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

[Chubigans]

Homework Statement

Homework 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"

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]

Homework Statement

Homework 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"

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.

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]

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

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 doesn't make any sense! Please help me solve it!

 

[PhanthomJay]

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 doesn't make any sense! Please help me solve it!

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 don't 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]

Can somebody verify this!? I'm not about to turn in homework questioning my textbook!

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