A hand pushes block A (m= 3 kg) with a constant force Nand. A= 75 N for a distance Ax = 2 m along a (mostly) frictionless table such that it speeds up from rest and is traveling at a speed of 8 m/s after it slides over a rough section of the table (H = 0.4). Block A then collides with a more massive block B (mg = 6 kg) that is initially at rest. Find Ax, the length of the rough section of the table. A) 1.0 m B) 15.4 m C) 4.5 m D) 7.5 m E) 2.6 m

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### Educational Content: Physics Problem Involving Friction and Motion

#### Description

A hand applies a constant force \( N_{\text{hand,A}} = 75 \, \text{N} \) to a block labeled as Block A (\( m_A = 3 \, \text{kg} \)). The block is pushed over a \( 2 \, \text{m} \) distance along a table that is primarily frictionless. Block A accelerates from rest and achieves a speed of \( 8 \, \text{m/s} \) upon passing over a rough section of the table with a coefficient of kinetic friction \( \mu_k = 0.4 \). After crossing this section, Block A collides with a larger block, Block B (\( m_B = 6 \, \text{kg} \)), which is initially at rest.

#### Task

Calculate \( \Delta x \), the length of the rough section of the table, using the provided information.

#### Options

A) \( 1.0 \, \text{m} \)  
B) \( 15.4 \, \text{m} \)  
C) \( 4.5 \, \text{m} \)  
D) \( 7.5 \, \text{m} \)  
E) \( 2.6 \, \text{m} \)

#### Diagram Explanation

The diagram illustrates the scenario:
- Two hands pushing Block A across a surface.
- Block A is moving to the right with a velocity \( v_A = 8 \, \text{m/s} \) after crossing the rough section.
- The rough section is marked with hatching to denote friction (\( \mu_k = 0.4 \)).
- Block B is stationary at the end of the rough section, ready to be impacted by Block A.

Please select the correct length for the rough section of the table from the given options.
Transcribed Image Text:### Educational Content: Physics Problem Involving Friction and Motion #### Description A hand applies a constant force \( N_{\text{hand,A}} = 75 \, \text{N} \) to a block labeled as Block A (\( m_A = 3 \, \text{kg} \)). The block is pushed over a \( 2 \, \text{m} \) distance along a table that is primarily frictionless. Block A accelerates from rest and achieves a speed of \( 8 \, \text{m/s} \) upon passing over a rough section of the table with a coefficient of kinetic friction \( \mu_k = 0.4 \). After crossing this section, Block A collides with a larger block, Block B (\( m_B = 6 \, \text{kg} \)), which is initially at rest. #### Task Calculate \( \Delta x \), the length of the rough section of the table, using the provided information. #### Options A) \( 1.0 \, \text{m} \) B) \( 15.4 \, \text{m} \) C) \( 4.5 \, \text{m} \) D) \( 7.5 \, \text{m} \) E) \( 2.6 \, \text{m} \) #### Diagram Explanation The diagram illustrates the scenario: - Two hands pushing Block A across a surface. - Block A is moving to the right with a velocity \( v_A = 8 \, \text{m/s} \) after crossing the rough section. - The rough section is marked with hatching to denote friction (\( \mu_k = 0.4 \)). - Block B is stationary at the end of the rough section, ready to be impacted by Block A. Please select the correct length for the rough section of the table from the given options.
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