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The elevation of the platform is controlled by two identical mechanisms, only one of which is shown. A load of 1200 lb is applied to the mechanism shown. Knowing th...

Question

The elevation of the platform is controlled by two identical mechanisms, only one of which is shown. A load of 1200 lb is applied to the mechanism shown. Knowing that the pin at $C$ can transmit only a horizontal force, determine $(a)$ the force in link $B E,(b)$ the components of the force exerted by the hydraulic cylinder on pin $H$.

The elevation of the platform is controlled by two identical mechanisms, only one of which is shown. A load of 1200 lb is applied to the mechanism shown. Knowing that the pin at $C$ can transmit only a horizontal force, determine $(a)$ the force in link $B E,(b)$ the components of the force exerted by the hydraulic cylinder on pin $H$.



Answers

The hydraulic system of a backhoe is used to lift a load as shown in Figure 11.48 . (a) Calculate the force $F$ the slave cylinder must exert to support the 400 -kg load and the $150-\mathrm{kg}$ brace and shovel. (b) What is the pressure in the hydraulic fluid if the slave cylinder is 2.50 $\mathrm{cm}$ in diameter? (c) What force would you have to exert on a lever with a mechanical advantage of 5.00 acting on a master cylinder 0.800 $\mathrm{cm}$ in diameter to create this pressure?

Told. The hydraulic system of backhoe is used to lift a load as shown in figure 11.48 So I've reproduced the backhoe here. There's a force from the hydraulic system acting here. That's a distance L one from our pivot point at a There's the weight of the arm, which, actually with center of mass. That's a distance l two from a. And then there's the way of the payload in the bucket. That accident distance L three from the pivot point. No, the point of a is fixed, so there's some of the moments about that. Point is zero. And if we take counterclockwise is positive, we wind up with our moment. Balance is the force from the hydraulic system times L and the force from the hydraulic system X perpendicular to the moment arm for the weight and the load. Do not at public a killer, so we need to take the side beginning to get the component that is perpendicular by taking a sign of this angle. So we get the weight of the arm times. A sign of that angle is the component in this direction. Kind 02 It's in the clap eyes direction. So we have a minus sign, likewise, for out for the weight of the payload. But now we have all three. And again we have a minus. Sign here because it's acting to rotate the bucket, the arm clockwise so we can solve for elf. And we get just this simple equation for our the force acting on hydraulic cylinder. We can start plugging in some numbers, so we have the have the length ratio l one over to over one. The weight of the arm is its mass times gravity and then sign the angle that the arm is acting, um, relative to the article is 30 degrees. And so we have our three over l one times the weight of the payload, which is 400 kilograms times t and then again, sign of 30 degrees. Now, if you plug everything in, we wind up with a force of 13.8 killings. If we figure out what the pressure in the slaves under is, well, that's just the force acting on the bucket arm divided by the area of the slave so under. So we have given that the the radius of the diameter of the slave cylinder is 2.5 centimeters, so it's one over its area. Is this value here multiplying it times the force and we get 28.1 killer pass scales. Now we're told that we have a a lever arm pushing on the master cylinder and that this lever arm has a mechanical advantage of five, meaning that this distance here is gonna be 1/5 of this distance here. You know the pressure in our hydraulic fluid In here? There's just 28.1 killer Pascal's so we can figure out what forces acting on our are master cylinder. And that is simply the pressure in the hydraulic fluid times the area of the master cylinder were given that the diameter of the master cylinder it is 2.8 centimeters. And so you plug that in and we get that their force acting on the master cylinder is 14. Point is one is 1413 Newtons, And so then, if we have a mechanical advantage of five, the force acting at our at the other end of the lever arm is 1/5 of that, and that is 283 Newtons and in fact this guy should be drawn the other way

We have force P acting along a member of a hydraulic cylinder were given the X component, or what I have. A label is a component of that force, which is perpendicular to member a B, and that's six under dunes. We need to find the magnitude of Force P, and it's vertical component. Or in this here I have labeled as people. Why so first, we we need this angle right here. So if we call angle favor, well of that angle is going to be 45 degrees minus 30. Hopefully you can see that, so that will be 15 degrees. So we have p of X, and we know that P of X is equal to P has the coastline of 15. So P is equal to Kiev X, divided by the coastline and 15 and that is equal to 621.2 news and then for the vertical component is just p of y is equal to p sign of 15 and that is equal to 160.8 Newtons

We have a force p acting a long hydraulic member and were given the component that runs perpendicular to member ABC, which is 750. Nunes. I've made that my X axis. We need to find the magnitude of P. And we also need to find the vertical observed the component that runs parallel to remember ABC, which I have marked his piece of. Why? So we can start with P, and we know that P of X is equal to p times a coastline of Fada and you could do a little bit of geometry and find out favor is equal to 70. That's all from the information we're given. So the ranges for P P is equal to p of X overpay co sign data and P be equal to 2100 90 Nunes and for the y component last just p times this sign of Fada. And that is 2060. Nunes

I'm going to draw the diagram, but put an angle in the diagram. Um, this is the point. A, uh, be and see. Not gonna worry about the other bar yet. Um, there is an angle with the vertical. I mean, with the horizontal. And I'm gonna call that angle data. And so at point A Why at point A is going to be, um, the distance from the pivot, which is 16 inches times the sign of theater. Why at point c is going to be, um that's eight inches. Oh, by the way, uh, if I said this to be my origin and then this why would be negative? Um, this why? It sees going to be positive, and it's going to be eight signed data now. We have other points f and E. Um, but they're going to move because d slides, they're going to move the same as, Ah, point c. And so, if i g o if I get DE y for C, that's gonna be the same as for e and F. So, um, eight co Cynthia de theater. So this applies Teoh e and F also de y a equals negative 16 kusa inthe Ada defeat. All right. So d u, which is zero is going to be. He is in the negative direction, and the displacement is also in the negative direction. Negative 16. Who sent data defeat? All right. And then e and F are both undergoing the same displacement. So I'm just gonna add them together. They're both in the negative direction, So plus, uh and e, there's £100 and f There's 100 £50. 100 plus 150 is 250 um, times distance. This is positive because point c is going positive. Displacement is going to be positive. Eight. Hussein Fada de Fade. Ah, he already wrote equal zero. I can equal zero again. Cancel out. Could sign data di Fada and I get 16 p equals eight times 250 2000. Divide by 16. That's not right. And I get 125 hands


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