To calculate the net force in the x and y directions:
\[ \text{Net Force X Direction} = F_1 \cos(a_1) + F_2 \cos(a_2) + \ldots \]
\[ \text{Net Force Y Direction} = F_1 \sin(a_1) + F_2 \sin(a_2) + \ldots \]
Where:
The net force is simply the sum of all forces acting on an object. This can be further complicated when the forces are acting in different directions. In this case, the forces need to be broken down into their x and y components and then summed.
Let's assume the following values:
Using the formulas:
\[ \text{Net Force X Direction} = 10 \cos(30°) + 5 \cos(60°) = 10 \times 0.866 + 5 \times 0.5 = 8.66 + 2.5 = 11.16 \text{ N} \]
\[ \text{Net Force Y Direction} = 10 \sin(30°) + 5 \sin(60°) = 10 \times 0.5 + 5 \times 0.866 = 5 + 4.33 = 9.33 \text{ N} \]
The net force is:
\[ \text{Net Force} = \sqrt{11.16^2 + 9.33^2} = 14.54 \text{ N} \]
The net angle is:
\[ \text{Net Angle} = \tan^{-1}\left(\frac{9.33}{11.16}\right) = 39.90° \]
The net force is 14.53 N at an angle of 39.90°.