1. **Problem Statement:** We are given a jib crane structure with Member 1 having length $L_1$ and angle $\alpha_1$ with the horizontal. The spring balance reading for Member 1 is $SB_1$, the theoretical force is $F_{1,th}$, and the experimental force is $F_{1,exp}$. We want to understand the relationship between these forces and the angle $\alpha_1$. 2. **Key Definitions and Formula:** - The algebraic difference between theoretical and experimental forces is $\Delta F_1 = F_{1,th} - F_{1,exp}$. - The force in Member 1 can be resolved along the member direction using the angle $\alpha_1$. 3. **Force Components:** The force measured by the spring balance $SB_1$ corresponds to the tension or compression along Member 1. The theoretical force $F_{1,th}$ is calculated based on static equilibrium equations considering the load $W$ and geometry. 4. **Equilibrium and Geometry:** Using the angle $\alpha_1$, the horizontal and vertical components of the force in Member 1 are: $$F_{1,x} = F_1 \cos \alpha_1$$ $$F_{1,y} = F_1 \sin \alpha_1$$ 5. **Calculating Theoretical Force:** Theoretical force $F_{1,th}$ can be found by applying equilibrium equations (sum of forces and moments) to the crane structure considering the load $W$ and geometry (lengths $L_1$, $L_2$, heights $h_1$, $h_2$, etc.). 6. **Comparing Forces:** The difference $\Delta F_1$ helps assess the accuracy of the experimental measurement: $$\Delta F_1 = F_{1,th} - F_{1,exp}$$ 7. **Interpretation:** - If $\Delta F_1$ is close to zero, the experimental measurement matches the theoretical prediction well. - A significant $\Delta F_1$ indicates discrepancies possibly due to measurement errors or assumptions in the theoretical model. **Final summary:** The forces in Member 1 are related through the angle $\alpha_1$ and length $L_1$. The algebraic difference $\Delta F_1$ quantifies the deviation between theory and experiment, guiding validation of the model or measurement accuracy.