Topic: Engineering Mechanics
Two equal forces are acting at a point with an angle of 60° between them. If the resultant force is equal to 60√3 what is the magnitude of each force?
- A. 30
- B. 50
- C. 40
- D. 60
Answer: D. 60
Explanation: Let the two equal forces be $F_1 = F_2 = F$. Using the parallelogram law of forces, the resultant $R = \sqrt{F_1^2 + F_2^2 + 2F_1F_2 \cos(\theta)}$. Given $R = 60\sqrt{3}$ and $\theta = 60^{\circ}$, we have $60\sqrt{3} = \sqrt{F² + F² + 2F^2 \cos(60^{\circ})}$. Since $\cos(60^{\circ}) = 0.5$, this simplifies to $60\sqrt{3} = \sqrt{2F^2 + F²} = \sqrt{3F^2} = F\sqrt{3}$. Thus, $F = 60$.