Hk = 0.200. The angle 0 of the incline is 27.5°. If block 2 is moving up the incline at constant speed, what is the mass m of block 1?

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### Problem Description

Two blocks are connected by a massless rope over a massless, frictionless pulley, as depicted in the figure. The setup includes:

- **Block 2**: Mass (\(m_2\)) is 10.1 kg.
- **Coefficient of Kinetic Friction** (\(\mu_k\)) between block 2 and the incline is 0.200.
- **Incline Angle** (\(\theta\)) is 27.5°.

The problem asks: If block 2 is moving up the incline at a constant speed, what is the mass (\(m_1\)) of block 1?

### Diagram Explanation

- The diagram shows a pulley system with:
  - **Block 1** (red, labeled as "1") vertically hanging on one side of the pulley.
  - **Block 2** (blue, labeled as "2") positioned on a green incline.
- The incline has an angle (\(\theta\)) indicated at its base, showing the orientation of block 2 on the slope.
  
### Solution Attempt

- The provided incorrect calculation for \(m_1\) is \(-2.8744\) kg.

### Important Notes

- **Constant Speed** implies zero net acceleration. Therefore, the forces on both sides of the pulley system need to be balanced.
- **Kinetic Friction** opposes the motion of block 2 up the incline.
Transcribed Image Text:### Problem Description Two blocks are connected by a massless rope over a massless, frictionless pulley, as depicted in the figure. The setup includes: - **Block 2**: Mass (\(m_2\)) is 10.1 kg. - **Coefficient of Kinetic Friction** (\(\mu_k\)) between block 2 and the incline is 0.200. - **Incline Angle** (\(\theta\)) is 27.5°. The problem asks: If block 2 is moving up the incline at a constant speed, what is the mass (\(m_1\)) of block 1? ### Diagram Explanation - The diagram shows a pulley system with: - **Block 1** (red, labeled as "1") vertically hanging on one side of the pulley. - **Block 2** (blue, labeled as "2") positioned on a green incline. - The incline has an angle (\(\theta\)) indicated at its base, showing the orientation of block 2 on the slope. ### Solution Attempt - The provided incorrect calculation for \(m_1\) is \(-2.8744\) kg. ### Important Notes - **Constant Speed** implies zero net acceleration. Therefore, the forces on both sides of the pulley system need to be balanced. - **Kinetic Friction** opposes the motion of block 2 up the incline.
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