3D Moment with force and couple

In summary, the problem involves determining the moment of a special-purpose milling cutter about point O, given a force of 1040 N and a couple of 211 N·m. The equation used is Mo = R x F + (Couple), and the attempt at a solution involved substituting the given values to find the moment. However, the resulting values were not entirely accurate and the user is unsure of where they went wrong. They have previously solved a similar problem correctly.
  • #1
Fantom
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Homework Statement


The special-purpoise milling cutter is subjected to the force of 1040 N and a couple of 211 N·m as shown. Determine the moment of this system about point O.
(Let's laugh at the text's typo)

Homework Equations


Mo = R x F + (Couple)

The Attempt at a Solution


I'm having a little difficulty with this... And I'm not sure why... I've done a question with the same question, different numbers and continue to get the right answer.

Anyways...

Mo = (0 - 654.5 * .265)i - (.21 * -808.2)j + (.21 * 654.5)k + <0, 211sin39, -211cos39>

This gave me... <-173i, 302j, -26.5k>

The "302j" is correct, the others are not. Not sure where I went wrong.~~~
Image: http://imgur.com/NB1zpeS
 
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  • #2
Anyone..?
 

1. What is a 3D moment?

A 3D moment is a measurement of the tendency of a force to cause an object to rotate around a specific point in three-dimensional space. It is a combination of both linear and rotational forces acting on an object.

2. How is a moment calculated in 3D space?

To calculate a moment in 3D space, we need to know the magnitude of the force, the perpendicular distance from the point of rotation, and the angle between the force and the line connecting the point of rotation to the point where the force is applied. Using this information, we can use the cross product formula to calculate the moment.

3. What is the difference between a force and a couple in 3D space?

A force is a single vector quantity that represents a push or pull on an object. A couple, on the other hand, is a pair of equal and opposite forces that act along parallel lines but in opposite directions. While a force can cause an object to move in a linear direction, a couple causes an object to rotate around an axis.

4. How do forces and couples affect an object's equilibrium in 3D space?

Forces and couples can affect an object's equilibrium in different ways. A force can cause an object to translate or rotate, while a couple only causes rotational motion. In order for an object to be in equilibrium, the sum of all forces acting on the object must be equal to zero, and the sum of all moments must also be equal to zero.

5. Can you give an example of how to calculate a 3D moment with force and couple?

For example, let's say we have a door that is being pushed by a force of 10 N at a distance of 2 meters from the hinge. Additionally, there is a couple of 5 Nm acting on the door at a distance of 1 meter from the hinge. To calculate the 3D moment, we would first calculate the moment caused by the force: (10 N) x (2 m) = 20 Nm. Then, we would calculate the moment caused by the couple: (5 Nm) x (1 m) = 5 Nm. The total 3D moment for this scenario would be 25 Nm.

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