Dievsky V.A. - Solving problem D4 option 30 task 2

Task 2 in the discipline D4-30, related to mechanics, is to determine the magnitude of the force F at which the mechanical system, shown in the figure using the Lagrange principle, is in equilibrium. There is friction in this system, and it is necessary to find the maximum value of this quantity.

To solve the problem, you need to use the following initial data: the weight of the load G is equal to 20 kN, the torque M is equal to 1 kNm, the radius of the drum R2 is equal to 0.4 m (the double drum also has r2 equal to 0.2 m), the angle α is equal to 300 and sliding friction coefficient f is 0.5.

In this system, blocks and unnumbered blocks are considered weightless, and friction on the axes of the drum and blocks can be neglected.

Solving the problem involves finding the minimum of the Lagrange functional, which is defined as the difference between the kinetic and potential energy of the system. By calculating the derivative of this functional with respect to the movement of the load, one can find the equation of motion of the system. Assuming the system is in equilibrium, Eq.

Task 2 in the discipline D4-30, related to mechanics, is to determine the magnitude of the force F at which the mechanical system, shown in the figure using the Lagrange principle, is in equilibrium. There is friction in this system, and it is necessary to find the maximum value of this quantity.

To solve the problem, you need to use the following initial data: the weight of the load G is equal to 20 kN, the torque M is equal to 1 kNm, the radius of the drum R2 is equal to 0.4 m (the double drum also has r2 equal to 0.2 m), the angle α is equal to 300 and sliding friction coefficient f is 0.5.

In this system, blocks and unnumbered blocks are considered weightless, and friction on the axes of the drum and blocks can be neglected.

Solving the problem involves finding the minimum of the Lagrange functional, which is defined as the difference between the kinetic and potential energy of the system. By calculating the derivative of this functional with respect to the movement of the load, one can find the equation of motion of the system. Provided that the system is in equilibrium, the equation of motion takes the form F - fG = 0, where F is the desired force value, f is the friction coefficient, and G is the weight of the load.

The maximum value of the force F, at which the system is in equilibrium, is achieved at the maximum value of the friction coefficient f, and is equal to Fmax = fG = 10 kN.

This product is a solution to problem D4-30, option 30, task 2, which describes the process of determining the magnitude of the force F at which the mechanical system shown in the figure is in equilibrium, taking into account the presence of friction. To solve the problem, it is necessary to use the Lagrange principle and initial data, such as load weight, torque, drum radius, angle and sliding friction coefficient. Solving the problem involves finding the minimum of the Lagrange functional and determining the equation of motion of the system. The maximum value of force F, at which the system is in equilibrium, is achieved at the maximum value of the friction coefficient and is equal to 10 kN.

This product is a solution to problem D4 option 30 task 2 in the discipline of mechanics, which was compiled by V.A. Dievsky. The task is to determine the magnitude of the force F at which the mechanical system, represented in the figure using Lagrange's principle, is in equilibrium. There is friction in this system, and it is necessary to find the maximum value of this quantity. To solve the problem, it is necessary to use the initial data: the weight of the load G is equal to 20 kN, the torque M is equal to 1 kNm, the radius of the drum R2 is equal to 0.4 m (the double drum also has r2 equal to 0.2 m), the angle α is equal to 300 and the coefficient sliding friction f is 0.5. In the system, blocks and unnumbered blocks are considered weightless, and friction on the axes of the drum and blocks can be neglected. Solving the problem involves finding the minimum of the Lagrange functional, which is defined as the difference between the kinetic and potential energy of the system. By calculating the derivative of this functional with respect to the movement of the load, one can find the equation of motion of the system. Provided that the system is in equilibrium, the equation of motion takes the form F - fG = 0, where F is the desired force value, f is the friction coefficient, and G is the weight of the load. The maximum value of the force F, at which the system is in equilibrium, is achieved at the maximum value of the friction coefficient f, and is equal to Fmax = fG = 10 kN.

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This product is a problem from the textbook by V.A. Dievsky. entitled "Solving problem D4 option 30 task 2". The problem proposes to determine the force F at which the mechanical system presented in the figure will be in equilibrium, using the Lagrange principle.

The initial data for solving the problem are as follows: 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 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 problem will be useful for students and teachers who study theoretical mechanics and want to practice solving problems using the Lagrange principle.

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