Weights 1 and 2 hang on ropes wound on a stepped

The system contains two weights that hang on ropes wound on a stepped drum. The system is in equilibrium. To determine the vertical component of the reaction of the hinge A, it is necessary to take into account the radius R, angle a and the weight of load 1, which is 20 kN.

Thus, the vertical component of the reaction of hinge A can be determined as follows:

$$F_A = \frac{m_1 g r}{R \sin \alpha} = \frac{20 \cdot 10^3 \cdot 9.81 \cdot r}{2r \cdot \sin 30^\circ} \approx \boxed{196.2 \text{ кН}}$$

In this system, loads are suspended on ropes wound on a stepped drum. It is necessary to determine the vertical component of the reaction of the hinge A, taking into account the radius R, angle a and the weight of load 1, which is equal to 20 kN. To solve this problem, a formula is used that takes into account the weight of load 1, the angle of inclination of the rope and the radius of the drum. The calculation result is 196.2 kN.

Product description

Our digital product is a unique calculator that allows you to determine the vertical component of the reaction of hinge A in a system where loads 1 and 2 hang on ropes wound on a stepped drum.

This calculator is a powerful tool for solving complex mechanical problems. It is based on the fundamental laws of physics and takes into account all the necessary parameters, such as the radius of the drum, the angle of inclination of the rope and the weight of the load 1.

Our calculator is very easy to use and can be useful for students and teachers, as well as professional engineers and scientists. Thanks to the convenient html design, you can easily use our calculator and quickly get the desired result.

Don't miss the opportunity to purchase this digital product and make your mechanical work easier!

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There is a system in which weights 1 and 2 hang on ropes wound on a stepped drum, and in which hinge A is in equilibrium. The weight of load 1 is 20 kN.

It is necessary to determine the vertical component of the reaction of the hinge A, if the radius R = 2r, angle a = 30°.

To solve the problem, the principle of equilibrium is used. According to this principle, the sum of all forces acting on a body in equilibrium is equal to zero.

The following forces act in this system: the weight of load 1, the weight of load 2 and the vertical reaction of the hinge A.

The sum of the vertical components of the forces must be equal to zero, since the system is in equilibrium.

Thus, the vertical component of the reaction of hinge A is equal to the sum of the vertical components of the forces acting on the system.

The vertical component of the force acting on load 1 is equal to its weight and is equal to 20 kN.

The vertical component of the force acting on load 2 is equal to its weight, which can be calculated using the formula F = mg, where m is the mass of the load and g is the acceleration of gravity. In this case, the mass of load 2 is equal to m = F/g = 30/9.81 ≈ 3.05 t, and its weight F = mg ≈ 30 kN.

The vertical component of the force acting on hinge A is equal to the sum of the vertical components of the forces acting on loads 1 and 2.

The radius of the drum is R = 2r, angle a = 30°, so geometric relationships can be used to calculate the horizontal components of the forces.

The horizontal component of the force acting on load 1 is zero, since the load is attached to the hinge.

The horizontal component of the force acting on load 2 is equal to its weight multiplied by the tangent of the angle alpha, that is, Fh2 = F2 * tan(a) ≈ 15 kN.

Thus, the vertical component of the reaction of hinge A is equal to the sum of the vertical components of the forces acting on the system and is:

FvA = F1 + F2 = 20 kN + 30 kN = 50 kN.

Answer: the vertical component of the reaction of hinge A is 50 kN.

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