USAPhO 2023, Първи кръг — Задача 18
2023 Exam · 1 т.
Указания
2023 Exam
25 QUESTIONS - 75 MINUTES
INSTRUCTIONS
DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN
- Use throughout this contest.
- You may write in this booklet of questions. However, you will not receive any credit for anything written in this booklet. You may only use the scratch paper provided by the proctor.
- This test contains 25 multiple choice questions. Select the answer that provides the best response to each question. Please be sure to use a No.2 pencil and completely fill the box corresponding to your choice. If you change an answer, the previous mark must be completely erased. Only the boxes preceded by numbers 1 through 25 are to be used on the answer sheet.
- All questions are equally weighted, but are not necessarily of the same level of difficulty.
- Correct answers will be awarded one point; incorrect answers or leaving an answer blank will be awarded zero points. There is no additional penalty for incorrect answers.
- A hand-held calculator may be used. 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 tables, books, or collections of formulas.
- The question booklet, answer sheet and scratch paper will be collected at the end of this exam.
- In order to maintain exam security, do not communicate any information about the questions (or their answers or solutions) on this contest until after February 25, 2023.
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, Kellan Colburn, Samuel Gebretsadkan, Abi Krishnan, Natalie LeBaron, Kye Shi, Mike Winer, and Kevin Zhou
Условие
Alice, Bob, and Carol are each given identical airtight bags containing identical rocks, and a large tub of water with a scale sitting on the bottom. Each of them measures the weight of their bag and rock by putting the bag on the scale, using three slightly different procedures.
- Alice closes the bag carefully, so that there is no air inside.
- Bob fills the rest of the bag with water before closing it.
- Carol closes the bag loosely, so that it contains some air.
What is the correct ranking of their measured weights , , and ?
- (A)
- (B)
- (C)
- (D)
- (E)
Отговори
- E
Решение
The scale’s measurement is the weight of the object not supported by the buoyant force. In other words, the scale measures , where is the mass of the bag, is the density of water, and is the volume of water. For Alice,
If Bob adds volume of water, he adds mass as well, so
Carol adds a volume while adding a negligible mass from the air, so
Therefore, the answer is (E).
Оригинал в Архива: 2023_F-ma_Exam.pdf · официални решения: 2023_F-ma_Solutions_v3.pdf