You're looking at a specific version of this model. Jump to the model overview.
pku-yuangroup /llava-cot:40c17578
Input
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>
Generated in