Question

Two forces of 560 N and 222 N act at a point. The resultant force is 634 N. Find the angle between the forces.

Answer 1

The angle between the two forces of 560 N and 222 N is 80.96°

What is the resultant of two vectors?

The resultant of two vectors P and Q refer to the magnitudes of the vectors and it can be expressed by the formula $\mathbf{R = \sqrt{P^2 +Q^2 +2PQ cos \theta }}$

Now, using the above equation, we can easily determine the angle between the forces of the two vectors as follows:

$\mathbf{634 = \sqrt{560^2 +222^2 + 2(560 \times 222) \ Cos \theta }}$

$\mathbf{401956 =313600 +49284 + 248640 \ Cos \theta }}$

$\mathbf{401956 -313600 -49284 = 248640 \ Cos \theta }}$

$\mathbf{39072= 248640 \ Cos \theta }}$

$\mathbf{ Cos \theta = \dfrac{39072}{248640}}}$

$\mathbf{Cos \theta =0.1571}$

$\mathbf{ \theta =80.96^0}$

Therefore, we can conclude that the angle between the forces is 80.96°

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