Vector Addition: 60 N and 80 N Forces at 60° Angle

Question:

Two forces of 60 N and 80 N acting at an angle of 60 degree with each other pull an object.What single pull would replace the given forces?

Solution: Vector addition

Let the two forces be represented as A and B which are inclined at an angle of 60 degree.The resultant of these two forces be R.

Here A = 60 N

B=80 N and

$$\theta = 60 degree$$

$$R=\sqrt{A^2+B^2+2 A B Cos\theta}$$

$$R=\sqrt{60^2+80^2+2(60)(80) Cos 60}$$

$$R=\sqrt{3600+6400+2 (4800)(\frac{1}{2}}$$

$$R=\sqrt{10000+4800}$$

$$R=\sqrt{14800}$$

$$R=\sqrt{148}\sqrt{100}$$

$$R=(12.17)(10)$$

$$R=121.7 N$$