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Model

@pku-yuangroup / llava-cot

Output

<SUMMARY> To solve the problem, I will use the relationship between shear modulus, force, and displacement. I will calculate the shear modulus using the given force and displacement values. </SUMMARY> <CAPTION> The image shows a rectangular block of acetal polymer fixed between two rigid plates. The block is subjected to a horizontal force (P = 2 kN) at the top, causing a horizontal displacement of 2 mm. The block's width is 100 mm. </CAPTION> <REASONING> The shear modulus (G) of a material is given by the formula: \[ G = \frac{P \cdot L}{A \cdot \delta} \] where: - \( P \) is the applied force (2 kN = 2000 N), - \( L \) is the length of the block (400 mm = 0.4 m), - \( A \) is the cross-sectional area of the block (width × height = 100 mm × 200 mm = 0.01 m²), - \( \delta \) is the horizontal displacement (2 mm = 0.002 m). Substituting these values into the formula: \[ G = \frac{2000 \, \text{N} \times 0.4 \, \text{m}}{0.01 \, \text{m}² \times 0.002 \, \text{m}} \] \[ G = \frac{800}{0.00002} \] \[ G = 20 \, \text{MPa} \] Thus, the shear modulus of the polymer is 20 MPa. </REASONING> <CONCLUSION> C </CONCLUSION>

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