A copper (shear modulus 4.2 x 1010 N/m²) cube, 0.442 m on a side, is subjected to two shearing forces, each of magnitude F = 3.70 x 10°N (see the drawing). Find the angle (in degrees), which is one measure of how the shape of the block has been altered by shear deformation. Number ! Units O <>

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**Shear Deformation of a Copper Cube**

**Problem Statement:**

A copper (shear modulus \(4.2 \times 10^{10}\) N/m\(^2\)) cube, 0.442 m on a side, is subjected to two shearing forces, each of magnitude \(F = 3.70 \times 10^6\) N. Find the angle \(\theta\) (in degrees), which is a measure of how the shape of the block has been altered by shear deformation.

**Diagram Explanation:**

The diagram illustrates a cubic block of copper with its side length labeled as 0.442 meters. Two forces, \(F\), of magnitude \(3.70 \times 10^6\) N, are shown acting parallel and opposite to each other on the top and bottom surfaces of the cube, creating a shear deformation. The angle \(\theta\) is shown between the initial vertical line and the deformed side of the cube.

**Input Space:**

- **Number:** There is an input field where the number (value of angle \(\theta\)) should be entered.
- **Units:** The units for the angle \(\theta\) are degrees, as hinted by the dropdown menu next to the input field.

**Shear Deformation Explanation:**

Shear deformation refers to the change in the shape of a material in response to the application of shear forces. In this scenario, the forces applied to the copper block cause it to deform at an angle \(\theta\), altering the original cube shape. The magnitude of the shear forces and the material's shear modulus influence the extent of deformation.

Find the angle \(\theta\) using the appropriate relationships and input your answer in degrees in the provided fields.
Transcribed Image Text:**Shear Deformation of a Copper Cube** **Problem Statement:** A copper (shear modulus \(4.2 \times 10^{10}\) N/m\(^2\)) cube, 0.442 m on a side, is subjected to two shearing forces, each of magnitude \(F = 3.70 \times 10^6\) N. Find the angle \(\theta\) (in degrees), which is a measure of how the shape of the block has been altered by shear deformation. **Diagram Explanation:** The diagram illustrates a cubic block of copper with its side length labeled as 0.442 meters. Two forces, \(F\), of magnitude \(3.70 \times 10^6\) N, are shown acting parallel and opposite to each other on the top and bottom surfaces of the cube, creating a shear deformation. The angle \(\theta\) is shown between the initial vertical line and the deformed side of the cube. **Input Space:** - **Number:** There is an input field where the number (value of angle \(\theta\)) should be entered. - **Units:** The units for the angle \(\theta\) are degrees, as hinted by the dropdown menu next to the input field. **Shear Deformation Explanation:** Shear deformation refers to the change in the shape of a material in response to the application of shear forces. In this scenario, the forces applied to the copper block cause it to deform at an angle \(\theta\), altering the original cube shape. The magnitude of the shear forces and the material's shear modulus influence the extent of deformation. Find the angle \(\theta\) using the appropriate relationships and input your answer in degrees in the provided fields.
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