Statics - Resultant Force

In summary, this person wrote an essay on how to solve a problem that originated from a previous post on this forum.
  • #1
kehler
104
0

Homework Statement


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If engine 3 suddenly fails, determine the resultant of the three remaining engine thrust vectors, each of which has a magnitude of 90kN. Specify the y and z-coordinates of the point through which the line of action of the resultant passes.


The Attempt at a Solution


I did it but I have no idea whether my working is right or not.
The resultant force is 90kN x 3 = 270kN in the x direction.
To find the y and z coordinates, I looked for the resultant moment about point 0 which i chose to be at (0,0,0).
This is where I'm not sure. Why do the 2m and 3m arrows pointing out from the engines in the x direction matter? (Actually, they probably don't matter too much as they cancel out. But I have to show my working so it'll be good if someone can explain their significance)
I assumed they must have some effect so I multiplied 90kN by (2/3) for the two outer engines.
So, the moment due to the first force on the left is -21 x 90kN x (2/3) = -2520kN (in the z direction, ie pointing upwards)
The moment due to the inner engine on the right is 12 x 90kN = 1080kN (pointing downwards)
And the moment due to the rightmost engine is 21 x 90kN x (2/3) = 2520kN (pointing downwards)
The resultant moment is 1080kN (pointing downwards)

I know that the sum of moments about O is equal to the moment of the resultant force about O (Varignon's Theorem). So to find the y-coordinate of the point which the line of action of the resultant passes, I equated
1080kN = r x 270kN
r = 4
Therefore, the resultant force is 4m to the right of point 0.
The z coordinate should be zero.

Can someone tell me if I did it right? Any help would be much appreciated :)
 
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  • #2
Yes this is correct!
 
  • #3
The 2m and 3m designations are the distance along the z-axis that the engines are away from the x-axis. These distances, coupled with the forces, will cause each engine to create moments, also.
edit: Oh, geez - I just noticed that this thread originated two years ago. Sorry...
 

What is a resultant force in statics?

A resultant force in statics is the single force that can replace multiple forces acting on an object. It is the net force that takes into account the magnitude and direction of all the individual forces.

How do you calculate the resultant force?

To calculate the resultant force, you need to first determine the magnitude and direction of each individual force acting on an object. Then, you can use vector addition to find the sum of all the forces, which will give you the resultant force.

What is the difference between a concurrent and non-concurrent resultant force?

A concurrent resultant force acts at a single point on an object, while a non-concurrent resultant force acts at multiple points. This means that a concurrent force has a single point of application, while a non-concurrent force has multiple points of application.

What is the principle of transmissibility in statics?

The principle of transmissibility states that the magnitude and direction of a force remain unchanged as long as the line of action of the force remains the same. This means that a force can be transmitted along its line of action to any point on an object without changing its effect.

How do you find the angle of the resultant force?

To find the angle of the resultant force, you can use trigonometric functions such as sine, cosine, and tangent. You will need to know the magnitude and direction of the individual forces, as well as the angle between them, in order to calculate the angle of the resultant force.

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