A block is placed on the surface of a sphere, as shown below. The coefficient of static friction between the block and the sphere is 0.680. Use Newton's 2nd Law to find the angle at which the mass will just begin to slide. (answer: 34.2%)

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Chapter1: Units, Trigonometry. And Vectors
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**Problem Statement:**

A block is placed on the surface of a sphere, as shown below. The coefficient of static friction between the block and the sphere is 0.680. Use Newton's 2nd Law to find the angle \( \phi \) at which the mass will just begin to slide. 

**Answer:** \( 34.2^\circ \)

**Diagram Explanation:**

The diagram illustrates a sphere with a small block of mass \( m \) positioned on its surface. The block is located at an angle \( \phi \) with respect to the vertical line passing through the center of the sphere (denoted as point O). 

Key features include:

- **Sphere:** Shaded and shown in a circular shape representing the surface on which the block rests.
- **Block:** A small rectangular block positioned tangent to the surface.
- **Angle \( \phi \):** The angle between the vertical line and the line connecting the center of the sphere (O) to the block.
- **Forces:** While not explicitly drawn, the diagram is intended to guide the application of forces such as gravitational force, normal force, and static friction to determine the critical angle where the block begins to slide.
Transcribed Image Text:**Problem Statement:** A block is placed on the surface of a sphere, as shown below. The coefficient of static friction between the block and the sphere is 0.680. Use Newton's 2nd Law to find the angle \( \phi \) at which the mass will just begin to slide. **Answer:** \( 34.2^\circ \) **Diagram Explanation:** The diagram illustrates a sphere with a small block of mass \( m \) positioned on its surface. The block is located at an angle \( \phi \) with respect to the vertical line passing through the center of the sphere (denoted as point O). Key features include: - **Sphere:** Shaded and shown in a circular shape representing the surface on which the block rests. - **Block:** A small rectangular block positioned tangent to the surface. - **Angle \( \phi \):** The angle between the vertical line and the line connecting the center of the sphere (O) to the block. - **Forces:** While not explicitly drawn, the diagram is intended to guide the application of forces such as gravitational force, normal force, and static friction to determine the critical angle where the block begins to slide.
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Coff. of static friction = 0.68

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