Question

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(i) For a force F ,Fx = 6N and Fy= 6N. What
is the angle between F and the x-axis?
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Answer 1

$\huge\bold{\textbf{\textsf{{\color{cyan}{Answer}}}}}$

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|

R² = A² + B² + 2AB cos X

F² = F² + F² + 2F² cos X

F² = 2F² + 2F² cos X

F² = 2F²(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 angle of 120 degrees.