In the figure shown below, the value of co- efficient of dynamic friction between 500 N block and incline is (Assume g = 10 m/sec²) 500 N 3 4 a= 1 m/s² 100 N

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**Title: Calculating the Coefficient of Dynamic Friction**

**Problem Statement:**
In the figure shown below, determine the coefficient of dynamic friction between a 500 N block and the inclined plane. Assume the acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \).

**Diagram Explanation:**
- The diagram features a 500 N block on an inclined plane angled as part of a 3-4-5 triangle (forming a right-angled triangle).
- The inclined plane is at an angle such that the ratio of vertical side to the hypotenuse is 3:5, and the horizontal side to the hypotenuse ratio is 4:5.
- The 500 N block is connected over a pulley to a 100 N weight hanging vertically.
- The system has an acceleration (\( a \)) of \( 1 \, \text{m/s}^2 \) acting upward for the hanging weight and along the plane for the inclined block.

**Step-by-Step Solution:**
1. **Identify Forces Acting on the Blocks:**
   - For the block on the incline (\( 500 \, \text{N} \)):
     - Gravitational Force (\( W \)): 500 N.
     - Normal Force (\( N \)): Perpendicular to the inclined plane.
     - Frictional Force (\( f \)): Parallel to the plane opposing the motion.
     - Component of Weight Parallel to the Plane (\( W_{\parallel} = W \cdot \sin(\theta) \)).
     - Component of Weight Perpendicular to the Plane (\( W_{\perp} = W \cdot \cos(\theta) \)).

2. **Calculate the Angle (\( \theta \)) of Incline:**
   - Using triangle properties (3-4-5 triangle):
     - \( \sin(\theta) = \frac{3}{5} \)
     - \( \cos(\theta) = \frac{4}{5} \)

3. **Determine the Components of Weight:**
   - \( W_{\parallel} = 500 \cdot \frac{3}{5} = 300 \, \text{N} \)
   - \( W_{\perp} = 500 \cdot \frac{4}{5} = 400 \, \text{N} \)

4. **Calculate the Net
Transcribed Image Text:**Title: Calculating the Coefficient of Dynamic Friction** **Problem Statement:** In the figure shown below, determine the coefficient of dynamic friction between a 500 N block and the inclined plane. Assume the acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \). **Diagram Explanation:** - The diagram features a 500 N block on an inclined plane angled as part of a 3-4-5 triangle (forming a right-angled triangle). - The inclined plane is at an angle such that the ratio of vertical side to the hypotenuse is 3:5, and the horizontal side to the hypotenuse ratio is 4:5. - The 500 N block is connected over a pulley to a 100 N weight hanging vertically. - The system has an acceleration (\( a \)) of \( 1 \, \text{m/s}^2 \) acting upward for the hanging weight and along the plane for the inclined block. **Step-by-Step Solution:** 1. **Identify Forces Acting on the Blocks:** - For the block on the incline (\( 500 \, \text{N} \)): - Gravitational Force (\( W \)): 500 N. - Normal Force (\( N \)): Perpendicular to the inclined plane. - Frictional Force (\( f \)): Parallel to the plane opposing the motion. - Component of Weight Parallel to the Plane (\( W_{\parallel} = W \cdot \sin(\theta) \)). - Component of Weight Perpendicular to the Plane (\( W_{\perp} = W \cdot \cos(\theta) \)). 2. **Calculate the Angle (\( \theta \)) of Incline:** - Using triangle properties (3-4-5 triangle): - \( \sin(\theta) = \frac{3}{5} \) - \( \cos(\theta) = \frac{4}{5} \) 3. **Determine the Components of Weight:** - \( W_{\parallel} = 500 \cdot \frac{3}{5} = 300 \, \text{N} \) - \( W_{\perp} = 500 \cdot \frac{4}{5} = 400 \, \text{N} \) 4. **Calculate the Net
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