Find the Moment (Torque) of the resultant in 3-D (Statics)

In summary: This will be the moment due to the resultant force.In summary, the problem at hand involves finding the moment caused by a resultant force using the equation τ = r x F, but the student is struggling because their professor did not cover resultants and 3-d moments. They have attempted to find the resultant force and are now trying to determine how to calculate the distance vector r in order to use the cross product. They are unsure if their approach is correct and are seeking alternative methods.
  • #1
fordrew
5
0
Hey guys... This problem is driving me bonkers. I really am not asking you to calculate anything but I only ask how to figure out how to get r to use τ = r x F . My professor did not even teach us anything about resultants and 3-d moments :grumpy:

Homework Statement



ak9005.jpg


Homework Equations



MO= τ = r X F

The Attempt at a Solution



Well, I found that the resultant F = 288.55 i + 985.97 j + 437 k .
The resultant is CORRECT. I can not figure out how to get the distance of this vector in respect to x, y , z for r so I can use the cross product to figure out the moment....Or perhaps I have approached the problem all wrong? Is there a different way to solve the problem? ( please do not use any numbers just to make it easier on you)

The book makes no mention of how to solve this problem and it is so so frustrating because even the professor has not done any problems pertaining to this question.
 
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  • #2
fordrew said:
Hey guys... This problem is driving me bonkers. I really am not asking you to calculate anything but I only ask how to figure out how to get r to use τ = r x F . My professor did not even teach us anything about resultants and 3-d moments :grumpy:

Homework Statement



ak9005.jpg


Homework Equations



MO= τ = r X F

The Attempt at a Solution



Well, I found that the resultant F = 288.55 i + 985.97 j + 437 k .
The resultant is CORRECT. I can not figure out how to get the distance of this vector in respect to x, y , z for r so I can use the cross product to figure out the moment.


...Or perhaps I have approached the problem all wrong? Is there a different way to solve the problem? ( please do not use any numbers just to make it easier on you)

The book makes no mention of how to solve this problem and it is so so frustrating because even the professor has not done any problems pertaining to this question.

If you are to find the torque about the origin, then the r vector would just be from the origin to the point that the force is applied (where the ropes are attached). It's a little hard to read the picture, but that would be my impression.
 
  • #3
So the r vector will just be 0i + 7j + 0k? I will test it out right now if it works... the answer is in the back of the book.. So I will get back with the results in a sec
 
  • #4
well, the answer to the problem is:

3080 i - 2070 k

however my answer is:

- 3059 i - 2019 kmaybe my resultant vector is slightly off? And cross product makes i negative =-\
 
  • #5
fordrew said:
well, the answer to the problem is:

3080 i - 2070 k

however my answer is:

- 3059 i - 2019 k


maybe my resultant vector is slightly off? And cross product makes i negative =-\

Can you show us your cross product math?
 
  • #6
fordrew said:
Hey guys... This problem is driving me bonkers. I really am not asking you to calculate anything but I only ask how to figure out how to get r to use τ = r x F . My professor did not even teach us anything about resultants and 3-d moments :grumpy:

Homework Statement



ak9005.jpg


Homework Equations



MO= τ = r X F

The Attempt at a Solution



Well, I found that the resultant F = 288.55 i + 985.97 j + 437 k .
The resultant is CORRECT. I can not figure out how to get the distance of this vector in respect to x, y , z for r so I can use the cross product to figure out the moment.


...Or perhaps I have approached the problem all wrong? Is there a different way to solve the problem? ( please do not use any numbers just to make it easier on you)

The book makes no mention of how to solve this problem and it is so so frustrating because even the professor has not done any problems pertaining to this question.

XX Take your moment about point O caused by one of the forces and sum it with the moment about point O caused by the other forces
 

1. What is torque?

Torque is a measure of the amount of rotational force applied to an object. It is calculated by multiplying the force applied by the distance from the pivot point to the point where the force is applied.

2. How is torque different in 3-D compared to 2-D?

In 2-D, torque is calculated by considering only the perpendicular distance from the pivot point to the line of action of the force. In 3-D, torque is calculated by taking into account both the perpendicular distance and the angle between the force vector and the line of action.

3. What is the resultant in 3-D?

The resultant in 3-D is the vector sum of all the individual forces acting on an object. It takes into account the magnitude, direction, and location of each force to determine the overall net force acting on the object.

4. How do you find the moment of the resultant in 3-D?

The moment of the resultant in 3-D is found by first finding the resultant force and its location on the object. Then, the moment is calculated by multiplying the magnitude of the resultant force by the perpendicular distance from the pivot point to the line of action of the resultant force.

5. Why is finding the moment of the resultant in 3-D important in statics?

Finding the moment of the resultant in 3-D allows us to understand how an object will rotate or remain in equilibrium when subjected to multiple forces acting on it. This is crucial in engineering and design to ensure the stability and safety of structures and machines.

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