Solution to problem 1.2.21 from the collection of Kepe O.E.

1.2.21. Hinge B and rope DE hold a horizontal beam weighing 200 N in equilibrium. Rope DE makes an angle ?=150° with side BD. It is necessary to determine the reaction of hinge B if it is known that 4 AB = AC. (Answer: 200)

We have a horizontal beam weighing 200 N, held in equilibrium by hinge B and rope DE forming an angle ?=150° with side BD. According to the conditions of the problem, it is known that 4 AB = AC. It is necessary to determine the reaction of hinge B.

Let's consider the forces acting on the beam. The rope DE exerts a tension force on it, which is directed along the rope and forms an angle ? with horizontal. Hinge B exerts a vertical reaction directed upward on the beam.

Using the equilibrium condition, we can write that the sum of the vertical components of all forces acting on the beam is equal to zero. Since the beam is in equilibrium, the sum of the moments of all forces relative to any point on the beam must also be equal to zero.

Let's consider the moments of the tension force of the rope DE and the reaction of the hinge B relative to point B. Since the rope passes through point D, the moment of the tension force relative to point B is equal to F·BD·sin?, where F is the tension force, BD is the distance from point B to points D, ? - the angle between the rope and side BD. The moment of reaction of hinge B relative to point B is equal to 0, since the reaction of hinge B is directed through point B.

Thus, the moment equilibrium condition in this problem can be written as:

F·BD·sin? = 0

Taking into account the fact that BD = AB/2 (from condition 4 AB = AC), we obtain:

F·(AB/2)·sin? = 0

Whence it follows that F = 0.

Since the tension force of the rope DE is 0, the reaction of the hinge B must be equal to the weight of the beam and be 200 N.

Solution to problem 1.2.21 from the collection of Kepe O.?.

This digital product is a solution to problem 1.2.21 from the collection of problems by Kepe O.?. in physics. The solution to the problem is carried out by a qualified specialist and is guaranteed to have the correct answer.

The problem is to determine the reaction of hinge B, which holds a horizontal beam weighing 200 N in equilibrium using a rope DE forming an angle ?=150° with side BD. To solve the problem, the condition of equilibrium of moments and forces is used, which allows us to obtain the correct answer.

By purchasing this digital product, you receive a ready-made solution to the problem with a beautiful design in HTML format, which is easy to read and use on any device.

No additional knowledge of physics is required to use this solution to the problem. Just open the file in any browser and study the ready-made solution to the problem!

This digital product is an excellent choice for students, teachers and physics enthusiasts who want a ready-made solution to a problem with the correct answer.

This digital product is a solution to problem 1.2.21 from the collection of problems in physics by Kepe O.?. The solution is carried out by a qualified specialist and is guaranteed to have the correct answer.

The problem is to determine the reaction of hinge B, which holds a horizontal beam weighing 200 N in equilibrium with the help of a rope DE forming an angle ?=150° with side BD. To solve the problem, the condition of equilibrium of moments and forces is used, which allows us to obtain the correct answer.

By purchasing this digital product, you receive a ready-made solution to the problem with a beautiful design in HTML format, which is easy to read and use on any device. No additional knowledge of physics is required to use this solution to the problem. Just open the file in any browser and study the ready-made solution to the problem!

This digital product is an excellent choice for students, teachers and physics enthusiasts who want a ready-made solution to a problem with the correct answer. Answer to the problem: the reaction of hinge B is 200 N.

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Solution to problem 1.2.21 from the collection of Kepe O.?.

In this problem, you need to determine the reaction of hinge B, which holds the horizontal beam in balance. To do this, it is known that the weight of the beam is 200 N, as well as the angle formed by the rope DE and the side BD, which is 150°.

To solve the problem, it is necessary to use the equilibrium conditions of the body. Since the horizontal beam is in equilibrium, the sum of all forces acting on it must be equal to zero. It is known that the force of gravity and the tension of the rope act on the beam.

To determine the reaction of hinge B, it is necessary to decompose the tension force of the rope into components along the X and Y axes. Then, using equilibrium conditions, we can write the moment balance equations about point B.

To solve the problem, the ratio of linear dimensions 4 AB = AC is also used.

As a result of solving the problem, it turns out that the reaction of hinge B is equal to 200 N, which is the answer to the problem.

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