Let's break down the problem step by step as per the instructions in the image. --- # Step 1: Draw the Free-Body Diagram (FBD) - **Identify all supports and points of force application.** - The structure is pinned at point **A** and has a roller at point **B**. - A **240 N** force is applied downwards at the end. ### **Support Reactions** - **At A (pin support):** Has both horizontal (\(A_x\)) and vertical (\(A_y\)) reaction forces. - **At B (roller support):** Only a vertical reaction (\(B_y\)). ### **Applied Force** - At the lower right, a downward force of \(240\, \text{N}\) is applied. --- # Step 2: Label All Applied Forces and Dimensions - **Horizontal segment:** \(500\,\text{mm}\) (.5 m) from A to B. - **Vertical segment:** \(300\,\text{mm}\) (.3 m) at both ends. - The force acts at the very end, \(300\,\text{mm}\) below the horizontal segment. --- # Step 3: Write Equilibrium Equations The body is in static equilibrium, so apply the following equations: ### 1. Sum of Forces in \( x \)-direction: \[ \sum F_x = : \quad A_x = \] ### 2. Sum of Forces in \( y \)-direction: \[ \sum F_y = : \quad A_y + B_y - 240 = \] ### 3. Sum of Moments about Point A (\( \sum M_A = \)) Take counterclockwise moments as positive. - The 240 N force has a horizontal distance of **.5 m** from A. - \(B_y\) acts at \(.5\,\text{m}\) from A (end B). \[ \sum M_A = : -240 \times .5 + B_y \times .5 = \] --- # Step 4: Solve for the Reactions ### 1. From Moment Equation: \[ -240 \times .5 + B_y \times .5 = \\ -120 + .5B_y = \\ .5B_y = 120 \\ B_y = 240\,\text{N} \] ### 2. Substitute \(B_y\) into Sum of Forces in \(y\): \[ A_y + 240 - 240 = \\ A_y = \] ### 3. \(A_x\) from Sum of Forces in \(x\): \[ A_x = \] --- # Step 5: **Box the Final Answers** ## **Final Answers** \[ \boxed{ A_x = ,\quad A_y = ,\quad B_y = 240\,\text{N} } \] --- ## **Summary Table** | Reaction | Value | |----------|--------------| | \(A_x\) | \(\) | | \(A_y\) | \(\) | | \(B_y\) | \(240\,N\) | --- ## **Explanation** - All the vertical load is carried by the roller at B due to the geometry of the structure and the position of the applied force. - The pin at A provides no vertical or horizontal reaction in this configuration. --- Let me know if you need the full free-body diagram drawn or any further clarifications!