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Three stage lights are mounted on a pipe fixture as shown. The lights at $A$ and $B$ each weigh 4.1 lb, while the one at $C$ weighs 3.5 lb. The fixture weighs 6 lb and has a centroidal radius of gyration of 24 in. The centroid of the pipe can be assumed to be 42 in. from point $D$. If the connection at $E$ fails so that the lights and fixture rotate about point $D,$ determine the angular acceleration of the system immediately after the failure at $E$. Assume point $D$ can be treated as a pinned connection and the lights can be modeled as particles.

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Physics 101 Mechanics

Chapter 16

Plane Motion of Rigid Bodies: Forces and Accelerations

Section 2

Constrained Plane Motion

Motion Along a Straight Line

University of Washington

Hope College

University of Sheffield

University of Winnipeg

Lectures

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In physics, kinematics is the description of the motion of objects and systems in the frame of reference defined by the observer. An observer has to be specified, otherwise the term is meaningless.

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In mathematics, a position is a point in space. The concept is abstracted from physical space, in which a position is a location given by the coordinates of a point. In physics, the term is used to describe a family of quantities which describe the configuration of a physical system in a given state. The term is also used to describe the set of possible configurations of a system.

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in this problem rates off each light eyes given in this hour in the problem on the that is read off the light off E Andre Dr V is £4.1 while the leadoff see is 3.5 and we have to find find the point off. Find the point of application off the resultant equi valent Fourths, and that that can call that will cause the same effect that these systems are causing. So basically, what we have to do that Let's see, This is our Ron. They're at the point. A one forced off 4.1 point is acting at point B, another portion off. Same magnitude is acting. We're going to win park on and at point C. The hard four off magnitude 3.5 point is acting on. We have to replace the system by an e component system. There are equal in pleasers. A resident force should act from the point de. So let's say this was the point D. So it's distance is etc okay. And in the first problem, they have provided the distance smartly on the value of these 25 inches. Part of question. So we're solving here. The first problem. Onda. So we can quit the post op a liquid the forces in these two systems. So this was the real system and this is the covenant system. So by force balance in vertical direction are comes out to be four point by Sorry, 4.1 this 4.1 less, 3.5 on it inside Toby seven 11.7 point. All right now for the calculation of the position or the point of application off this equivalent force on the line E. For that, we can balance moment about any point. Let's say we're going to consider the moment about pointed D, So if you can call it moment about point of the post case, so it will be a since it is at a distance of 10 in so moment because of this port point, when foreign force will be 4.1 multiplied by then in clockwise. So I'm considering here clockwise to be positive so again you can to the anti clockwise to be he's not going to affect our reason on the second term, so it's a distance. Perpendicular distance will be particle, and that will be 44 So four point one are deployed by 44 again, This will cause the clockwise couple on the plus three point by multiplied by assistance particle bless the distance is given us inputs Part 25 incident. So it comes out to be 69 on this must be will do the moment caused by caused by this equivalent force about the same point. The and that will be our modified by value of our we have calculated here so we can get the value of the piece comes out to be 4.1 more deployed Britain less 4.1 murder 40 less, 3.5 multiplied by 69 divided by all and which is 11.7. So if you solve this it comes out to be 39 0.16 39.6 not in second part If they're asking the value off the that is what should be this distance So that, uh, it should be the value of the S O that are the equivalent Pores are the result In there the earthen force passes through the middle point off the six and e since e so we can are dry here, Uh, be easier to understand the scenario, what they are asking. So it's second part. They are saying that this was the and this was on this. This 4.1 born force is acting at Point E. Another 4.1 point force is acting at point B and that hurt See point by point forces acting at Point C and they're asking to find distance. And that is the distance between B and C that is smarty. In such of that, the resulting pours passes through the midpoint off the lying E. Since length off the DEA's it in Queens, it means that the point of application off this sport from the distance of this distance would be 42. No, this is already so any command system, if violence, the force so are comes out to be submission off all these forces so we can get the value of our which will be one point less 4.1 last 3.5 on this comes out to be £11.7 off this team. No other course, no extra forces going to work here. That's why this seemed to dust off the previous part a year so that it doesn't moment. Resident force. I will be 11.7. Phone. No. If you talk about the moment that it's about point D. So moment about point will be. Since this is a fixed point, it's distances fixed and that it then Egypt's So it will be a moment will be all 0.1 modified button less moment because of the second, that will be 4.1 like I Okay, bliss this distance plus and see here in Bagram less plus moment. Because of this 3.5 that point Marty Black by 44 plus d and this must be the This must be equal to the moment because of this Valent board, that is 11.7 were deployed. 40 eso Here in this equation there is only one variable that is the and we can get it, Get it value. So he comes out to be. We saw this 33 point systems on with 33.1. So in West Part we got the distance that be 39.6 inches. So the island talent is a poor will pass at a distance off 39.6 inch from the point be towards the life side and in second part, our on cities started. 3.1 in means that if the distance between the Force B and C is 33.1 in, then the equal or system, if we draw it, then it will pass through the midpoint off the six and

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