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43. Iwo blocks are connected by a massless rope as shown below. The mass of the block on the table is 4.0 kg and the hanging mass is 1.0 kg. The table and the pulley are frictionless. (a) Find the acceleration of the system. (b) Find the tension in the rope. (c) Find the speed with which the hanging mass hits the floor if it starts from rest and is initially located 1.0 m from the floor.

43. Iwo blocks are connected by a massless rope as shown below. The mass of the block on the table is 4.0 kg and the hanging mass is 1.0 kg. The table and the pulley are frictionless. (a) Find the acceleration of the system. (b) Find the tension in the rope. (c) Find the speed with which the hanging mass hits the floor if it starts from rest and is initially located 1.0 m from the floor.

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### 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.
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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