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Basic Statics

by 00PS
Tags: basic, statics
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00PS
#1
Sep25-08, 01:34 PM
P: 29
the attached file is an old exam my professor sent out. i my struggles were with 2 and 3.

number 2:
I am having trouble calculating the moments and picking a vector for r in the equation M=r x F which reads the cross product of the r and F vectors. Also to find the thetas, for part 2, can I use the dot product to find the angle between them and thus theta?
Attached Files
File Type: pdf exam 11.pdf (194.4 KB, 11 views)
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vineroon
#2
Sep25-08, 11:33 PM
P: 12
For problem 2, r is just the distance from O to a point in the line of action of force F. In other words, this is just the distance from O to B. I believe this is <4, -3, 1.5>.

I'm not sure as to how you would use a dot product to find theta x, y, and z. However, the easiest solution here is to break your force F down into components (ijk form). You can do this by taking F times the unit vector of the force. The unit vector is just the direction components of the force divided by the magnitude of the direction components.

In other words:

F[(4/[tex]\sqrt{106}[/tex])i - (3/[tex]\sqrt{106}[/tex] )j - (9/[tex]\sqrt{106}[/tex] )k]

This will give you distinct Fx, Fy, and Fz components for the force F and you can find thetax, thetay, and thetaz forms by:

thetax = cos-1(Fx/F)

thetay = cos-1(Fy/F)

thetaz = cos-1(Fz/F)

I hope this helps. :)
00PS
#3
Sep25-08, 11:39 PM
P: 29
thanks. I sort of figured it out after consulting a friend. To calculate the moment you evaluate a determinant of i,j,k being the first row, r components being the second, and F components being the third. As for the thetas, find the unit vector and set the components equal to arccosine like you said. This way is a bit easier because the hypotenuse is 1. This seems to be the correct way to do it.


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