Problem Analysis #2

[THOUGHT] The problem asks us to identify the correct statement based on the provided text and a specific scenario involving bimetallic strips.

1. Analyze the Text and Scenario:

• Bimetallic Strip Principle: A strip made of two materials (P and Q) bends if their Linear Thermal Expansion Coefficients (LTEC) differ. If Q has a larger LTEC than P, the strip bends towards P (the side with the smaller coefficient) upon heating.
• Key Factors for Bending:
  • LTEC Difference: A larger difference leads to more bending (higher curvature).
  • Temperature Change: A larger temperature change leads to more bending.
  • Flexural Sensitivity (휨 민감도): Represents how much a strip bends for a given temperature change. Higher sensitivity means more bending.
• Actuator Characteristics:
  • Max Moving Distance: The distance the tip moves when there is no external resistance. This corresponds to the state of maximum curvature where the force exerted on the outside becomes zero.
  • Force: The strip exerts force while bending. This force vanishes when the strip reaches its maximum moving distance (maximum curvature).
  • Response Completion Time: Time to reach the maximum moving distance. Thinner strips have shorter times.
• Scenario in <Example>:
  • Two strips, $a$ and $b$.
  • LTEC difference: $b > a$. (So $b$ bends more for the same $\Delta T$).
  • Dimensions: Same thickness and length.
  • Grippers A (using $a$) and B (using $b$).
  • At $T_1$: B grabs the object, A does not. (B bent enough, A did not).
  • At $T_2$ ($T_2 > T_1$): A also grabs the object.

2. Evaluate the Options:

• ① T0에서 T1로 올렸을 때보다 T0에서 T2로 올렸을 때, a와 b 모두 외부에 가할 수 있는 힘이 소멸되는 시점의 곡률은 더 크겠군.

  • The "point where the force exerted on the outside vanishes" is defined in the text as the state where the strip reaches its maximum moving distance and maximum curvature (the stress-free bent state).
  • The text states: "Other conditions being equal... the larger the temperature change, the more the strip bends."
  • Bending more means a larger curvature.
  • Since the temperature change $T_0 \to T_2$ is larger than $T_0 \to T_1$ (because $T_2 > T_1$), the maximum curvature (at the force vanishing point) for $T_2$ will be larger than for $T_1$.
  • This applies to both strips $a$ and $b$.
  • Therefore, this statement is correct.

• ② T0에서 T1로 올렸을 때, a와 b 각각의 휨이 멈춘 시점에서의 a의 곡률 반지름은 b의 곡률 반지름보다 작겠군.

  • At $T_1$, B grabs the object (bends significantly), while A does not (bends less).
  • Even theoretically, since the LTEC difference of $b > a$, strip $b$ bends more than $a$ for the same temperature.
  • Bending more means higher curvature and smaller radius of curvature.
  • So, Radius($b$) < Radius($a$).
  • The option claims Radius($a$) < Radius($b$). This is incorrect.

• ③ T0에서 T1로 올렸을 때, A와 B 각각의 동작이 멈추는 데 걸린 시간이 서로 같았다면 b의 반응 완료 시간이 a보다 짧겠군.

  • Let $t_{stop}$ be the time when movement stopped.
  • A stops because it reaches its maximum displacement (it didn't grab anything). So $t_{stop} = \text{Response Completion Time of } a$ ($RCT_a$).
  • B stops because it hits the object. This happens before it reaches its full potential displacement (since it exerts force on the object, it hasn't reached the "force vanishes" point). So $t_{stop} < \text{Response Completion Time of } b$ ($RCT_b$).
  • Given $t_{stop}$ is the same for both, we have $RCT_a = t_{stop} < RCT_b$.
  • So $RCT_b > RCT_a$.
  • The option claims $b$'s time is shorter ($RCT_b < RCT_a$). This is incorrect.

• ④ T0에서 T2로 올렸을 때, a의 최대 이동 거리가 b보다 더 크겠군.

  • Max moving distance depends on the degree of bending.
  • Since strip $b$ has a larger LTEC difference, it bends more than $a$ for the same temperature change.
  • Therefore, $b$ has a larger maximum moving distance.
  • The option claims $a > b$. This is incorrect.

• ⑤ B와 달리, T2가 되어야 A가 물체를 잡을 수 있었던 것은 a가 b보다 휨 민감도가 크기 때문이겠군.

  • Flexural sensitivity indicates how much a strip bends for a given temperature.
  • Since $b$ bent enough at $T_1$ but $a$ needed a higher temperature $T_2$, $b$ is more sensitive than $a$.
  • Also, sensitivity is linked to the LTEC difference, which is larger for $b$.
  • The option claims $a$ has greater sensitivity. This is incorrect.

Conclusion: Option 1 correctly interprets the relationship between temperature change and the curvature at the theoretical state of maximum expansion (where force vanishes).

\boxed{①}