Answer to Question #96112 in Mechanics | Relativity for Tour Godfred

Question

Two forces act on a point objects as follows :100N at 170° and 100N at 50°.find their resultant

Answer 1

The resultant force of two forces is a vector sum of the vectors of these forces. A vector sum can be found by the law of cosines:

$$F_{resultant}^2=F_1^2+F_2^2+2F_1F_2cos(\alpha-\beta)$$

After setting given values we have:

$F_{resultant}=\sqrt{10^4+10^4+2*10^2*10^2*(-1/2)}$

$F_{resultant}=\sqrt{10^4+10^4-10^4}$

$F_{resultant}=\sqrt{10^4}$

$F_{resultant}=100N$

The action angle of the resultant force equals:

$\gamma=(\alpha+\beta)/2=(170°+50°)/2=110°$

Answer: The resultant force equals 100N at 110°.