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
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Chapter1: Units, Trigonometry. And Vectors
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How do I find the torque of the forces? The vertical ones confuse me.
![## Torque Calculation Example
### Problem Statement
The plywood sheet shown in the above picture measures \(2.0 \, \text{m} \times 2.0 \, \text{m}\) and each of the four forces the sheet is subjected to has a magnitude of \(8.0 \, \text{N}\). 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.
### Diagram Description
The diagram shows a square plywood sheet divided into smaller squares by a grid, with a side length of \(2.0 \, \text{m}\). There are four forces acting on the sheet, labeled as \(F_1\), \(F_2\), \(F_3\), and \(F_4\). The center of rotation is marked at the top left corner of the sheet.
- **\(F_1\):** Acts downward at the center of the bottom edge.
- **\(F_2\):** Acts leftward at the center of the right edge.
- **\(F_3\):** Acts rightward at the center of the right edge, parallel to \(F_2\).
- **\(F_4\):** Acts upward at the center of the top edge.
### Calculation of Torque
The torque (\(\tau\)) generated by a force (\(F\)) is given by the equation:
\[
\tau = r \times F \times \sin(\theta)
\]
Where:
- \(r\) is the distance from the point of rotation to the point where the force is applied.
- \(\theta\) is the angle between the force vector and the lever arm.
Since all forces are applied perpendicularly to the lever arms, \(\theta = 90^\circ\), and \(\sin(90^\circ) = 1\).
#### Torque due to \(F_1\):
- Distance \(r\) from the center of rotation to the point of application: \(2.0 \, \text{m}\).
- Torque: \(\tau_1 = 2.0\, \text{m} \times 8.0 \, \text{N} = 16.0 \, \text{Nm}\).
- Direction: Clockwise (negative torque).
#### Torque due to \(F](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6a5d5111-1d2a-4970-848c-d397a90063e1%2Fc00ba835-f5e4-4f1e-a977-5a2699f4a09c%2Fvl2iygb_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Torque Calculation Example
### Problem Statement
The plywood sheet shown in the above picture measures \(2.0 \, \text{m} \times 2.0 \, \text{m}\) and each of the four forces the sheet is subjected to has a magnitude of \(8.0 \, \text{N}\). 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.
### Diagram Description
The diagram shows a square plywood sheet divided into smaller squares by a grid, with a side length of \(2.0 \, \text{m}\). There are four forces acting on the sheet, labeled as \(F_1\), \(F_2\), \(F_3\), and \(F_4\). The center of rotation is marked at the top left corner of the sheet.
- **\(F_1\):** Acts downward at the center of the bottom edge.
- **\(F_2\):** Acts leftward at the center of the right edge.
- **\(F_3\):** Acts rightward at the center of the right edge, parallel to \(F_2\).
- **\(F_4\):** Acts upward at the center of the top edge.
### Calculation of Torque
The torque (\(\tau\)) generated by a force (\(F\)) is given by the equation:
\[
\tau = r \times F \times \sin(\theta)
\]
Where:
- \(r\) is the distance from the point of rotation to the point where the force is applied.
- \(\theta\) is the angle between the force vector and the lever arm.
Since all forces are applied perpendicularly to the lever arms, \(\theta = 90^\circ\), and \(\sin(90^\circ) = 1\).
#### Torque due to \(F_1\):
- Distance \(r\) from the center of rotation to the point of application: \(2.0 \, \text{m}\).
- Torque: \(\tau_1 = 2.0\, \text{m} \times 8.0 \, \text{N} = 16.0 \, \text{Nm}\).
- Direction: Clockwise (negative torque).
#### Torque due to \(F
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