Statics - Balancing moment and resultant force

• lax1113
In summary, the problem involves replacing a force system with a resultant and determining where its line of action intersects AB from point B. The solution involves finding the components of the X and Y forces, calculating the resultant and its angle of inclination, and accounting for the moment of the couple before determining the line of the resultant force.
lax1113

Homework Statement

Replace the force system with a resultant and specify where its line of action intersects AB from point B.

so I guess the imagine didn't work...
http://yfrog.com/htstaticspicp

I realize it is very small I apologize for that, if anything in the picture is unclear please let me know.

Homework Equations

Fresultant = sum of Forces
Moment = sum of Moments

The Attempt at a Solution

I have solved the components of the X and Y forces of each of the 3 forces and got a resultant of 542N and also got the angle of inclination of this resultant, as 10.6 degrees. However, I am not getting the right answer when I sum the moments. Since it wants where this would be along AB, I set up my moment equation as 533N (the y portion of F resultant) * y = {sum of all of the moments that are acting perpendicular to the line segment AB}. However, I am not getting the correct answer? Is this the right way to go about this problem?

Last edited by a moderator:
Hi lax1113!

I think you're missing that there's a resultant (linear) force and a couple (a disembodied moment).

The moment of the couple is the same about any point, and you'll need to subtract it before you can find the line of the resultant (linear) force.

1. What is the difference between a moment and a resultant force?

A moment is a turning effect caused by a force acting on an object, while a resultant force is the single force that has the same effect as all the individual forces acting on an object combined.

2. How do you calculate the moment of a force?

The moment of a force is calculated by multiplying the magnitude of the force by the perpendicular distance from the point of rotation to the line of action of the force.

3. What is the principle of moments?

The principle of moments states that for an object to be in equilibrium, the sum of the clockwise moments must be equal to the sum of the anticlockwise moments.

4. How do you balance moments in a system?

To balance moments in a system, the principle of moments can be applied by ensuring that the sum of the clockwise moments is equal to the sum of the anticlockwise moments.

5. What are some real-world applications of balancing moments and resultant forces?

Some real-world applications of balancing moments and resultant forces include designing bridges, buildings, and other structures to withstand external forces, as well as understanding the stability of objects such as boats and airplanes.

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