USAPhO 2024, Първи кръг — Задача 13

2024 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 24, 2024.

DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN

We acknowledge the following people for their contributions to this year’s exams (in alphabetical order):

Tengiz Bibilashvili, Orhun Ciftcioglu, Kellan Colburn, Natalie LeBaron, Brian Skinner, Elena Yudovina and Kevin Zhou

Условие

Two frictionless blocks of mass mm are connected by a massless string which passes through a fixed massless pulley, which is a height hh above the ground. Suppose the blocks are initially held with horizontal separation xx, and the length of the string is chosen so that the right block hangs in the air as shown.

A pulley hangs from the ceiling at height h above the ground; a string runs from a block on the ground diagonally up to the pulley and down to a second block hanging in the air; the horizontal separation x between the blocks and the height h are marked with arrows.

If the blocks are released, the tension in the string immediately afterward will be TT. Which of the following shows a plot of TT versus xx?

Five answer plots (A)–(E) of T against x with the level mg marked on the T axis: (A) constant at mg; (B) starting at mg and decreasing gently to a lower plateau; (C) starting below mg and rising towards mg; (D) starting at mg and decreasing steeply towards zero; (E) starting at mg and increasing.

Отговори

Решение

Оригинал в Архива: 2024_F-ma_Exam.pdf · официални решения: 2024_F-ma_Solutions.pdf