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E43 Both pulleys are fixcd t0 the shafl and us the snaft turns with conslani angular vclocity the power Ol pulley ^ i transmitted to pulley B. Delermine the horizon...

Question

E43 Both pulleys are fixcd t0 the shafl and us the snaft turns with conslani angular vclocity the power Ol pulley ^ i transmitted to pulley B. Delermine the horizontal tension Tlin thebellkoppuliey Buand Lhexy Krcuclinuauelhekjnuroun Fehmponenesmon hearing EGhn4 lhruxk heuring Din 0" Thc bearings &rc in proper alignmenl and exert only HEsnsHaehe Lirunshon CheuehuflUekhmai IewUHUm KALD Mni"S0 N'L50 mmS0 mm65 N SOT

E43 Both pulleys are fixcd t0 the shafl and us the snaft turns with conslani angular vclocity the power Ol pulley ^ i transmitted to pulley B. Delermine the horizontal tension Tlin thebellkoppuliey Buand Lhexy Krcuclinuauelhekjnuroun Fehmponenesmon hearing EGhn4 lhruxk heuring Din 0" Thc bearings &rc in proper alignmenl and exert only HEsnsHaehe Lirunshon Cheuehufl Uekhmai IewUHUm KALD Mni" S0 N 'L50 mm S0 mm 65 N SOT



Answers

Both pulleys are fixed to the shaft and as the shaft turns with constant angular velocity, the power of pulley $A$ is transmitted to pulley $B$. Determine the horizontal tension $\mathbf{T}$ in the belt on pulley $B$ and the $x, y, z$ components of reaction at the journal bearing $C$ and thrust bearing $D$ if $\theta=0^{\circ} .$ The bearings are in proper alignment and exert only force reactions on the shaft.

And this problem. We have a shaft with a couple pulleys on it. And then there's some belt around those police with forces in them. Uh, so again, in this problem, they actually tell us to set the angle the wrap angle of the larger fully, instead of being at some angle data to just set to be zero so that they're both coming parallel to one another belt. So it's wrapped 100 degrees. I saw that in general so that the belt comes off at an angle. They that which means that the point where where it is leaving the holy is ridiculous. That and that's assuming that the bill is perfectly flexible, which is probably a reasonable exemption that pounds and how tight it is so that we don't have something like this. So I saw that generally, with the terms of data, we're Joan is good because then we can use that to solve that problem. The set that 45 degrees. So we have lots of forces here because there is three constraint forces at E, which is the origin. We should realize quickly that this component is going to be zero because there's no other no applied forces in the direction. So we know that this and we have that's our origin. And then at the other end of the shaft way have constraints in the Y direction. And it is 750 millimeters from the origin in the X direction. The applied load in the no, it's a 50 Newton blow, as in the book from the top of the larger pulling, it has a direct. It has a magnitude at three, which is 15 and then a direction given by this unit director. The position of this force is 200 millimeters in the X direction and then its particular to the force director in Y Z playing. So that is minus our one the radius that fully sign it. Data are one co sign of things Now the in the bottom belt of the lower belt coming off the big, larger police. We just have a force in the and the Y direction because that belt is in the wind direction and what has a magnitude key and its position is 200 millimeters in the X direction and minus the radius. I love the poorly in the Y direction now looking at the other. Next quote, the smaller pulley. We have a force. Both of these. These forces are in the Z direction. So we have the belt. So it's a wrapped 100 degrees and the one force is minus 65 Newtons in the direction and the other is minus 80 direction. And the the smaller pulley is located 450 millimeters from the origin in the X direction and it has a radius of eating. So we just have a whole lot of forces. Here we have. We have six forces the positions to each of those forces. We have 12345 unknown and we'll see that, uh, one of the one of the moment equations is trivially satisfied. And that is, but that wouldn't know. It's Oh, no, sorry, we have an extra. Now we have 600 so we have six equations. Six and it's actually the force in the X direction. That's basically just gonna tell us that that component is zero because you can see we have no other for its components in direction. So in the first case, where said where told data equals zero and we can do that here and we can crank through forcing more balances. Six Equation, six unknowns and crank through them and we find again The F one X is zero f one y minus 79 points to live in a one C it's 58 at the other constraint we have a force that has a magnitude of to minus 28.8 degree, 20.8 Newtons in the Y direction and 87 Newton's in the sea direction. And then, in this case, the attention keep this thing in equilibrium is going to be 58 news. Now, if we set the if we set the angle here 45 degrees What? Actually, if we saw this in general, what will see generally is that the P is independent of doesn't depend on what day it is. Basically, that is because the torque generated from that belt is always gonna be the same. Because there this radio rector is always perpendicular to the force. So no matter what that angle waas, we're gonna have a moment that defined by the magnitude of that force times the radius of the holy. So in the end, t winds up being independent. And so we see that if we just plug in 25 degrees, we get that he is again 58. Now. These other things change, obviously. And now we have minus 68 point five Newtons for one. Why and 32.11 z on the other constraint we cannot minus 24.9 Newton's in the Y direction at 77.6 Nunes in the Z direction. Um and that would be for problem 40 44 84.

So is that Sarah was. We know everyone is equal to our one Double one, Wilson. That V two is equal to R two terms w chill. And this everything that we know is something one is equal to 32 So we can replace the to. To say that well, are one double one is equal to, aren't you? W two And so then we know by both sides there are to to get us are one and the vie politicised by simply 12 guests are one over. Our two is equal to wh you over doubly one.

Applying the creation off motion. So I'm applying the creation off motion to deter mine the angular acceleration. So just look at it carefully. We can writes a mission off I'm not is equal toe I not into Alfa now in the next step taking anti clock moment as positive so I can write equation like this. So this equation is very important in solving the problem further. So I just put all the values here. So in the next step, I will calculate this value. So on further going, I just calculate the values so we can write. I'll find 2. 25 into 0.25 per square is equal to 33.75 in the next. Steve, we get Alfa is equal to 33.75 by this and on solving we get Alfa is equal to this answer

But a off the human problem. The leader Speed off a port on the belt. One belt one is given by everyone is equal to our a times Omega, eh? This is 15 72 times 10 radian per second. This uses 1.5 times still power too. Ah, centimeter per second. But be the angular speed off the coolie be Willie B is given by our be omega Be usually called to our a homemade I eat from here Omega be will be called to our a omega a divided by r b So student rallies we get Omega B to B 15 divide by 10 times 10 Excuse us 15 Radio 15 Radian per second. Since the two police are urgently attached to each other, the cooler speed off the pony be dish be dish is the salmon is to be that is omega be dish will be then 50 Canadian per second Rdd linear speed off a point on the belt belt too. He's a me too musical to R B. Who may God be dish. There is a total of five times 15 medians. This is 75 son de Viteri per second partied angular speed off the police. See, policy is given by then. Our C you may go see is a call to our Derby Omega Be dish from here. Omega cuz, Kal toh R b omega the dish divided by our seat. So this is five divided by 25 times 15 radian per second. Excuse us three radiant per second.


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