Dievsky V.A. - Solving problem D4 option 21 task 2

To solve the problem of determining the force F at which the mechanical system will be in equilibrium, we use the Lagrange principle. The figure shows the corresponding diagram.

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 R2 is 0.4 m (the double drum also has r2 = 0.2 m), the angle α is equal to 300 and the sliding friction coefficient f is equal to 0.5. Unnumbered blocks and rollers are considered weightless, and friction on the axes of the drum and blocks is neglected.

To determine the magnitude of the force F, we use the equilibrium equation:

ΣF = 0

Here ΣF denotes the sum of all forces acting on the mechanical system.

The force F acts in the direction of the roller, and the friction force is directed in the opposite direction. Thus, the equilibrium equation has the form:

F - fGsinα - M/R2 = 0

where f is the coefficient of sliding friction, G is the weight of the load, α is the angle at which the load is lifted, M is the torque, R2 is the radius of the drum.

The maximum value of the force F, at which the mechanical system will be in equilibrium, is achieved at the highest value of the friction force. Thus, the maximum value of force F is:

Fmax = fGsinα + M/R2

Substituting the known values, we get:

Fmax = 0.5 * 20 * sin(300) + 1 / 0.4 ≈ 51.6 кН

Thus, in the presence of friction, the maximum value of the force F at which the mechanical system will be in equilibrium is 51.6 kN.

Dievsky V.A. - Solving problem D4 option 21 task 2

This digital product is a solution to problem D4, option 21, task 2, compiled by V.A. Dievsky. The solution to this problem was carried out at a high level of professionalism and is intended for students, teachers and anyone interested in mechanics and physics.

In solving this problem, the Lagrange principle is used to determine the magnitude of the force F (in the presence of friction, the maximum value of this value) at which the mechanical system will be in equilibrium. All necessary initial data are given in the task.

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This product is a task from a physics textbook, authored by V.A. Dievsky. The task is to determine the magnitude of the force F at which the mechanical system shown in the diagram in the figure will be in equilibrium. To solve the problem it is necessary to use the Lagrange principle. The initial data indicates the weight of the load G, the torque M, the radius of the drum R2 (the double drum also has r2), the angle α and the sliding friction coefficient f. Unnumbered blocks and rollers are considered weightless, and friction on the axes of the drum and blocks can be neglected. The task also states that it is necessary to determine the maximum value of the force F in the presence of friction.

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