# Moments Of A Couple probably just something simple.

• withthemotive
In summary, the question asks for the magnitude F of the couple forces given a magnitude of M. The solution attempts to set up the equation M=Fd and solve for F using the given values. The user seeks confirmation on the correctness of their attempt and asks for guidance if it is incorrect.
withthemotive

## Homework Statement

http://i124.photobucket.com/albums/p27/lollipopgourmet/untitled.jpg

If the couple has a magnitude of M, determine the magnitude F of the couple forces.
Since this is an X-Y plane, I assumed the equation would simple just be M=Fd, where I know the moment, and just have to add the the the forces multiplied by their respective distances.

## The Attempt at a Solution

My attempt was simple set it up like this.

M=Fd
250 = F(3/5)(sqrt(17)) - F(4/5)(9)
Mostly I just want some certification that this is either right or wrong and if it's wrong to be steered in the right direction with possibly a new answer.

Last edited by a moderator:
The moment between 2 || forces is going to be the ⊥ distance between their lines of action isn't it?

I'm not certain that's what you found.

I would like to provide a response to this content by saying that the equation M=Fd is correct for calculating the moment of a couple. However, it is important to note that the distances used in the equation should be perpendicular to the direction of the force. In this case, the distances should be measured from the point of rotation to the lines of action of the forces, rather than the point of rotation to the points where the forces are applied.

Additionally, the equation should be set up as follows:

M = F1*d1 + F2*d2

Where F1 and F2 are the magnitudes of the two forces and d1 and d2 are the perpendicular distances from the point of rotation to the lines of action of the forces.

In this problem, the magnitude of the couple forces can be determined by rearranging the equation and solving for F:

F = M/d1 + d2

Substituting the given values, we get:

F = 250/(3/5)(sqrt(17)) + (4/5)(9)

Simplifying, we get:

F = 250/(3/5)(sqrt(17)) + 36/5

Therefore, the magnitude of the couple forces is approximately 180.7 units.

It is also important to note that the direction of the couple forces can be determined by the right-hand rule, where the fingers of the right hand curl in the direction of the first force and the thumb points in the direction of the second force. The direction of the couple forces will be perpendicular to the plane formed by the two forces.

In conclusion, the approach used in the attempt is correct, but there were some errors in the setup of the equation and the distances used. It is important to pay attention to the directions and distances when calculating the moment of a couple.

## 1. What is a moment of a couple?

A moment of a couple is the measure of the force that a couple exerts on an object. It is a vector quantity with both magnitude and direction.

## 2. How is a moment of a couple different from a moment of a force?

A moment of a couple is different from a moment of a force because it involves two parallel forces with equal magnitude but opposite direction, while a moment of a force involves only one force.

## 3. What is the formula for calculating the moment of a couple?

The formula for calculating the moment of a couple is M = F x d, where M is the moment, F is the magnitude of one of the forces, and d is the perpendicular distance between the two forces.

## 4. How does the direction of the moment of a couple affect its effect on an object?

The direction of the moment of a couple determines the direction in which the object will rotate. If the moment of the couple is clockwise, the object will rotate clockwise, and if it is counterclockwise, the object will rotate counterclockwise.

## 5. Can a moment of a couple be zero?

Yes, a moment of a couple can be zero if the two parallel forces are equal in magnitude and act in the same direction, canceling each other out.

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