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Referring to Prob. 10.45 and using the value found for the force exerted by the hydraulic cylinder $B D,$ determine the change in the length of $B D$ required to raise the platform attached at $C$ by 2.5 in.
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Physics 101 Mechanics
Method of Virtual Work
University of Michigan - Ann Arbor
University of Washington
University of Winnipeg
In physics, work is the transfer of energy by a force acting through a distance. The "work" of a force F on an object that it pushes is defined as the product of the force and the distance through which it moves the object. For example, if a force of 10 newtons (N) acts through a distance of 2 meters (m), then doing 10 joules (J) of work on that object requires exerting a force of 10 N for 2 m. Work is a scalar quantity, meaning that it can be described by a single number-for example, if a force of 3 newtons acts through a distance of 2 meters, then the work done is 6 joules.
Work is due to a force acting on a point that is stationary-that is, a point where the force is applied does not move. By Newton's third law, the force of the reaction is equal and opposite to the force of the action, so the point where the force is applied does work on the person applying the force.
In the example above, the force of the person pushing the block is 3 N. The force of the block on the person is also 3 N. The difference between the two forces is the work done on the block by the person, which can be calculated as the force of the block times the distance through which it moves, or 3 N × 2 m = 6 J.
In physics, mechanical energy is the sum of the kinetic and potential energies of a system.
The hydraulic cylinder $B …
The position of boom $A B …
At the instant under consi…
Okay, So we are looking at Yeah, Chapter 10 problem 10.56 And this problem does reference. Mm. Problem 10.45 and uses the answer from this question. So I would recommend doing problem 10.45 1st, but I'll go ahead and use the answer that I got for this problem. Okay, So if you're looking at your book right now, um you should be looking at a construction lift. And the first thing that we're going to do is draw our free body diagram. So the lift looks somewhat like this. This is going to be our ride. And we have our basket here with our construction workers. This is going to be point see up here, point B right here. Point a right here. And then we have another right here, and this is going to be point D. So this is what we're looking at. The problem asks, what is the difference in height of B D. That results in the lifting of point C by 2.5 inches. Mm. So we want this to go up 2.5 inches and we want to know how much does this point b d have to increase for C to go up 2.5 inches. So the first thing that we're gonna do is we're going to draw all of our forces acting on this body, ABC. So from the problem, it states that the construction workers and the platform both weigh a total of £500. And then we also know that this supporting Rod B. D, uh, has forces that act in both directions. So we have the rest of the construction life down here, and then we have our forces that act outwards on this rod, ABC and then down here at Pindi. And we can just call this force of B. D. And this is the answer that we found from problem 10.45 you'll have to find another video to help you solve that one. But the answer that I got from solving it myself, I got the force of B D to equal £17,452 so we'll use that later. So for good measure, we'll give ourselves an access here. This will be your X axis. This will be our Y axis. And then we are going to calculate the differences in height. So we know we want an increase in height at sea, which is the 2.5 inches here. And we also know that the height between B. D is also going to extend. And we're also going to assume that this point ABC, that that Rod does not change so we can do length of a C equals zero. That's difference in length. That does not change. We know the difference of height and BD is going to increase. And we know the height difference of where point C is in the Y direction is also going to increase Mhm. So with this information, we can find what we're looking for. Mhm. Since we know that the length of the arm A C doesn't change, we can look at the rest, um, in terms of length. So what we're gonna do is we're going to add up all the forces in length that, um that are, with respect to this Rod a C. Our first equation is going to look something like this. We're going to look at the forces on this rod a c. Mm hmm. So we have the distance of a C equals zero, and we're going to add up all the forces. So first we have our force of C plus, the distance were increasing, so that's going to be 2.5 inches plus the forces of the rod B D times the distance that that increases or changes. And that is all equal to zero. Yeah, so let's now do some plugging in. Also, I wrote this over here is if right what I see. Okay, so we know the force at sea. We just plug in now. So we know the force of C is £500 and that is gonna be negative since it's facing down. Mm hmm. Then the force that I found for the Rod Beattie is going to be 17,000 or 52 mhm times. The length difference equals zero. And this right here is what we're looking for. And since it's our only unknown, we can easily solve for the length change in Rod B. D. So for this I got change in length is equal to zero point 0716 inches. So that is the difference in length of B D. That is needed to raise points, see 2.5 inches and there should be consistent with both signs and variables.
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