As shown below, a box with a mass of 1.00 kg is released from rest at point A. It travels down a frictionless quarter-circle arc to point B. It slides on a horizontal track from B to C where it compresses a spring a distance of 85.2 cm before stopping. The horizontal track from B to C is 1.63 m long and has a constant 2.8 N frictional force acting on the box as it slides from B to when it stops. Find the spring constant of the spring in N/m. m = 1.0 kg A r= 2.0 m

College Physics
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Chapter1: Units, Trigonometry. And Vectors
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As shown below, a box with a mass of 1.00 kg is released from rest at point A. It travels down a frictionless quarter-circle arc to point B. It slides on a horizontal track from B to C where it compresses a spring a distance of 85.2 cm before stopping. The horizontal track from B to C is 1.63 m long and has a constant 2.8 N frictional force acting on the box as it slides from B to C when it stops.

Find the spring constant of the spring in N/m.

**Diagram Explanation:**

The diagram provides a visual representation of the scenario:

- Point A: The starting position of the box, with a mass \( m = 1.0 \, \text{kg} \).
- Quarter-circle path: From A to B, with a radius \( r = 2.0 \, \text{m} \), the path is frictionless.
- Horizontal track: Extends from B to C, measuring 1.63 m in length.
- Point C: The location where the spring starts compressing.
- Spring: Compresses a distance of 0.852 m until the box stops.
- Friction: A constant force of 2.8 N acts on the box as it slides from B to C. 

The objective is to determine the spring constant, \( k \), in N/m.
Transcribed Image Text:As shown below, a box with a mass of 1.00 kg is released from rest at point A. It travels down a frictionless quarter-circle arc to point B. It slides on a horizontal track from B to C where it compresses a spring a distance of 85.2 cm before stopping. The horizontal track from B to C is 1.63 m long and has a constant 2.8 N frictional force acting on the box as it slides from B to C when it stops. Find the spring constant of the spring in N/m. **Diagram Explanation:** The diagram provides a visual representation of the scenario: - Point A: The starting position of the box, with a mass \( m = 1.0 \, \text{kg} \). - Quarter-circle path: From A to B, with a radius \( r = 2.0 \, \text{m} \), the path is frictionless. - Horizontal track: Extends from B to C, measuring 1.63 m in length. - Point C: The location where the spring starts compressing. - Spring: Compresses a distance of 0.852 m until the box stops. - Friction: A constant force of 2.8 N acts on the box as it slides from B to C. The objective is to determine the spring constant, \( k \), in N/m.
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