Question

I need help with geometry/ trig problem.... see attachment please

Answer 1

Not sure how they are finding "d". All they say is "through trigonometry". I didn't do well on my last test and it wasn't because I didn't know the concepts of this class (statics) it was mainly because I couldn't do things like this so I actually need an explanation if you are able. Thanks in advance

Answer 2

here we have to apply this vector equation:
\[{\mathbf{M = OP \times F}}\]
where \(P\) is the application point of force \(F\)

Answer 3

I am actually ok with the ideas in this section.... I see what your trying to say, that the cross product of the position vector and the force vector is the moment about the point. I don't have a problem with that. In this problem they want you to use the M=Fd where d is the moment arm. I can't figure out how to dissect the diagram in a way that I can find d. So I am trying to take a step back and understand how they did it. All they said was "the moment arm d in the figure can be found from trigonometry. I am good with trig, but I don't see how they are doing it.

Answer 4

we can compute such vector, developing the determinant of the subsequent matrix, along the first row:
\[\left\| {\begin{array}{*{20}{c}}
{{\mathbf{\hat x}}}&{{\mathbf{\hat y}}}&{{\mathbf{\hat z}}} \\
{d\cos 30}&{d\cos 60}&0 \\
{F\cos 45}&{ - F\sin 45}&0
\end{array}} \right\|\]
where \(d=3\) and \(F=5\)

Answer 5

as we can see, only the \(z-\) component is different from zero

Answer 6

They are doing two things in the diagram :
1) extend the force vector
2) draw a perpendicular from point O to the force extended force vector; the length of this perpendicular is \(d\).

Answer 7

@ganeshie8 my thought was that they give me an angle 75 degrees and it is on a right triangle so the other angle between the 3m pole is 15 degrees. Is it valid to use the law of sines when there is a right triangle? If so I thought I could find d that way. Somehow that is not what I think they did. I tried drawing this out and using simple concepts to find something that helped but I couldn't come up with anything. If you could show me visually how they did this I would greatly appreciate it