# Basic Statics

by 00PS
Tags: basic, statics
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
 exam 11.pdf (194.4 KB, 11 views)
 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/$$\sqrt{106}$$)i - (3/$$\sqrt{106}$$ )j - (9/$$\sqrt{106}$$ )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. :)
 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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