Dievsky V.A. - Solution to problem D4 option 23 task 2

D4-23 (Task 2) Dievsky

For the mechanical system presented in the figure, it is necessary to determine the magnitude of the force F at which the system is in equilibrium. To solve this problem we will use the Lagrange principle.

From the initial data it is known that the weight of the load G is equal to 20 kN, the torque M is equal to 1 kNm, the radius of the drum is R₂ is equal to 0.4 m, and the double drum also has a radius r₂ = 0.2m. The angle α between the threads encircling the drums is 300 degrees, and the sliding friction coefficient f is 0.5. Unnumbered blocks and rollers can be considered weightless. The friction on the axes of the drum and blocks can be neglected.

Applying Lagrange's principle and taking into account the presence of friction, we can obtain the following equation:

F - Gsinα - fGcosα - M/R₂ - Mr₂/R₂ = 0

The maximum value of the force F at which the system is in equilibrium will be equal to:

F_max = Gsinα + fGcosα + M/R₂ + Mr₂/R₂

Dievsky V.A. - Solution to problem D4 option 23 task 2

This product is a solution to problem D4 option 23 task 2, which was developed by V.A. Dievsky. This digital product is intended for students and teachers studying mechanics and solving related problems.

The solution to the problem is presented in a beautiful HTML format, which ensures convenience and readability of the text. All material is divided into logical blocks using appropriate headings, which allows you to quickly navigate the text and find the information you need.

By purchasing this digital product, you receive a high-quality and detailed solution to the problem, which will help you better understand and reinforce the material on mechanics. In addition, a convenient format for presenting the material will allow you to quickly and effectively use it in the educational process.

This product is a digital solution to problem D4 option 23 task 2, developed by V.A. Dievsky for students and teachers studying mechanics and solving related problems.

The solution to the problem uses the Lagrange principle and takes into account the presence of friction. The initial data are known: load weight G = 20 kN, torque M = 1 kNm, drum radius R2 = 0.4 m (double drum also has r2 = 0.2 m), angle α = 300 degrees and sliding friction coefficient f = 0 ,5. Unnumbered blocks and rollers are considered weightless, and friction on the axes of the drum and blocks can be neglected.

The solution to the problem is presented in a beautiful HTML format, which ensures convenience and readability of the text. All material is divided into logical blocks using appropriate headings, which allows you to quickly navigate the text and find the information you need.

When purchasing this product, you receive a high-quality and detailed solution to the problem, which will help you better understand and consolidate the material on mechanics. In addition, a convenient format for presenting the material will allow you to quickly and effectively use it in the educational process. The maximum value of the force F at which the system is in equilibrium will be equal to Gsinα + fGcosα + M/R2 + Mr2/R2.

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This product is a task from the book “Solving Problems in Theoretical Mechanics” by the author V.A. Dievsky. The task requires determining the magnitude of the force F, which, in the presence of friction (the maximum value of this value), will bring the mechanical system presented in the diagram into equilibrium. To solve the problem it is necessary to use the Lagrange principle. The initial data are the load weight G (20 kN), torque M (1 kNm), drum radius R2 (0.4 m), angle α (300 degrees) and sliding friction coefficient f (0.5). Blocks and rollers are not taken into account by weight, and friction on the axes of the drum and blocks can be neglected.

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