Съдържание

Условие Отговори Решение

USAPhO 2001, Четвъртфинал — Задача 1

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Всички материали от USAPhO 2001

2001 Preliminary Exam — Open Response Questions · 25 т.

Preliminary Exam

Open Response Questions

4 Questions, 60 minutes

Указания

DO NOT OPEN THIS TEST UNTIL YOU ARE TOLD TO BEGIN

Show all your work. Partial credit will be given.
Start each question on a new sheet of paper. Be sure to put your name in the upper right-hand corner of each page, along with the question number and the page number/total pages for this problem. For example, Doe, Jamie / Q1 – 1/3
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. You may not use any tables, books, or collections of formulas.
Each of the four questions is worth 25 points. The questions are not necessarily of the same difficulty.

Possibly Useful Information

Gravitational field at the Earth’s surface $g=9.8\ N/kg$

Newton’s gravitational constant $G=6.67\times10^{-11}\ N\cdot m^2/kg^2$

Binomial expansion $(1+x)^n\approx1+nx$ for $|x|\ll1$

Moment of Inertia about Center of Mass – Uniform Object (will not be provided on the second screening exam)

Object	Moment of Inertia
Disk	$\frac12MR^2$
Sphere	$\frac25MR^2$
Rod	$\frac1{12}ML^2$

Solutions to Problems

Any correct solution should be awarded equivalent points. Suggested partial-credit points are presented in square brackets at the right margin. You may further break down the listed points into one point increments. If it is clear they have done an intermediate step, they should get credit for it even if they have not presented it. For example, in 1.a., if a student wrote down $mv_0r_0=mvr$ , they should get 6 points credit. Students should not be penalized in a subsequent part for using the wrong answer to a previous part. (No double jeopardy.)

Условие

A mass $m$ attached to a massless string moves around a circle of radius $r_0$ with speed $v_0$ on a frictionless table as shown in the accompanying diagram. The string passes through a small hole in the table. Starting at time $t=0$ , the string is pulled downward with a constant speed $V$ . Determine:

[Mass on a table moving around a hole while the string is pulled downward]

a The tangential speed $v$ of mass $m$ as a function of $r$ . [7 т.]

b The tangential speed $v$ of mass $m$ as a function of time $t$ . [6 т.]

c The force needed to pull the string as a function of time $t$ . [6 т.]

d The work done on the mass by the string from time $t=0$ to time $t$ . [6 т.]

Отговори

Решение

Теми и трудност

Трудност: неоценена.

Механика · Момент на импулса · Работа и енергия

Предпоставки: Разширена олимпиадна подготовка

Оригинал в Архива: Quarterfinal 2001.pdf · официални решения: Quarterfinal 2001 Solutions.pdf