A body is acted upon by two forces \(F_{1} = (5 N, 060°)\) and \(F_{2} = (10 N, 180°)\). Find the magnitude of the resultant force.

A body is acted upon by two forces \(F_{1} = (5 N, 060°)\) and \(F_{2} = (10 N, 180°)\). Find the magnitude of the resultant force.

Answer Details

We can use vector addition to find the resultant force. Let's first convert the given forces into their x and y components. For \(F_1 = (5 N, 060°)\), the x component is \(F_{1x} = F_1 \cos(60°) = 5 \cos(60°) = 2.5 N\) and the y component is \(F_{1y} = F_1 \sin(60°) = 5 \sin(60°) = 4.33 N\). For \(F_2 = (10 N, 180°)\), the x component is \(F_{2x} = F_2 \cos(180°) = -10 N\) and the y component is \(F_{2y} = F_2 \sin(180°) = 0 N\). Now we can add the x and y components separately to get the resultant force: $$F_{Rx} = F_{1x} + F_{2x} = 2.5 N - 10 N = -7.5 N$$ $$F_{Ry} = F_{1y} + F_{2y} = 4.33 N + 0 N = 4.33 N$$ The magnitude of the resultant force is then given by: $$F_R = \sqrt{F_{Rx}^2 + F_{Ry}^2} = \sqrt{(-7.5)^2 + 4.33^2} \approx 8.66 N$$ Therefore, the answer is \boxed{8.66 N}.