Calculate torque for F4 **Determining Torque on a Plywood Sheet**The plywood sheet illustrated in the diagram measures 2.0 m × 2.0 m. Each of the four forces acting on the sheet has a magnitude of 8.0 N. The sheet is subjected to these forces relative to an axis perpendicular to the page, passing through the top left corner of the sheet.**Objective:** Calculate the magnitude of the torque for each force.### Diagram Review:- **Center of Rotation:** This is located at the top left corner of the plywood sheet.- **Grid Layout:** The sheet is divided into a grid by orange lines.- **Forces:** - \( F_1 \) (acting downward at the center of the bottom edge) - \( F_2 \) (acting leftward at the center of the right edge) - \( F_3 \) (acting rightward at the center of the sheet) - \( F_4 \) (acting upward at the center of the top edge) To determine the torque (\( \tau \)) generated by each force, we utilize the equation:\[ \tau = F \cdot r \cdot \sin(\theta) \]Where:- \( F \) is the magnitude of the force,- \( r \) is the perpendicular distance from the axis of rotation to the line of action of the force,- \( \theta \) is the angle between \( F \) and \( r \).Since all forces are perpendicular to their respective \( r \)-distances (\(\theta = 90^{\circ}\)), \(\sin(90^{\circ}) = 1\), simplifying the torque equation to:\[ \tau = F \cdot r \]### Detailed Calculation of Torque:1. **Torque Due to \( F_1 \):** - Distance (\( r \)) from the center of rotation (top left corner) to the acting point of \( F_1 \) is 2.0 m. - \( \tau_{1} = 8.0 \, \text{N} \times 2.0 \, \text{m} = 16.0 \, \text{Nm} \) (clockwise).2. **Torque Due to \( F_2 \):** - Distance (\( r \)) from the center of rotation to the acting point of \(

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The plywood sheet shown in the above picture measures 2.0 m x 2.0 m and each of the four forces the sheet is subjected to has a magnitude of 8.0 N. Relative to an axis that is perpendicular to the page and passes through the top left corner of the sheet, determine the magnitude of the torque due to each of the forces. Center of Rotation F4 F3 F2 F1

The plywood sheet shown in the above picture measures 2.0 m x 2.0 m and each of the four forces the sheet is subjected to has a magnitude of 8.0 N. Relative to an axis that is perpendicular to the page and passes through the top left corner of the sheet, determine the magnitude of the torque due to each of the forces. Center of Rotation F4 F3 F2 F1

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

Calculate torque for F4

**Determining Torque on a Plywood Sheet**

The plywood sheet illustrated in the diagram measures 2.0 m × 2.0 m. Each of the four forces acting on the sheet has a magnitude of 8.0 N. The sheet is subjected to these forces relative to an axis perpendicular to the page, passing through the top left corner of the sheet.

**Objective:** Calculate the magnitude of the torque for each force.

### Diagram Review:
- **Center of Rotation:** This is located at the top left corner of the plywood sheet.
- **Grid Layout:** The sheet is divided into a grid by orange lines.
- **Forces:**
- \( F_1 \) (acting downward at the center of the bottom edge)
- \( F_2 \) (acting leftward at the center of the right edge)
- \( F_3 \) (acting rightward at the center of the sheet)
- \( F_4 \) (acting upward at the center of the top edge)

To determine the torque (\( \tau \)) generated by each force, we utilize the equation:

\[ \tau = F \cdot r \cdot \sin(\theta) \]

Where:
- \( F \) is the magnitude of the force,
- \( r \) is the perpendicular distance from the axis of rotation to the line of action of the force,
- \( \theta \) is the angle between \( F \) and \( r \).

Since all forces are perpendicular to their respective \( r \)-distances (\(\theta = 90^{\circ}\)), \(\sin(90^{\circ}) = 1\), simplifying the torque equation to:

\[ \tau = F \cdot r \]

### Detailed Calculation of Torque:

1. **Torque Due to \( F_1 \):**
- Distance (\( r \)) from the center of rotation (top left corner) to the acting point of \( F_1 \) is 2.0 m.
- \( \tau_{1} = 8.0 \, \text{N} \times 2.0 \, \text{m} = 16.0 \, \text{Nm} \) (clockwise).

2. **Torque Due to \( F_2 \):**
- Distance (\( r \)) from the center of rotation to the acting point of \(

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