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For question 43
### Physics Problem: Two-Block System with Pulley **Problem 43:** Two blocks are connected by a massless rope as shown in the diagram. The mass of the block on the table, labeled as \( m_1 \), is 4.0 kg and the hanging mass, labeled as \( m_2 \), is 1.0 kg. The table and the pulley are both frictionless. - **(a)** Determine the acceleration of the system. - **(b)** Calculate the tension in the rope. - **(c)** Find the speed at which the hanging mass (\( m_2 \)) hits the floor if it starts from rest and is initially located 1.0 m from the floor. **Diagram Explanation:** - The diagram illustrates a setup with two blocks and a pulley. - Block \( m_1 \) is on a horizontal surface and is connected via a pulley to block \( m_2 \), which hangs vertically. - The acceleration of block \( m_1 \) is labeled as \(\vec{a}_1\), pointing horizontally to the right. - The acceleration of block \( m_2 \) is labeled as \(\vec{a}_2\), pointing vertically downward. - A massless rope runs over a pulley connecting the two blocks, indicating that they are part of a single system. This problem involves understanding Newton's laws, specifically analyzing forces and motion in a connected system with a pulley.
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Transcribed Image Text:### Physics Problem: Two-Block System with Pulley **Problem 43:** Two blocks are connected by a massless rope as shown in the diagram. The mass of the block on the table, labeled as \( m_1 \), is 4.0 kg and the hanging mass, labeled as \( m_2 \), is 1.0 kg. The table and the pulley are both frictionless. - **(a)** Determine the acceleration of the system. - **(b)** Calculate the tension in the rope. - **(c)** Find the speed at which the hanging mass (\( m_2 \)) hits the floor if it starts from rest and is initially located 1.0 m from the floor. **Diagram Explanation:** - The diagram illustrates a setup with two blocks and a pulley. - Block \( m_1 \) is on a horizontal surface and is connected via a pulley to block \( m_2 \), which hangs vertically. - The acceleration of block \( m_1 \) is labeled as \(\vec{a}_1\), pointing horizontally to the right. - The acceleration of block \( m_2 \) is labeled as \(\vec{a}_2\), pointing vertically downward. - A massless rope runs over a pulley connecting the two blocks, indicating that they are part of a single system. This problem involves understanding Newton's laws, specifically analyzing forces and motion in a connected system with a pulley.
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