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2.Ametalbar can slide on two frictionless rails. The resistor R-6 and 2.5 magnetic field directed perpendicularly downward, into the paper: Let length I-L.2m. Cal...

Question

2.Ametalbar can slide on two frictionless rails. The resistor R-6 and 2.5 magnetic field directed perpendicularly downward, into the paper: Let length I-L.2m. Calculate the applied force required to move the bar to the right at a constant speed of Zm/s:#PPBin

2.Ametalbar can slide on two frictionless rails. The resistor R-6 and 2.5 magnetic field directed perpendicularly downward, into the paper: Let length I-L.2m. Calculate the applied force required to move the bar to the right at a constant speed of Zm/s: #PP Bin



Answers

Figure P31.23 shows a top view of a bar that can slide on two frictionless rails. The resistor is $R=6.00 \Omega,$ and a 2.50 - T magnetic field is directed perpendicularly downward, into the paper. Let $\ell=1.20 \mathrm{m}$ (a) Calculate the applied force required to move the bar to the right at a constant speed of $2.00 \mathrm{m} / \mathrm{s} .$ (b) At what rate is energy delivered to the resistor?

Okay, so we know mine. Any force can be able to be ill, which is even beat has B r v o artists out Since the currents I can it will be Albil are so those are wrenching here who have f mac which is the magnetic force is going to be square. Outsports has three of our so one of the men had a few is given to one Francesca out is 1.2 meter and we also know that a species give us two meters per second and the resistance skip past six omega. So not his father needs about who spent into the equation. Determining force which is equal to 2.50 Tesla to a bar to times 1.0 mir to a power to 10 times, um, to meter per second over six omega and it will give us you might enforce is equal to three newton. Therefore, the apply force required to move the bar to the right and a constants B off two meters per second should be you go to three. Newton is not that's determine the, um rate of energy, which is the power, and this can be able to ice core are, and we know the current commute to be All of you are therefore, have peaches with V over R to a bar to times are, as you can tell, are here can be cancel and this will give us P is he will be our veto barb two of our we know that my nephew is 2.5 Tessa. How is 1.2 meter speed is two meters per second and resistance is six omega. It's not as plugging these values back into the equation to Termini rate of energy, which is equal to to a point y zero Tessa times one point to meter and sometimes to meet of a second. Some of our two over six omega and it will give us your rate of energy, which is the power is ego toe six watts and these are the answers. But his question

So this the top you off the bar, their slides without region magnetic field is applied perpendicular. Lee don't watch and we want to keep the right in motion to the right with constant disappeared by applying the force, let this forces f air. When the road is in motion in a magnetic field then and you see him will be produced and we can find magnitude off. Induce him of by using the relation and you say mythical toe three times b times l sign off. Cheetah, get here really is the superior road which is to part 00 meter par sicken B is strength off magnetic field that is two point 50 Tesla on Ellis length off the bar which is 1.20 m into sign off Kida anti ties angle between the road and magnetic field which is 90 degree. This gives us the amount off and you say my produce as a result off emotional bar Equal toe six world do toe dis induce him enough induce Karen will produced inside a circuit on the direction off in US Girl in the bar will be from be to wear Andi the direction Afghan along the register will be from Had to be no. We can find the remote Afghan flowing through register by using Angela that is Indios jmf Equal toe High times residence. This gives us current through the historical toe induce him off divided by residence as we have calculated that induce him off in the circuit is six mold and resistance off that is studies 65 00 excuse us. The current in the circuit equal toe one NPR So this induce Cran will apply our force on the conductor in the left direction That is the force you do a news Kern and we can find this force by using the relation have induced equal toe I I'll be sign off Kita as we have India's current equal to one NPR length off conductor is 1.20 m. So gentle Our magnetic field is two point 50 m on Dhere to dies The angle between turn and magnetic field which is 90 degree. This gives us induce force on the bar Equal toe key Newton. So, in order to keep the rot in motion with constant repeat, they applied force should be equal toe. That is the magnitude of applied force should be called toe magnitude off in U. S. Force. So we have applied force equal toe G. Newton. Now, in the second part of this problem, we want to find the rate off energy delivered. So the register s by using the relation power dissipated in The rest are equal toe. I secure times are here current flowing through the histories one NPR and resistances six home. This gives us the rate off energy delivered to the historical toe. Six. What?

Hi. In the given problem, there are two rails metallic reels over which a metallic roar it's slighting. It is three to slight or these rails in a given direction. And there is a resistance are joining these two reals. There is a magnetic field in the region for ventricular to the plane off paper and dot It did into it like this. Initially, a force is applied on this roar metallic role which gives it a speed we so we can see initially means at time zero the initial speed in the bar in destroyed metallic roar It's we and we have to find the distance traveled by this roar when the roar will come to rest means b f means the final speed achieved by the wrong should be zeal. We have to find the total distance traveled by the roar in orderto achieve zero speak this distance. Suppose this is missing here? No, the even if induced in the roar as a result of its motion in the magnetic were we begin by be in tow me in tow where l is the length of this roar and we is It's instantaneous velocity. So this is the instantaneous value off the M if induced across this roar. So the current passing through the circuit will become using arms low. I was too. He enough induced, provided by the assistance off the circuit. Or we can say this is B the l divided by r. So finally, the force exerted on this roar will be given by the magnetic force will become B I in tow. L Oh, as this force is opposite to the direction of motion so we can say this is negative off B i l the forces negative in nature so we can see this is indicative off b multiplied by B the l divided by R times off l. So finally this force becomes minus B squared B El Square by our and using Newton's second law motion, this force can also be given us mass off the roar into acceleration and using calculus, we know acceleration. It's given us the daddy victim off instantaneous velocity. So here becomes m times off. David by DT is equal to minus B squared three times off elsewhere divided by, uh, we re arrange it to get one. Bybee Davey is equal to minus B squared El Square divided by M times so far into Getty so planete if we integrate book the sites the left hand side business integration off one by the rest of daily. And this integration is having delivers off a speed from initial we toe any instantaneous VT which is the function off time is equal toe integration off minus b square Ellis squared, invited by m time. So ah, with respect to DT And here time is wearing from zero to okay, this minus B square elsewhere, divided by M times so far can be taken as a constant out. So it will be just the invigoration off one with respect to BP having the limits off zero to be again. So finally the integration becomes here. Integration off one by B comes out to be natural logarithms off. We having the limits from veto me as a function of time is equal to minus B square at the square divided by M times off our he delivers off time from zero to D. So here it becomes natural. Gary them off reedy A parliament minus the natural algorithm off we when we put the limits and here it becomes minus Be swell squared, divided by m times are a parliament e minus. Lauren it zero four. It becomes natural. Getting them off me means instantaneous speed at any time. Bt divided by the The initial speed is equal to minus B square Any square be invited by m time, So Ah, so when we convert this logarithmic form into exponential form get B d B as a function of time divided by B is equal toe Okay. The rest of the poverty minus b square every square divided by M in tow are de. So finally we can see in standing is a speech at you by the road at any time. D means that as a function off time is given us three times off e minus B squared Ellie Square divided by m r. Into t her sister expression for instantaneous speed achieved by the raw No, if we have to find the distance travelled by the road to achieve finally state to be zero So four read a will be zero. The time should be in for a night because we know Onley eat the par minus in finite is having a zero value. So to achieve Finally, Speed, Toby zero The time should be in finite. No, In the previous expression, this sweetie can be written nous and given us the decorative off instantaneous displacements so we can say where it becomes very, very active off instantaneous distance d differentiation off X as a function of time with respect to did it, we begin by we each bar minus b square, Ellie square divided by m r Into the or we can say de X'd is equal no three times off e minus the square and that's squared, divided by em. Uh, okay, baby. So making an integration off both the sides again. This is the defence integration off DX as a function of time here, the initial position off the roar is supposed to be zero. And finally we have to find the final position. X of integration will be from zero to X is equal to be. Was that initially speed means a constant so cannot be integrated. It will be taken out and then it will be the integration off to the bottom minus B square. Really squired by him. R b DT having the limits for time from zero in finite because of speed will be zero at in finite time. So here it becomes X as a function off time, having the limits from zero toe X we as a constant then integration off E to the party Acciones de to the Parex only means eat a bar minus b squared Any square by m. R in today then divided about the differentiation off this function, which is the power off this e. So it's the differentiation with destructive time will come out. We minus B square elsewhere by M. R. Into tea and the limits are from zero two in fine it and more work here. We should have a negative sign also reveal. Yes, we are having this negative sign with the power. So no. When we put elements in the left hand side, we get X minus zero. You see Quito and then we put the lemurs in the right hand side. Outside places we, which is a constant and inside it becomes e to the bottom minus b squared The square divided by M. R. In place off it is in front of a so it becomes e to the power minus ing finite, divided by the same thing, William in same. And what Over here there will be No it because this is their differentiation off this whole function, we just have to time. So the time will not be here. So it will remain same as minus B square. Really squared by M dime so far, minus eight apart. Minor zero. When we put time to be zero, it becomes minus b squared, Really square divided by m. R. So here it becomes acceptable toe the in the onion Editor, this is Siegel. So minus B square, Ellie square by Emma all of the first time will become zero. And here it becomes Bless M times off are divided by P square, the square because even the par minus zero is one. So finally this distance come So could be m r. V divided by please, Claire. And it's quite this is the distance travelled by the road before coming to rest. Thank you


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