Solution to problem 1.2.23 from the collection of Kepe O.E.

Task 1.2.23

Given: the weight of a homogeneous horizontal beam AB is 180N, angle ?=45°.

Find: reaction of hinge A.

Answer:

According to the conditions of the problem, a vertical weight force equal to 180 N acts on the beam. The angle between the beam and the vertical is 45 degrees, therefore the angle between the beam and the horizontal is 45 degrees.

Let's break down the weight force into its components:

F_x = F_y = F/√2 = 127Н

Since hinge A does not support the horizontal component of the force, the reaction of the hinge will be directed only vertically and is equal to 127N.

Answer: 127.

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Hello! I present to you a digital product - a solution to problem 1.2.23 from the collection of Kepe O.?.

The problem is as follows: there is a homogeneous horizontal beam AB, the weight of which is 180N, and the angle between the beam and the vertical is 45 degrees. It is necessary to determine the reaction of hinge A.

To solve the problem, we decomposed the weight force into components along the coordinate axes. Since hinge A does not support the horizontal component of the force, the reaction of the hinge will be directed only vertically and is equal to 127N.

Answer to the problem: 127.

You can purchase this solution to the problem in our digital goods store. The design is made in a beautiful html format for ease of use. I hope that this solution will help you successfully solve the problem!

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Problem 1.2.23 from the collection of Kepe O.?. consists in determining the reaction of hinge A of a homogeneous horizontal beam AB, the weight of which is 180N, at a given angle of inclination of the beam ?=45°. Solving this problem requires the application of the laws of equilibrium and the theory of moments.

To determine the reaction of hinge A, it is necessary to find the horizontal and vertical components of the support reaction force. To do this, it is necessary to apply the law of horizontal and vertical equilibrium, as well as the theory of moments.

The solution to this problem consists of the following steps:

1. Find the horizontal component of the ground reaction force using the law of horizontal equilibrium.
2. Find the vertical component of the support reaction force using the law of vertical equilibrium.
3. Find the moment of forces acting on the beam relative to hinge A, using the theory of moments.
4. Find the reaction of hinge A using the law of moment equilibrium.

As a result of solving this problem, we find that the reaction of hinge A is 127 N.

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