USAPhO 2026, Първи кръг — Задача 24

2026 F=maF = ma Exam · 1 т.

Указания

25 QUESTIONS - 75 MINUTES

DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN

  • Use g=10 N/kgg = 10\ \mathrm{N/kg} throughout, unless otherwise specified.
  • You may write in this question booklet and the scratch paper provided by the proctor.
  • This test has 25 multiple choice questions. Select the best response to each question, and use a No.2 pencil to completely fill the box corresponding to your choice. If you change an answer, completely erase the previous mark. Only use the boxes numbered 1 through 25 on the answer sheet.
  • All questions are equally weighted, but are not necessarily equally difficult.
  • You will receive one point for each correct answer, and zero points for each incorrect or blank answer. There is no additional penalty for incorrect answers.
  • You may use a hand-held calculator. Its memory must be cleared of data and programs. You may use only the basic functions found on a simple scientific calculator. Calculators may not be shared. Cell phones may not be used during the exam or while the exam papers are present. You may not use any external references, such as books or formula sheets.
  • The question booklet, answer sheet and scratch paper will be collected at the end of this exam.
  • To maintain exam security, do not communicate any information about the questions or their solutions until after February 13, 2026.

DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN

We acknowledge The US Physics Team coaches and other contributors to this year’s exams:

Tengiz Bibilashvili, Eddie Chen, Orhun Ciftcioglu, Kellan Colburn, Evan Erickson, Harry Kroft, Natalie LeBaron, Mai Qi, Elena Yudovina

Условие

A thin sheet of air with density ρ\rho is blown at a uniform speed vv toward a smooth, convex cylindrical surface of radius RR. The sheet has uniform thickness t≪Rt \ll R and remains everywhere tangent to the cylinder while it stays attached. Neglect gravity and viscosity.

The pressure on the outer side of the air sheet is constant and equal to PP. The pressure on the side adjacent to the cylinder is lower by an amount ΔP\Delta P. The air sheet follows the curvature of the cylinder until it can no longer remain attached.

Given the parameters below, what is the maximum integer speed vmax⁡v_{\max} for which the sheet can remain attached to the surface?

A circle of radius R (a radius line drawn from the centre dot) with a thin curved band of thickness t wrapped around its upper-left side. Arrows inside the band point along it, upward, labelled v; the pressure P is marked outside the band and P − ΔP inside the circle next to the band.
ρ=1.2 kg/m3,t=5.0 mm,R=5.0 cm,ΔPmax⁡=120 Pa.\rho = 1.2\ \mathrm{kg/m^3}, \qquad t = 5.0\ \mathrm{mm}, \qquad R = 5.0\ \mathrm{cm}, \qquad \Delta P_{\max} = 120\ \mathrm{Pa}.

(A) 8 m/s

(B) 22 m/s

(C) 31 m/s

(D) 44 m/s

(E) 60 m/s

Отговори

Решение

Оригинал в Архива: 2026_FMA_exam.pdf · официални решения: 2026_FMA_solutions.pdf