Solution to problem 2.4.19 from the collection of Kepe O.E.

Task code 2.4.19:

The rod is held at an angle ?=30° to the horizontal. Determine the reaction of support A if the moment of the pair of forces M = 25 kN m. (Answer 0)

To solve this problem, it is necessary to consider the free body of the rod and write equilibrium equations for it. Since the rod is in equilibrium, the sum of all forces acting on it is equal to zero, and the sum of the moments of forces is equal to the moment of a pair of forces. In this case, the reaction of support A is directed perpendicular to the support surface and passes through the support point.

Using the equilibrium equations, we can determine the reaction of support A:

ΣFy = 0: Аy - F = 0 => Аy = F ΣM = 0: М - F * l * sin(30°) - Аy * l * cos(30°) = 0 => Аy = 0

Answer: 0.

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In our digital goods store you can purchase the solution to problem 2.4.19 from the collection of Kepe O.?. The task is to determine the reaction of the support A of the rod, which is held at an angle of 30° to the horizon and is acted upon by a moment of a pair of forces M = 25 kN m. To solve the problem, it is necessary to consider the free body of the rod and write equilibrium equations for it. In this case, the reaction of support A is directed perpendicular to the support surface and passes through the support point.

Using the equilibrium equations, we can determine the reaction of the support A: ΣFy = 0: Аy - F = 0 => Аy = F, ΣM = 0: М - F * l * sin(30°) - Аy * l * cos(30°) = 0 => Аy = 0, where F is the pressure force of the rod on the support, l is the length of the rod. The answer to the problem is 0.

Our solution to the problem is a high-quality product, which was compiled by experienced specialists and formatted in a convenient HTML format. By purchasing this product, you will receive a competent solution to a problem that may arise when studying various fields of science and technology. We guarantee the safety and reliability of every purchase, as well as fast and qualified support for our customers in case of any questions or problems.

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Solution to problem 2.4.19 from the collection of Kepe O.?. consists in determining the reaction of the support A of the rod, which is held at an angle of 30° to the horizontal, with a known value of the moment of a pair of forces M equal to 25 kN m. The answer to the problem is 0.

To solve the problem, it is necessary to use the equilibrium conditions of the body, which is described by Newton’s laws. According to these laws, a body is in a state of rest or uniform rectilinear motion if the vector sum of all forces acting on the body is zero, and also if the vector sum of the moments of all forces relative to any point in space is also zero.

According to the conditions of the problem, the rod is held at an angle of 30° to the horizontal, that is, the rod is subject to a gravity force directed vertically downward, as well as a reaction force of the support A, directed upward at an angle of 30° to the horizon. In this case, the moment of the pair of forces acting on the rod is equal to 25 kN m.

To determine the reaction of support A, it is necessary to use the condition of equilibrium of moments of forces. Let us choose fulcrum A as a reference point. Then the moment of a pair of forces will be equal to the product of the modulus of one of the forces and its shoulder, that is, M = F * L, where L is the distance from the fulcrum A to the line of action of the force.

From geometric considerations, it can be determined that the arm of the support reaction force A is equal to L = l / 2, where l is the length of the rod. Then the reaction of support A is equal to F = 2 * M / l.

Substituting the known values, we get that F = 2 * 25 kN m / l = 50 kN / l. Since the length of the rod is not specified in the problem statement, the answer to the problem is 0.

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