Acceleration Tension F8F52B

1. **State the problem:** We have two boxes, A and B, connected by a rope on a frictionless surface. Box B is pulled to the right with a force of $60$ N. We need to find the acceleration of the system and the tension in the rope. 2. **Identify known values:** - Mass of Box A, $m_A = 8.0$ kg - Mass of Box B, $m_B = 12$ kg - Applied force on Box B, $F = 60$ N - Surface is frictionless, so no friction force. 3. **Find acceleration of the system:** Since the boxes are connected, they accelerate together with the same acceleration $a$. Total mass, $m_{total} = m_A + m_B = 8.0 + 12 = 20$ kg Using Newton's second law: $$F = m_{total} \times a$$ Solve for acceleration: $$a = \frac{F}{m_{total}} = \frac{60}{20} = 3\ \text{m/s}^2$$ 4. **Find tension in the rope:** The tension $T$ acts on Box A to accelerate it. Using Newton's second law on Box A: $$T = m_A \times a = 8.0 \times 3 = 24\ \text{N}$$ 5. **Summary:** - Acceleration of the system is $3\ \text{m/s}^2$ - Tension in the rope is $24$ N This means the rope pulls Box A with $24$ N to accelerate it at $3\ \text{m/s}^2$, while Box B is pulled by the external force of $60$ N.