Calculating the moment about an axis?

[mneox]

Homework Statement

Hi friends, I have uploaded the problem and picture at the link below. Please take a look.

http://img64.imageshack.us/img64/4753/sam0247i.jpg

Homework Equations

F(vector) = F(cos$$\alpha$$i + cos$$\beta$$j + cos$$\gamma$$k)
Ma = u_a(vector) $$\bullet$$ M_o (vector) = u_a $$\bullet$$ (r x F)

$$\bullet$$ is supposed to denote dot product. Sorry my latex sucks.

The Attempt at a Solution

Okay so for this problem, I currently have:

F = 30 (cos60i + cos60j + cos45k) = (15i + 15j + 21.2k)

Now I know I need to find the unit vector u, and position vector r. How do I find these? From the examples I've done, I've kinda known what to use for vectors u and r, but this example is different from the ones that I've worked on previously.

The force for this one is extending right from origin, whereas the problems I've previously worked on had forces away from origin.

So how would I find the unit and position vectors for this problem? And how can I determine the coordinate direction angles to produce the max moment and the max moment itself? Is there some sort of equation?

Thanks for your help and time. I'm not looking for answers here, but just something to get me rolling cause I'm stuck and I really want to figure this out but don't know how!

 

[tiny-tim]

hi mneox!

(have an alpha: α and a beta: β and a dot: · and try using the X² icon just above the Reply box )

Now I know I need to find the unit vector u, and position vector r. How do I find these? From the examples I've done, I've kinda known what to use for vectors u and r, but this example is different from the ones that I've worked on previously.

The force for this one is extending right from origin, whereas the problems I've previously worked on had forces away from origin.

So how would I find the unit and position vectors for this problem? And how can I determine the coordinate direction angles to produce the max moment and the max moment itself? Is there some sort of equation?

u is the unit vector along the pipe (so that's j)

r is any vector from the line of the force to the pipe …

the reason you can use any vector is that you're only interested in (r x F)·u, and if you increase r by a multiple of F or of u, it makes no difference

 

[mneox]

Thanks for the reply tiny-tim! I think I'm grasping it now, but what do I do about the maximum moment part? How would I go about doing this?

ps thanks for the nifty copy and paste lol

 

[tiny-tim]

Thanks for the reply tiny-tim! I think I'm grasping it now, but what do I do about the maximum moment part?

you need to maximise the value of u.(r x F), keeping u r and the magnitude of F constant, and varing only the direction of F …

which direction will do that?

 

[rwisz]

Calculating the moment about an axis involves finding the product of the force and the distance from the axis of rotation. In this problem, the force vector is given as (15i + 15j + 21.2k) and the axis of rotation is not specified. To find the unit vector, you can use the formula u = F/|F| where |F| is the magnitude of the force vector. In this case, |F| = √(15^2 + 15^2 + 21.2^2) = 30.3. Therefore, the unit vector is u = (15/30.3)i + (15/30.3)j + (21.2/30.3)k.

To find the position vector, you can use the distance formula r = √(x^2 + y^2 + z^2) where x, y, and z are the coordinates of the point where the force is applied. In this problem, the force is applied at the origin, so the position vector is r = (0i + 0j + 0k) = 0.

To determine the coordinate direction angles, you can use the formula cosθ = u(dot)i where θ is the angle between the force vector and the x-axis. In this problem, the force vector is in the first quadrant, so the angle between the force vector and the x-axis is 60 degrees. Therefore, the coordinate direction angles are cosα = cos60 = 0.5 and cosβ = cos60 = 0.5.

To calculate the maximum moment, you can use the formula M = r x F where r is the position vector and F is the force vector. In this problem, r = 0 and F = (15i + 15j + 21.2k). Therefore, the maximum moment is zero.

I hope this helps you understand how to calculate the moment about an axis. If you have any further questions, please don't hesitate to ask. Good luck with your problem!