcles. (.01/.045 = energy lost/total starting energy = .222)

451Slide 6: 01-aste here the y position and veloJKGcity magnitude plots versus time for the IJFball kiJKGcked into motion from the IJFbottom position. ´rom the initial speed JKGcalJKGculate the maximum height that would IJFbe expeJKGcted, and JKGcompare with the aJKGctual maximum height. max height: 0.116 m )*&ur expeJKGcted maximum height, whiJKGch is .072 m, is lower than the aJKGctual maximum height, .116 m. 562This JKGcould IJFbe IJFbeJKGcause of a numIJFber of reasons. 562The JKGcomputer may have traJKGcked the initial veloJKGcity as too low, or the IJFball may not have IJFbeen fully at rest when it was pushed, IJFboth of whiJKGch would lead to a higher height than JKGcould IJFbe JKGcalJKGculated theoretiJKGcally.

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451Slide 7: Write a thoughtful JKGconJKGclusion on the results of your experiments. 451Summarize your main results. ¸id they agree with what was expeJKGcted theoretiJKGcally? What proIJFblems affeJKGcted the measurements, and how JKGcould the measurements IJFbe JKGcarried out more aJKGcJKGcurately? 340Results may have had inJKGconsistenJKGcies due to inaJKGcJKGcuraJKGcy of the 7rCLGZkPKr program not IJFbeing aIJFble to effeJKGctively traJKGck out pendulum. 562This theory is supported when analyzing our veloJKGcity vs time graph JKGconsidering the trend line is jagged and not smooth, meaning the traJKGcker traJKGcked the pendulum at the inJKGcorreJKGct loJKGcation due to speed of the pendulum. 562This is an indiJKGcation of an inJKGconsistenJKGcy. ±long with this, our first trial with the oIJFbjeJKGct at rest at 30 o JKGcould have had the most inJKGconsistenJKGcies due to a possiIJFble skew in our JKGcamera angle. )*&ur JKGcamera JKGcould have potentially not IJFbeen exaJKGctly perpendiJKGcular with the pendulum and therefore JKGcontriIJFbuted to having inJKGconsistenJKGcies in our y values hitting the x-axis when y=0. ´or example, our seJKGcond trial with the tap has a JKGconsistenJKGcy in shape as the y value hits the x-axis every period, however, our trial 1 graph has varying y values for JKGcompleting a period. 562This is an indiJKGcation of an inJKGconsistenJKGcy. )*&verall, the results of our experiment are JKGconsistent with what would IJFbe expeJKGcted theoretiJKGcally. µn this experiment we were aIJFble to see how potential and kinetiJKGc energy are related to eaJKGch other, and how when one inJKGcreases the other deJKGcreases and viJKGce versa. We were also aIJFble to see how the total energy, kinetiJKGc + potential, added up to a relatively JKGconstant or slightly deJKGcreasing value. )*&ur JKGcalJKGculated vmax was higher than our experimental vmax, whiJKGch is also JKGconsistent with experimental JKGconditions IJFbeJKGcause vmax theoretiJKGcal does not aJKGcJKGcount for air friJKGction, rotation of the IJFball as it swings, and more. ±dditionally, for the seJKGcond trial, our JKGcalJKGculated value for max height was lower than the aJKGctual value for max height. 562There JKGcould have IJFbeen a few reasons for this, suJKGch as JKGcomputer/equipment error, or the IJFball having an initial veloJKGcity (IJFbefore IJFbeing pushed, the IJFball was in motion). )*&verall, our results were mostly JKGconsistent with what we expeJKGcted, and the inJKGconsistenJKGcies JKGcould have IJFbeen explained IJFby real-world JKGconditions and the JKGcomputer errors we were having.

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