USAPhO 2024, Първи кръг — Задача 17

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

Consider the following system of massless and frictionless pulleys, ropes, and springs.

An upper pulley hangs from the ceiling by two springs, k on the left and 2k on the right; a rod connects it to a lower pulley below; a rope over the lower pulley is tied on the left to a spring 3k fixed to the floor and on the right carries the block m.

Initially, a block of mass mm is attached to the end of a rope, and the system is in equilibrium. Next the block is doubled in mass, and the system is allowed to come to equilibrium again. During the transition between these equilibria, how far does the end of the rope (where the block is suspended) move?

(A) 712mgk\dfrac{7}{12}\dfrac{mg}{k}

(B) 1112mgk\dfrac{11}{12}\dfrac{mg}{k}

(C) 1312mgk\dfrac{13}{12}\dfrac{mg}{k}

(D) 76mgk\dfrac{7}{6}\dfrac{mg}{k}

(E) 116mgk\dfrac{11}{6}\dfrac{mg}{k}

Отговори

Решение

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