Question

If the resultant of two equal forces is equal to their sum then find the angle

Answer 1

Answer:

Let the two forces be F1 and F2 at an angle X where |F1| = |F2|

Let the resultant of the 2 forces be R.

So |R| = |F1| = |F2| =|F|

R^2 = A^2 + B^2 + 2AB cos X

F^2 = F^2 + F^2 + 2F^2 cos X

F^2 = 2F^2 + 2F^2 cos X

F^2 = 2F^2(1 + cos X)

Cancelling F^2 on both sides

1 = 2(1 + cos X)

1 + cos X = 1/2

cos X =-1/2

X = 120 degrees

So the resultant of two forces having the same magnitude as the initial force is only possible when the two forces are at an angle of 120 degrees.

Explanation:

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