the crate, however, and it remains stationary. If necessary, use Fs for the force of static friction, and Fk as the force of kinetic friction

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### Understanding Forces on a Stationary Crate

A crate sits on a rough surface. Using a rope, a man applies a force to the crate as shown in a figure. The force is not enough to move the crate, however, and it remains stationary. If necessary, use \( F_s \) for the force of static friction, and \( F_k \) as the force of kinetic friction.

---

#### Free Body Diagram Explanation

The interactive image depicts a Free Body Diagram for the crate. Here's a detailed explanation:

1. **Axes**:
   - The coordinate system is defined with the \( x \)-axis horizontal and the \( y \)-axis vertical.

2. **Forces**:
   - **\( F_n \)** (Normal Force): This force is represented by a vertical arrow pointing upwards. It counteracts the weight of the crate and is perpendicular to the surface.
   - **\( F_g \)** (Gravitational Force): This force is represented by a vertical arrow pointing downwards, indicating the weight of the crate due to gravity.
   - **\( F \)**: This force is represented by an arrow applied at an angle \( \theta \) above the horizontal, indicating the pulling force of the rope.
   - **\( F_s \)** (Static Friction Force): This force is represented by an arrow pointing to the left and parallel to the surface. It prevents the crate from sliding and opposes the applied force.

3. **Graphical Interface**:
   - The right side of the image appears to be a control panel used to manipulate the forces labeled “Add Force” and “Reset All”. Each force is listed with its direction (in degrees), which can be adjusted.
   - The bottom of the interface shows buttons labeled "Submit," "Help," "Feedback," and "I give up!" designed to guide interactions within the tool.

4. **Vectors and Summation**:
   - The combined forces result in \(\Sigma F_{x} = 0 \) and \( \Sigma F_{y} = 0 \), verifying that the crate remains stationary and in equilibrium.

The static friction \( F_s \) adjusts to balance the applied force \( F \) until it reaches the maximum limit. If \( F \) exceeds this limit, the crate would begin to move, and \( F_k \) would come into play.
Transcribed Image Text:### Understanding Forces on a Stationary Crate A crate sits on a rough surface. Using a rope, a man applies a force to the crate as shown in a figure. The force is not enough to move the crate, however, and it remains stationary. If necessary, use \( F_s \) for the force of static friction, and \( F_k \) as the force of kinetic friction. --- #### Free Body Diagram Explanation The interactive image depicts a Free Body Diagram for the crate. Here's a detailed explanation: 1. **Axes**: - The coordinate system is defined with the \( x \)-axis horizontal and the \( y \)-axis vertical. 2. **Forces**: - **\( F_n \)** (Normal Force): This force is represented by a vertical arrow pointing upwards. It counteracts the weight of the crate and is perpendicular to the surface. - **\( F_g \)** (Gravitational Force): This force is represented by a vertical arrow pointing downwards, indicating the weight of the crate due to gravity. - **\( F \)**: This force is represented by an arrow applied at an angle \( \theta \) above the horizontal, indicating the pulling force of the rope. - **\( F_s \)** (Static Friction Force): This force is represented by an arrow pointing to the left and parallel to the surface. It prevents the crate from sliding and opposes the applied force. 3. **Graphical Interface**: - The right side of the image appears to be a control panel used to manipulate the forces labeled “Add Force” and “Reset All”. Each force is listed with its direction (in degrees), which can be adjusted. - The bottom of the interface shows buttons labeled "Submit," "Help," "Feedback," and "I give up!" designed to guide interactions within the tool. 4. **Vectors and Summation**: - The combined forces result in \(\Sigma F_{x} = 0 \) and \( \Sigma F_{y} = 0 \), verifying that the crate remains stationary and in equilibrium. The static friction \( F_s \) adjusts to balance the applied force \( F \) until it reaches the maximum limit. If \( F \) exceeds this limit, the crate would begin to move, and \( F_k \) would come into play.
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