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2 years, 2 months ago

The resultant of two forces acting on the same point simultaneously will be the greatest when the angle betweem them is A=180 B=45 C=0 D=90

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mielu_istetz | 2 years, 2 months ago
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Let F1 and F2 be the forces acting on the point
The resultant is the vector F=F1+F2, which is the diagonal starting from the same point of the parallelogram made by F1 and F2
see the graph
http://image.tutorvista.com/content/motion-laws/resultant-force.gif

Suppose |F|, |F1| and |F2| are the magnitudes(lengths) of the vectors F, F1 and F2 respectively.
Suppose also that "t" is the angle between F1 and F2
We will apply the generalized Phytagorean Theorem in the triangle made by F2 and the side parallel to F1. This side will also have magnitude |F1|
You can easily prove if an angle in a parallelogram is t, the angle at the next vertex is π-t .
The generalized Phytagorean Theorem gives you
|F|^2=|F1|^2+|F2|^2-2*|F1|*|F2|* cos(π-t)
Now, cos(π-t)=-cos(t) from the list of trigonometric formulas
so you get
|F|^2=|F1|^2+|F2|^2+2*|F1|*|F2|* cos(t)
For different angles the value on the right side may be bigger or smaller. It is clearly biggest when cos(t) is biggest since all other values in the expression are positive and constant.
Now, if you look at the values for cosine from the unit circle , you will find for each angle cos(t) is the biggest
If you have further questions, please ask in the comments.
You can see the video "A trick to remember the unit circle to familiarize with the unit circle.

You will see that the theory confirms the intuition: if you act on a point with forces in the same direction, the forces will add up, while if the forces are in the opposite direction, they subtract.
Think what happens if two persons push an object from opposite directions.
Also, think what happens physically when two persons push an object from different angles. Will the force be smaller or bigger than when they both push in the same direction?

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pixelsilva | 2 years, 2 months ago Report

To a complex Question comes a complex Answer...

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philipy | 2 years, 2 months ago Report

I'm afraid for anyone that needed to ask that question, your answer would probably only scare and confuse them.

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mielu_istetz | 2 years, 2 months ago Report

thanks for comments

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runghen23 | 2 years, 2 months ago
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C. When the angle is 0, the resultant force is the sum of the 2 forces.

With A it is the difference between them as they are acting in opposite directions. With B and D, the resultant is less than with C, though it is higher than the maximum of the 2 forces.

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