Math Problem Statement

如图所示,质量均为 m 的木块 A、B 齐放在一起,B 通过轻绳与质量为 2m 的木块 C 相连。三木块放置在可绕固定转轴 OO' 转动的水平转台上。木块 A、B 与转轴 OO' 的距离为 2L,木块 C 与转轴 OO' 的距离为 L。A 与 B 间的动摩擦因数为 μ(取最大静摩擦力等于滑动摩擦力)。若圆盘从静止开始缓慢加速转动,直到木块即将发生相对滑动为止。用 ω 表示圆盘转动的角速度,下面说法正确的是( )

Solution

The image describes a system involving three wooden blocks (A, B, and C) on a rotating platform. The blocks are connected to a rotating axis with frictional forces between them and the platform. The problem involves analyzing the rotational motion and frictional interactions.

The options listed suggest different statements about the forces and behaviors of the system as the platform accelerates.

Let's break down the choices:

  • A: When ω=3μg4L\omega = \sqrt{\frac{3\mu g}{4L}}, the light frictional force is zero.
  • B: The friction between block B and the platform increases continuously.
  • C: When ω=μgL\omega = \sqrt{\frac{\mu g}{L}}, the frictional force between block C and the platform is zero.
  • D: The maximum angular speed ω\omega is 2μgL\sqrt{\frac{2\mu g}{L}}.

These are multiple-choice questions related to the mechanics of the system. Do you want me to analyze or explain the details of any specific option, or walk you through solving the problem?

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Math Problem Analysis

Mathematical Concepts

Rotational Motion
Friction
Angular Velocity

Formulas

ω = √(3μg/4L)
ω = √(μg/L)
ω = √(2μg/L)

Theorems

Newton's Laws of Motion
Centripetal Force
Frictional Force

Suitable Grade Level

Grades 10-12