Calculating Total Moment and Distance from Point A

In summary, when calculating the resultant of the four forces shown and their total moment about A, the perpendicular distance from A to the line of the single force which would have the same effect as the forces F1, F2, F3 and F4 combined can be found.
  • #1
Jellypa
3
0
Calculate the resultant of the four forces shown and their total moment about A. Hence determine the perpendicular distance from A to the line of the single force which would have the same effect as the forces F1, F2, F3 and F4 combined.
Assume the following values:
F1 = 55N, F2 = 33N, F3 = 74N and F4 = 68N
Note that, in this diagram, angles shown are not drawn accurately



Could you please give me some clue of how to answer this question? my main problem is that I don't know how to find the distance between A and each forces, I'm so confused.
Thanks for your help.
 

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  • #2
If you break up each of the forces into their x and y components, the perpendicular distances from the line of action of the forces components to point A will become obvious. Then the moment about A of all forces can be obtained by summing all moments of each component force. Watch plus and minus signs.
 
  • #3
PhanthomJay,Thank you very much,Considering what you said I used this formula to find each force and then The total force:

F * (sin or cos) * perpendicular distance = MomentF1 * sin90 * 2 = 110
F2 * sin78 * 5 = 161.39
F3 * sin42 * 3 = 148.54
-(F4) * cos77 * 2 = -30.59

the total force = 389.34

If this is right then how can I find the prependicular distance for the total force? or how can I draw the total force on the picture?
 
  • #4
Jellypa said:
PhanthomJay,Thank you very much,Considering what you said I used this formula to find each force and then The total force:

F * (sin or cos) * perpendicular distance = Moment


F1 * sin90 * 2 = 110
F2 * sin78 * 5 = 161.39
F3 * sin42 * 3 = 148.54
-(F4) * cos77 * 2 = -30.59
These values are the correct moments of the y components of the forces about A. You need to calculate the moments of the x components also.
the total force = 389.34
This is the total moment about A from the y component of forces. You need to determne the total moments from the x component of the forces also.
If this is right then how can I find the prependicular distance for the total force? or how can I draw the total force on the picture?
The sum total of the y components of forces is the y component of the resultant single force, Ry. The sum of the total x components of forces is the x component of the resultant single force, Rx. If you divide the total moment of the y component forces by the total y component forces, you get the perp distance from the line of action of Ry to A. If you divide the total moment of the x component forces by the total x component forces, you get the perp distance from the line of action of Rx to A. The magnitude and direction of R is determined from pythagoras' theorem and trig, and it passes through the coordinate where Rx and Ry meet.
 
  • #5
PhanthomJay , You are brilliant, Thank you so much, couldn't be explained better than that.
wonderful.
 

What is the definition of "Moment about a point"?

The moment about a point is a measure of the tendency of a force to rotate an object about a specific point. It is calculated by multiplying the magnitude of the force by the distance from the point to the line of action of the force.

How is the moment about a point calculated?

The moment about a point is calculated by multiplying the magnitude of the force by the perpendicular distance from the point to the line of action of the force. This distance is also known as the lever arm or moment arm.

What are the units of measurement for moment about a point?

The units of measurement for moment about a point depend on the units used for the force and distance. In the SI system, the moment is measured in newton-meters (Nm). In the imperial system, it is measured in foot-pounds (ft-lb).

How does the direction of the moment about a point affect the rotation of an object?

The direction of the moment about a point affects the rotation of an object by determining the direction in which the object will rotate. If the moment is clockwise, the object will rotate in a clockwise direction, and if the moment is counterclockwise, the object will rotate in a counterclockwise direction.

What are some real-life applications of moment about a point?

Moment about a point is used in various real-life applications, such as engineering, architecture, and physics. It is used to calculate the stability of structures, determine the torque needed to rotate an object, and analyze the forces acting on a machine or structure.

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