STATICS couples problem (I solved it but it doesnt make sense!)

Chubigans

1. The problem statement, all variables and given/known data




2. Relevant equations
M = r x F, where r is "a vector directed from the line of action of one of the forces to the line of action of any other force"

3. The attempt at a solution

Well, for the 250 lb couple the r = {3i - 4j - 2k{, F = 250 {3/5i - 4/5j}
M = {-400i - 300j} (I verified this by taking the moments individually)

For F1, r = 3i and F = f_yj
so M = 3F_y*k

For F2, r = {-2k} F = {f_xi} so M = {-2F_xj}

When we sum the moments, we get {-400i -300 - 2F_xj + 3F_yk }
The x component can never equal zero!

There are two possibilities: I'm misreading the diagram, I'm missing something entirely, or I don't understand the couples idea of getting the vector r between two forces. Please help, i've been doing this for over 5 hours now.

PhanthomJay

You deserve a break after 5 hours! What I see as the problem, is that you are trying to use the cross product rule for determining moments, and in 3D, that is one bear of a problem. Instead, you should break up the given couple (250*2 = 500 ft-lbs) into its components about the x and y axes. Once you do that, try summing moments about the x and y axes separately. That will simplify your time spent to 5 minutes, if you do it right

Chubigans

But Jay i have a question, What direction is F2 in? Is it entirely in the X direction? And what about F1? Is it entirely in the negative y direction? This homework is due tomorrow! It doesnt make any sense! Please help me solve it!

PhanthomJay

Wow, sorry, you are quite sharp after 5 hours, I looked at the problem quickly, and missed the fact that as shown, +/-F1 is directed along the y axis, and produces a ccw torque about the vertical z axis. Since the other torques do not have any torques or torque components about the z axis, there is no way the sum can be 0, so you are 100% correct. I guess you can state that result in your homework, and maybe get some bonus points.

Chubigans

Can somebody verify this!? I'm not about to turn in homework questioning my textbook! The answers in the back are F2 = 200 and F1 = 150. It seems impossible. help?

nvn

Chubigans: I worked the problem quickly, and got an answer. Post your answer, and then I can tell you whether or not your answer matches what I got.

Chubigans

My answer was sum of moments = {-400i + 300j - 2F2j + 3F1k} which never equals 0

I already emailed my professor telling him it was impossible, hope i dont look like a dumbass!

nvn

But that doesn't answer the given question, which is asking for F1 and F2. What is your answer for F1 and F2?

PhanthomJay

why not? If you're wrong, so be it, and move on to the next problem; but if you're right................