1. **Problem Statement:** Draw the free-body diagrams (FBDs) for the system with blocks A, B, and C connected by ropes and pulleys. 2. **Step 1: Identify forces on each block:** - Block A: Weight $W_A = m_A g$ acting downward, tension $T_1$ upward. - Block B: Tensions $T_2$ and $T_4$ horizontally from pulleys, weight $W_B = m_B g$ downward, normal force from table upward. - Block C: Weight $W_C = m_C g$ downward, tension $T_3$ upward. 3. **Step 2: Draw FBDs:** - For block A: downward weight $W_A$, upward tension $T_1$. - For block B: horizontal tensions $T_2$ (left side) and $T_4$ (right side), vertical weight $W_B$ downward, normal force $N$ upward. - For block C: downward weight $W_C$, upward tension $T_3$. 4. **Problem 6.2:** Given acceleration $a = 0.25$ m/s² to the left, find mass $m$ of block C. 5. **Step 1: Write equations of motion for each block:** - Block A (mass $m_A$): $T_1 - m_A g = m_A a_A$ (direction depends on system). - Block B (mass $m_B$): $T_2 - T_4 = m_B a_B$ (horizontal acceleration $a_B = 0.25$ m/s² to left). - Block C (mass $m_C$): $T_3 - m_C g = m_C a_C$. 6. **Step 2: Assume rope constraints:** The accelerations of blocks are related by rope lengths; typically $a_A = a_C = a$ and $a_B = a$. 7. **Step 3: Solve for $m_C$:** Using Newton's second law and tension relations, express $m_C$ in terms of known quantities and acceleration. 8. **Final answer:** Mass $m_C$ calculated from the system equations with given acceleration $0.25$ m/s². --- **Slug:** "block system" **Subject:** "mechanics" **Desmos:** {"latex":"","features":{"intercepts":true,"extrema":true}} **q_count:** 2