Add ITA 2025 Physics Essay Exam Solutions

[lgabs]

Solves #3 .Solutions can be found at Poliedro or Elite websites.

Questions added and reviewed:

• Question 1: pass, total points: 10.
• Question 2: pass, total points: 10.
• Question 3: failed all three parts. It made a incorrect assumption about the relation between accelerations when the llm said a_{\text{mov}} = a_{\text{fixa}} - a_M \, \sin\alpha. total points: 0.
• Question 4: failed on part b, when it treated the difference in kinetic energy \delta as a positive value (it said \delta = \frac{E_{\text{inicial}} - E_{\text{final}}}{E_{\text{inicial}}}, instead of negative value, which would be correct if the llm said \delta = \frac{E_{\text{final}} - E_{\text{inicial}}}{E_{\text{inicial}}}. Considering each part valued at 10/3=3.33 points, we could consider only half for part (b) for the mistake. total points: 3.33 * 2 + 3.33/2=8.33
• Question 5: failed on part (b). When the llm said the v_{\text{NS}} &= v_0 + v_e, this is only valid if m<<M. Checking the solution, we can see that v_{\text{NS}} &= v_0 + \frac{M}{M+m} \cdot v_e, i.e., o1 would be correct only if m<<M (which is probably true in real life, but the problem statement does not says that. total points: 5
• Question 6: pass, total points: 10.
• Question 7: pass partially. For part (b), it got the equations to plot intensity right, but o1 is not so good yet to follow instructions to make LaTeX code to really plot images when solving the question. We can discount points since it did not make graphs, but when asking o1 directly only to plot the images from equations obtained, it produced correct graphs, which we'll include to present a better solution. Discounting half points in (b): total points: 3.33 + 3.33/2 + 3.33=8.33.
• Question 8: failed in parts (b) and (c). o1-preview understood how the forces would act in the system, but it did not understand that \omega was not given in the problem statement and used it to answer (b). Part (c) was a terrible answer, it expressed \omega in terms of F_{\text{resultante} and then showed this force in terms of \omega, which is a circular reference. total points: 3.33 + 0 + 0 = 3.33.
• Question 9: failed. This question involves a complex image, which we know can affect performance. First, when establishing the equilibrium of the balance, it did not consider the counterweight. Second, GPT-4 was unable to describe the image in a way that allowed the angular coefficient to be calculated, so o1 organized its solution in terms of an unknown coefficient S. total points: 0.
• Question 10: pass. Very interesting, since it's a modern physics. total points: 10
• Add comments about the test (summary from above comments)

Total points so far: (10+10+0+8.33+5+10+8.33+3.33+0+10) / 10 = 6.50