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Statics  Resultant Force 
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#1
Sep2208, 06:42 AM

P: 104

1. The problem statement, all variables and given/known data
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 zcoordinates of the point through which the line of action of the resultant passes. 3. 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 ycoordinate 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 :) 


#2
Oct610, 02:50 PM

P: 1

Yes this is correct!!



#3
Oct710, 11:19 AM

P: 137

The 2m and 3m designations are the distance along the zaxis that the engines are away from the xaxis. 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... 


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