The conservation of energy for the case of a descending glider on an inclined air-track is examined.https://nsuworks.nova.edu/physics_labs/1004/thumbnail.jp

Castano, Diego

Castro, Victor

English

NSU Works

Nova Southeastern University NSUWorks Physics Lab Experiments with Simulated Data for Remote Delivery Department of Chemistry and Physics 1-2022 Experiment 1.05: Energy Diego Castano Nova Southeastern University, castanod@nova.edu Victor Castro Nova Southeastern University, castvict@nova.edu Follow this and additional works at: https://nsuworks.nova.edu/physics_labs  Part of the Physics Commons Recommended Citation Castano, Diego and Castro, Victor, "Experiment 1.05: Energy" (2022). Physics Lab Experiments with Simulated Data for Remote Delivery. 7. https://nsuworks.nova.edu/physics_labs/7 This Book is brought to you for free and open access by the Department of Chemistry and Physics at NSUWorks. It has been accepted for inclusion in Physics Lab Experiments with Simulated Data for Remote Delivery by an authorized administrator of NSUWorks. For more information, please contact nsuworks@nova.edu. I. EXPERIMENT 1.05: ENERGYA. AbstractA body slides down a frictionless inclined surface. The total energy of the body iscalculated at several stages during the fall and examined for constancy.B. FormulasKE =12mv2 (1)Ug = mgy (2)where Eq. (2) is the gravitational potential energy for a body of mass m near the surface ofthe earth.C. Description and BackgroundConsider an object of mass, m, moving with speed, v. Its translational kinetic energy isdened to beKE =12mv2Gravity, being a conservative force, has a potential energy that depends only on congura-tion, and, in the particular setting of this experiment, on the position of the object relativeto the earth. If an object is lifted from a height y1 to a height y2, its change in gravitationalpotential energy is dened to beUg = mg (y2   y1) = mgywhereUg = mgyis the gravitational potential energy at position (altitude) y, measured with respect to anarbitrary origin (the zero level of potential energy). Because the dependence is only on1altitude, the change in gravitational potential energy in dropping a box to the ground, forexample, is the same as if it slides down a ramp.Dene the total mechanical energy of a system as the algebraic sum of the kinetic andpotential energiesE = KE + UIn the absence of dissipative forces, such as friction, the total mechanical energy of a systemneither increases nor decreases in a process; it remains constant. In such cases, mechanicalenergy is conserved. This is expressed asE2 = E1FIG. 1. Body sliding on an inclined air-track.In this experiment, you will use an inclined air track and measure the speed along theincline as well as the height above the table (Fig. 1) of a descending glider. The speeds willFIG. 2. Schematic depiction of the air track set-up.be determined using two photogates positioned along the air track (Fig. 2). By noting the2FIG. 3. Glider with ag/fence.length, `F , of the (opaque) "ag," or "fence," attached to the glider (Fig. 3), and the timeof the gates light-beam obstruction, the speeds are calculated asvA;B =`FtA;BThese measurements will allow one to nd the kinetic, potential, and total mechanicalenergy at two locations in the gliders path. This will be used to examine the conservationof mechanical energy in the gliders motion.3D. Procedure1. Position the two photogates at two locations, A and B, along the air track.2. Make sure the photogates are positioned properly so the fence on the glider blocks thegateslight beams.3. Because the potential energy is arbitrary, the vertical location of anything mirroringthat of the gliders can serve as y in (2). There is a guy-wire, which runs the length ofthe air track, whose vertical location above the table at the position of the photogatescan easily be measured with a meterstick to the millimeter. Record these verticallocations above the table at positions A and B along the air track (yA;B).4. Identify a position on the track (before photogate A) from which to repeatably releasethe glider from rest.5. After releasing the glider, it will pass through the gates, and it will bounce o¤ the endof the track, so make sure it does not run through the second gate again.6. Record the two time intervals (A and B) from the CPO timer. Repeat this procedureseveral times.Nota Bene: The transparent parts of the fence attachement must be free of smudges ormarks that could obstruct the photogate beams after the opaque strip has. An indicationthat this may have occurred is an anomalously short time reading for either tA and/or tB.4E. Measurementsglider mass, m [ gram ]fence length, `F [ cm ]location A above table: yA [ cm ]location B above table: yB [ cm ]Time IntervalsTrial tA [ sec ] tB [ sec ]123455F. Instructions1. Calculate the kinetic energy and gravitational potential energy of the glider based themeasurements. Add these to determine the total energy:Etotal =12mv2 +mgy (3)2. Assuming conservation of energy, any variation in the total energy is random, so themean should be a good estimate for the theoretical value. Calculate the mean energy,Etotal, in Joules.3. What is the standard error,  Etotal, associated with the previous calculation?4. For location A, calculate the uncertainty in the total energy, EA, using the following(propagated error) formulaE2 = KE2 + U2gmm2+ 4KE2"`F`F2+tt2#+ U2gyy2(4)taking m = 0:1 g; `F = 0:02 cm; t = 0:0001 sec; and y = 0:3 cm.5. For location B, calculate the uncertainty in the total energy, EB, using (4).6. Do the two intervals, (EA   EA; EA + EA) and (EB   EB; EB + EB) overlap?7. What does the answer to the question above imply about conservation of energy?6G. Calculationslocation t [ sec ] v = `F = t [ m=s ] KE [ J ] Ug [ J ] Etotal [ J ]ABEtotal [ Joules ] Etotal [ Joules ]EA [ Joules ]EB [ Joules ](EA   EA; EA + EA) \ (EB   EB; EB + EB)Answer to 7 above:7

Experiment 1.05: Energy

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Experiment 1.05: Energy

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