Moment couple (opposite direction on same line)

So, in summary, the question is about a homework problem involving a moment couple and the attempt at a solution is considering the forces on the same straight line in opposite directions and whether they cancel out or create a moment. The person is also asking for clarification on the values of d and F in the homework equations.
  • #1
yecko
Gold Member
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DF47BF0A-A189-4B78-B537-1750C7C82952.jpeg
1. Homework Statement
It is a part of the question in my homework and I extract this out just for the part i m confused(in the picture above)

Homework Equations


Moment couple=d*F
[d is the difference in point of application (=sqrt41) or the perpendicular distance of the forces(=0) ?]

The Attempt at a Solution


As the forces on the same straight line in oppsite direction, I think they will cancel out each other...
Yet, I am not sure if there would be moment formed by the couple...

Thanks
 
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  • #2
yecko said:
As the forces on the same straight line in oppsite direction, I think they will cancel out each other...
This is good intuition, but if you are unsure you should back it up with mathematics.
 
  • #3
This is my mathematical prove
image.jpg
 
  • #4

1. What is a moment couple?

A moment couple is a pair of equal and opposite forces that act on a body at different points, but along the same line. This results in a moment, or turning effect, on the body.

2. How is a moment couple different from a single force?

A single force acts on a body at a single point, whereas a moment couple consists of two forces acting at different points. This difference in force application results in a moment, rather than a linear force, being exerted on the body.

3. What is the direction of a moment couple?

The direction of a moment couple is perpendicular to the plane formed by the two forces. It follows the right-hand rule, where the thumb points in the direction of the first force and the fingers curl towards the direction of the second force.

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

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

5. How does a moment couple affect the motion of a body?

A moment couple does not result in linear motion, but rather causes the body to rotate about its center of mass. This rotation is dependent on the magnitude of the moment and the inertia of the body.

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