three forces 3N,4N,5N, act on 0 degrees, 90 degrees, 217 degrees. what is the net force
Answers
The forces acting at the point are 3N at 0^o, 4N at 90^o and 5N at 217^o
I presume that the angles given are with respect to the positive X axis.
\Rightarrow \qquad The forces are 3\hat i, 4\hat j and 5\cos 217^o\hat i + 5\sin 217^o\hat j.
\Rightarrow \qquad The net force is 3\hat i + 4\hat j + 5\cos 217^o\hat i + 5\sin 217^o\hat j.
\qquad \qquad = (3+5\cos 217^o)\hat i + (4+5\sin 217^o)\hat j
\qquad \qquad = (3-3.99318)\hat i + (4-3.00908)\hat j \qquad = \qquad -0.99318\hat i + 0.99092\hat j.
The magnitude of the net force is \sqrt{(-0.99318)^2+(0.99092)^2} = \sqrt{1.96834} = 1.40298 N.
The angle made by the net force with the positive X axis is
\qquad \qquad \arctan\left(\frac{0.99092}{-0.99318}\right)
\qquad \qquad = \arctan (-0.99772) = 135.0653^o.