Old Exam: Struggles with Questions 2 and 3

[00PS]

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?

 

[vineroon]

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 F_x, F_y, and F_z components for the force F and you can find theta_x, theta_y, and theta_z forms by:

theta_x = cos^-1(F_x/F)

theta_y = cos^-1(F_y/F)

theta_z = cos^-1(F_z/F)

I hope this helps. :)

 

[00PS]

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.