Problem 1: Acircular air hockey puck of radius r slides across a frictionless air hockey table and is subjected to several forces as shown below. The magnitude and direction of each force is given. Forces are applied at either the center of mass of the puck, the outer edge (a distance r from the center), or a distance halfway (r/2) between the center and the outer edge. F 2 r F PA Select the examples below that have a net torque of zero about the axis perpendicular to the page and extending from the center of the puck. 3F 3F 2F

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**Problem 1: Torque and Circular Motion**

**Objective:**
Analyze the net torque acting on an air hockey puck on a frictionless air hockey table.

**Problem Statement:**
A circular air hockey puck of radius \( r \) slides across a frictionless air hockey table. Several forces are applied as illustrated. The magnitude and direction of each force are given. The forces are applied at:

- The center of mass of the puck
- The outer edge (a distance \( r \) from the center)
- A point halfway (\( \frac{r}{2} \)) between the center and the outer edge

**Task:**
Select the configurations in which the net torque about the axis perpendicular to the page, extending from the center of the puck, is zero.

**Diagram Explanation:**

1. **Top Right Diagram:**
   - Puck with radius \( r \).
   - Forces \( F \) are applied at various points—one at the edge and one at the halfway point.

2. **Examples: (Select zero net torque)**
   - **Top Left Diagram:** 
     - Forces: \( 3F \) (left) at the outer edge, \( F \) (right) at center, \( 2F \) (right) at edge.
   - **Top Middle Diagram:**
     - Forces: \( F \) (left) at center, \( 2F \) (right) at edge.
   - **Top Right Diagram:**
     - Forces: \( F \) (right) at edge, \( 3F \) (right) at edge.
   - **Bottom Left Diagram:**
     - Forces: \( F \) (right) at edge, \( F \) (left) at edge.
   - **Bottom Right Diagram:**
     - Forces: \( F \) (left) at center, \( 3F \) (right) at edge.

**Instructions:**
Choose the examples where the torques from opposing forces cancel each other out, resulting in a net torque of zero. Consider the direction of each force and its distance from the rotation axis to determine the torque. Submit your selections once you're certain of your choices. Use hints if needed, and seek feedback to clarify your understanding.

**Interactive Elements:**
- **Submit:** Confirm your selection.
- **Hint:** Access hints to guide you.
- **Feedback:** Review explanations for further understanding.
Transcribed Image Text:**Problem 1: Torque and Circular Motion** **Objective:** Analyze the net torque acting on an air hockey puck on a frictionless air hockey table. **Problem Statement:** A circular air hockey puck of radius \( r \) slides across a frictionless air hockey table. Several forces are applied as illustrated. The magnitude and direction of each force are given. The forces are applied at: - The center of mass of the puck - The outer edge (a distance \( r \) from the center) - A point halfway (\( \frac{r}{2} \)) between the center and the outer edge **Task:** Select the configurations in which the net torque about the axis perpendicular to the page, extending from the center of the puck, is zero. **Diagram Explanation:** 1. **Top Right Diagram:** - Puck with radius \( r \). - Forces \( F \) are applied at various points—one at the edge and one at the halfway point. 2. **Examples: (Select zero net torque)** - **Top Left Diagram:** - Forces: \( 3F \) (left) at the outer edge, \( F \) (right) at center, \( 2F \) (right) at edge. - **Top Middle Diagram:** - Forces: \( F \) (left) at center, \( 2F \) (right) at edge. - **Top Right Diagram:** - Forces: \( F \) (right) at edge, \( 3F \) (right) at edge. - **Bottom Left Diagram:** - Forces: \( F \) (right) at edge, \( F \) (left) at edge. - **Bottom Right Diagram:** - Forces: \( F \) (left) at center, \( 3F \) (right) at edge. **Instructions:** Choose the examples where the torques from opposing forces cancel each other out, resulting in a net torque of zero. Consider the direction of each force and its distance from the rotation axis to determine the torque. Submit your selections once you're certain of your choices. Use hints if needed, and seek feedback to clarify your understanding. **Interactive Elements:** - **Submit:** Confirm your selection. - **Hint:** Access hints to guide you. - **Feedback:** Review explanations for further understanding.
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