USAPhO 2026, Първи кръг — Задача 16
2026 Exam · 1 т.
Указания
25 QUESTIONS - 75 MINUTES
DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN
- Use 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 small puck of mass slides without friction inside a rigid, uniform triangle rack of mass , whose inner boundary is an equilateral triangle . The rack is initially at rest and can move freely on a frictionless horizontal table. All collisions between the puck and the rack are perfectly elastic.
At some instant, the puck strikes the midpoint of side from inside the rack. Just before this collision, the puck’s velocity is parallel to side .
After the collision at the midpoint of , the puck collides with the rack again, and then collides once more. At which part of the triangle does this second collision after the initial one occur?
(Some answer choices refer to the midpoint of side .)
(A) a point in the interior of segment
(B) a point in the interior of segment
(C) a point in the interior of segment
(D) a point in the interior of segment
(E) the point
Отговори
- E
Решение
During each impact, the contact force produces zero net torque on the rack about its center of mass, so the triangle does not rotate. For an elastic collision between frictionless bodies, the tangential component of the relative velocity at the point of contact is unchanged, while the normal component reverses sign without changing its magnitude, independent of the masses of the colliding objects. Thus, in the rack’s instantaneous rest frame, the collision is equivalent to specular reflection from a frictionless wall. After the first collision at the midpoint of , the puck next collides with the midpoint of , and the subsequent collision asked for in the problem occurs at point .
Оригинал в Архива: 2026_FMA_exam.pdf · официални решения: 2026_FMA_solutions.pdf