1. A 20 N crate is held at rest on an incline by a rope that is parallel to the incline as shown on the figure to the right. The incline is 30° above the horizontal. The coefficient of static friction, µs, between the crate and the incline is 0.35. m a) Draw two free body diagrams for the forces acting on the crate. In the first, indicate the forces pointing along the ramp and in the second, indicate the forces pointing perpendicular to the ramp b) Rank all forces acting on the crate from largest to smallest. c) Write down two separate equations for Newton's second law with static friction: one for forces pointing along the ramp and one for forces pointing perpendicular to the ramp. Do some forces appear in only one of the Newton's law equations? For forces that have some component in both, make sure you break down those force vectors correctly in the equation.

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1. A 20 N crate is held at rest on an incline by a rope that is parallel to the incline as shown on the figure to the right. The incline is 30° above the horizontal. The coefficient of static friction, \( \mu_s \), between the crate and the incline is 0.35.

a) Draw two free body diagrams for the forces acting on the crate. In the first, indicate the forces pointing along the ramp and in the second, indicate the forces pointing perpendicular to the ramp.

b) Rank all forces acting on the crate from largest to smallest.

c) Write down two separate equations for Newton’s second law with static friction: one for forces pointing along the ramp and one for forces pointing perpendicular to the ramp. Do some forces appear in only one of the Newton’s law equations? For forces that have some component in both, make sure you break down those force vectors correctly in the equation.

**Diagram Explanation:**
The diagram illustrates a crate of mass \( m \) resting on an inclined plane with angle \( \theta \). A rope is parallel to the incline assisting the crate to stay at rest. The forces to consider include gravitational force, normal force, static friction, and tension in the rope.
Transcribed Image Text:1. A 20 N crate is held at rest on an incline by a rope that is parallel to the incline as shown on the figure to the right. The incline is 30° above the horizontal. The coefficient of static friction, \( \mu_s \), between the crate and the incline is 0.35. a) Draw two free body diagrams for the forces acting on the crate. In the first, indicate the forces pointing along the ramp and in the second, indicate the forces pointing perpendicular to the ramp. b) Rank all forces acting on the crate from largest to smallest. c) Write down two separate equations for Newton’s second law with static friction: one for forces pointing along the ramp and one for forces pointing perpendicular to the ramp. Do some forces appear in only one of the Newton’s law equations? For forces that have some component in both, make sure you break down those force vectors correctly in the equation. **Diagram Explanation:** The diagram illustrates a crate of mass \( m \) resting on an inclined plane with angle \( \theta \). A rope is parallel to the incline assisting the crate to stay at rest. The forces to consider include gravitational force, normal force, static friction, and tension in the rope.
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