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

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In summary, the conversation is about a homework problem involving the determination of moments using the cross product rule. The conversation includes calculations and questions about the direction and values of the forces involved. The final question is asking for verification of the given answers.
  • #1
Chubigans
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Homework Statement



2rgpfur.jpg

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 = fyj
so M = 3Fy*k

For F2, r = {-2k} F = {fxi} so M = {-2Fxj}

When we sum the moments, we get {-400i -300 - 2Fxj + 3Fyk }
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.
 
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  • #2
Chubigans said:

Homework Statement



2rgpfur.jpg



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 = fyj
so M = 3Fy*k

For F2, r = {-2k} F = {fxi} so M = {-2Fxj}

When we sum the moments, we get {-400i -300 - 2Fxj + 3Fyk }
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:wink:
 
  • #3
PhanthomJay said:
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:wink:

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!
 
  • #4
Chubigans said:
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. :rolleyes:
 
  • #5
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?
 
  • #6
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.
 
  • #7
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!
 
  • #8
But that doesn't answer the given question, which is asking for F1 and F2. What is your answer for F1 and F2?
 
  • #9
Chubigans said:
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...
 

1. What is the concept of "STATICS couples problem"?

The "STATICS couples problem" is a concept in physics that deals with the equilibrium of a system of forces acting on a rigid body. It involves analyzing the balance of forces and moments acting on an object to determine its stability and motion.

2. How is the "STATICS couples problem" solved?

The "STATICS couples problem" is typically solved by using the principles of statics, such as Newton's laws of motion and the concept of torque. The process involves setting up and solving equations to determine the unknown forces and moments acting on the object.

3. What is a couple and how does it relate to the "STATICS couples problem"?

A couple is a pair of forces that are equal in magnitude, opposite in direction, and not in the same line of action. In the "STATICS couples problem", couples play a significant role in determining the rotational equilibrium of an object.

4. What are some common mistakes when solving the "STATICS couples problem"?

One common mistake when solving the "STATICS couples problem" is incorrectly identifying the direction and magnitude of the forces and moments acting on the object. It is also important to carefully consider the direction of rotation when calculating torques.

5. How can one ensure their solution to the "STATICS couples problem" is correct?

To ensure a correct solution to the "STATICS couples problem", it is important to carefully check all calculations and equations used. It can also be helpful to draw diagrams and visually analyze the forces and moments acting on the object to confirm the solution.

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