Question

A 1600 lb crate is supported by three cables as shown determine the tension in each cable

Answer 1

Answer:

So in this problem way have a great, um supported by three tables. As you can see in the figure in the book and the points of interest are the point where the cables meet Thio support Create on That is, uh let's see here 60 inches below in the Y direction below the origin. Um, these three points where the cables attached to the ceiling and those all have are in the xz plane, so be attach is in minus 36 in the inches in the X direction and minus 27 inches in the Z See cable. A C attach is at 32 inches in the Z direction and cable a D attach is at 40 inches in the X direction of minus 27 inches in the Z direction. So, again we have forced from each of these tables, has the magnitude and the direction where we can find the unit vectors from these position vectors, just like we've done in all the previous problems. And let's see, here we have the load. We're told that the load weighs £1600 and it is in the minus y direction and so we know at point a where all of these forces meat has to be. Some of these forces has to be equal to zero the vector sum, which means that each of the components has to be equal to zero. So we take the X component and we get zero point uh minus 0.48 f A B plus your 0.5 to f A B equals zero. So f A C should not have a component in the X direction and so see Yeah, so you can see our A C minus. R A B does not have a component in the X direction. So Unit vector in F A c. This has no component in the X direction, so that gives us one equation and two unknowns. Now we can dio look at the Y direction on we get zero point f A B 0.8 f a B plus 0.78 f A d. But 0.88 f A c then minus this part minus 1600. And that has to be zero. And so now we have two equations and took three announced. So we look at the Z direction and we get minus zero point 35 f A d plus 0.47 f A C minus 0.36 f A b and that has to be zero. So now you have three equations and three unknowns, and we can crank through the algebra and we get that F A B is £571. F A c is £830 on F A. D is £528 Yeah.