1. **State the problem:** We have a closed curved shape with a horizontal length of 80 cm and vertical height of 40 cm. There is a horizontal force of 10 N to the left at the left side and a vertical distributed force of 30 N/m acting into the shape along the vertical side. We want to find the equivalent force system at point A, located at the right end of the curve. 2. **Convert units:** Length $L = 80$ cm $= 0.8$ m Height $h = 40$ cm $= 0.4$ m 3. **Calculate resultant of distributed force:** The distributed force is $30$ N/m acting over height $0.4$ m. Resultant force magnitude: $$F_d = 30 \times 0.4 = 12 \text{ N}$$ This force acts at the centroid of the distribution, which is at half the height from the bottom: $$y_d = \frac{0.4}{2} = 0.2 \text{ m}$$ 4. **Identify forces and their positions relative to point A:** - Horizontal force $F_h = 10$ N to the left, located at the left side (distance from A is $0.8$ m horizontally). - Distributed force resultant $F_d = 12$ N vertically into the shape, located at $0.2$ m from bottom on the left side (distance from A is $0.8$ m horizontally and $0.2$ m vertically). 5. **Calculate moments about point A:** - Moment due to horizontal force $F_h$: $$M_h = F_h \times \text{vertical distance} = 10 \times 0.4 = 4 \text{ Nm}$$ Direction: clockwise (assuming positive clockwise) - Moment due to distributed force $F_d$: $$M_d = F_d \times \text{horizontal distance} = 12 \times 0.8 = 9.6 \text{ Nm}$$ Direction: counterclockwise 6. **Calculate net force components at A:** - Horizontal force at A: $$F_{x} = -10 \text{ N}$$ (left is negative) - Vertical force at A: $$F_{y} = -12 \text{ N}$$ (into the shape is negative) 7. **Calculate net moment at A:** $$M = M_h - M_d = 4 - 9.6 = -5.6 \text{ Nm}$$ Negative means net moment is counterclockwise. **Final equivalent force system at point A:** - Horizontal force: $-10$ N (left) - Vertical force: $-12$ N (into the shape) - Moment: $-5.6$ Nm (counterclockwise) This system replaces the original forces with a single force and moment at point A.