BPO 2019, Теория — Задача 2

1st Balkan Physics Olympiad – 2019 BPO · 14 юли 2019 г. · 25 т.

Условие

Two identical bodies $A$ and $B$ lie on a smooth horizontal surface. The two bodies are connected by a spring, with negligible mass, that obeys the Hooke’s Law, with spring constant $k$ and relaxed length $L_0$. A third body $C$, is suspended to the body $B$, by means of an ideal string (non-extensible and of negligible mass), passing over a smooth pulley $P$. The three bodies have the same mass $m$. Initially, the three-body system is at rest and the spring has its relaxed length. The system is accordingly released from rest.

a) Draw a free body diagram for each body after the system is released [3 т.]

b) Calculate the minimum and maximum distance between the bodies $A$ and $B$. Mind that during the three-body motion, body $B$ doesn’t hit on the pulley and body $C$ doesn’t reach the ground. [10 т.]

c) Calculate the minimum value for the friction coefficient as well as the distance between the bodies $A$ and $B$, in order for the system to remain at rest when it is released. [6 т.]

d) Calculate the value of the friction coefficient as well as the distance between the bodies $A$ and $B$ in order for the system to move at constant speed. [6 т.]

Отговори

Решение

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Оригинал в Архива: problems.pdf · официални решения: solutions.pdf