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(II) A 75 -kg adult sits at one end of a 9.0 -long board. His25 -kg child sits on the other end. (a) Where should the pivotbe placed so that the board is balanced, ignoring the board'smass? (b) Find the pivot point if the board is uniform andhas a mass of 15 $\mathrm{kg} .$

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A. $2.25 \mathrm{m}$ from adultB. $2.54 \mathrm{m}$ from adult

Physics 101 Mechanics

Chapter 12

Static Equilibrium; Elasticity and Fracture

Equilibrium and Elasticity

Cornell University

University of Washington

Hope College

Lectures

04:12

In physics, potential energy is the energy possessed by a body by virtue of its position relative to others, stresses within itself, electric charge, and other factors. The unit for energy in the International System of Units is the joule (J). One joule can be defined as the work required to produce one newton of force, or one newton times one metre. Potential energy is the energy of an object. It is the energy by virtue of an object's position relative to other objects. Potential energy is associated with restoring forces such as a spring or the force of gravity. The action of stretching the spring or lifting the mass is performed by a force which works against the force field of the potential. The potential energy of an object is the energy it possesses due to its position relative to other objects. It is said to be stored in the field. For example, a book lying on a table has a large amount of potential energy (it is said to be at a high potential energy) relative to the ground, which has a much lower potential energy. The book will gain potential energy if it is lifted off the table and held above the ground. The same book has less potential energy when on the ground than it did while on the table. If the book is dropped from a height, it gains kinetic energy, but loses a larger amount of potential energy, as it is now at a lower potential energy than before it was dropped.

04:17

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ground first. So here small M is the most off detained capital. M is the mass off the adult on envy is the miles off the world. Oh, you have small end to the 25 pages Capital and Hands 75 G's The Len Constable, the total land capital L It's given to the night he does on DDE. Mass. Of the board is 15. Gettys. My the pivot should be pleased so that the Net talk on the board is CEO or the board is invitational equilibrium. Let's say that F B is the upward force at the bigger point. Ah, but it exerts no talk about the bigger point because it passes through that point. Now we calculate the talks about this point. I'm assuming that positive, dark present clock on the clockwise direction No, in order to make this problem a little simple, as you know that for the first part, you have to ignore the marks off the boat. And in the second part of the problem, you have to consider envy. Uh, but to make this problem a little bit simply, I'm going to consider this mass and the life Oh, an equation for X, which is the distance off the pivot from the other ex. After diving X, I'll get an expression for ex basically having all these perimeters. Then for the first part where we have to ignore the moss, I can just plug in bait of the equal to zero because we're ignoring it on find the value effects. So let me just start Ah, doing it so again, that a clear idea of what I want to say wants to be a constituting. They're taking the talk about the favor point on the stark. The next talk should be CEO because, ah, the board is at equilibrium. So about this point, it's a water. The talks ah, likely have. So we have m G capital M G dimes. Thanks. That is giving. They found it, so that should be positive. Then we have a clockwise stock from months of the wood on the perpendicular. Distance from this force is hello, hello Over to mine sex. Plus it's so this is also ah, clock, one stock. So there's a bloke Let's start from the months off the child on this is MG times and so l minus X because that's the distance from the people and the start with sequel Placido. Now from here we can get an expression for X. It's indicates the position off the river. No X. It's because I do small m plus capital it and over too times Oh gosh Capital and less small lamb plus And we basically the d n a minute. That is the total mass. So now let's keep in mind this a question. So this is the question. It's going to the question one that we will be using for both first and second part. Now, for the first part, we have to ignore the minds of the board. So what they're going to do is sec nd to be equal to zero or simply ignore all the domes that have anybody in them. So finally they will get X to be Quito end overs capital m small am times with blood. The values into that, a question that we have here and we get extra the equal do to the point to five meter. Make sure you in you indicate what is X So basically this is the distance from the other. Now, for the second part, we have to consider it must be so. We will just use this a question and block all unplugged older values that we have. So in that case, let me just right that a question again that we got and this will come out. Toby, do point. I fooled me from the note. Now, why I found by I took this approach is ah, because this reduces Ah, lot of calculation that you might have done, uh, in case you took you choose toe sol for GNB separate so far, it would have right the topic question without taking the mask off the board. We have got this equation and then solve it. And then again for the second part, right? Another question for X taking the mass in the inter consideration. So the extract calculation that you might that you would have needed you know, that Raj is going now. But either way, you should give the same lesson as this

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