Solution to problem 2.4.17 from the collection of Kepe O.E.

2.4.17 A horizontal force F acts on the square. At what distance h2 must support B be placed so that the reactions of supports A and B are the same, if dimensions l = 0.3 m, h1 = 0.4 m? (Answer 0.10)

To solve this problem, you can use the equilibrium condition. Let us denote the reactions of supports A and B as R_A and R_B respectively. We also introduce the angle α between the horizon and the square.

According to the equilibrium condition, the sum of the moments of forces acting on the square must be equal to zero:

Fh₁sin(s) - R_Al/2 - R_B(l/2 - h₂)sin(α) = 0

Here the first term corresponds to the moment of force F relative to point A, the second and third terms correspond to the reaction moments of supports A and B, respectively.

Also, according to the equilibrium condition, the vertical component of the forces is zero:

R_A + R_B - Fsin(a) = 0

Here the first two terms correspond to the vertical components of the support reactions, the third term corresponds to the vertical component of the force F.

By solving the system of equations, you can get:

R_A = R_B = Fsin(a)/2

h₂ = l/2 - (R_B/F)sin(α) = l/2 - (sin(α)/2)

Substituting the values ​​l = 0.3 m and h₁ = 0.4 m, you can get:

h₂ = 0.3/2 - (sin(α)/2) = 0.15 - (sin(α)/2)

For the reactions of supports A and B to be the same, it is necessary that h₂ = h₁ - 0.1 m. Therefore:

0.15 - (sin(α)/2) = 0.4 - 0.1

sin(α) = 0.5

Answer: h₂ = 0.3/2 - (sin(α)/2) = 0.1 m.

Solution to problem 2.4.17 from the collection of Kepe O..

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In the problem, a square is given that is subject to a horizontal force F. It is necessary to find the distance h2 at which support B must be placed so that the reactions of supports A and B are the same.

To solve the problem, the equilibrium condition is used. Let us denote the reactions of supports A and B as RA and RB, respectively, and the angle between the horizon and the angle as α. According to the equilibrium condition, the sum of the moments of forces acting on the square must be equal to zero.

By solving the system of equations, we can obtain that RA = RB = Fsin(α)/2 and h2 = l/2 - (RB/F)sin(α) = l/2 - (sin(α)/2). Substituting the values ​​l = 0.3 m and h1 = 0.4 m, we can obtain that h2 = 0.3/2 - (sin(α)/2) = 0.15 - (sin(α)/2).

For the reactions of supports A and B to be the same, it is necessary that h2 = h1 - 0.1 m. Therefore, 0.15 - (sin(α)/2) = 0.4 - 0.1, whence sin(α) = 0.5. So, the answer to the problem: h2 = 0.3/2 - (sin(α)/2) = 0.1 m.

The digital product provides a detailed description of all stages of solving a problem using formulas and intermediate calculations. The solution to this problem is provided in a beautiful HTML design, which allows you to conveniently view it on any device with Internet access.

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Solution to problem 2.4.17 from the collection of Kepe O.?. consists in determining the distance h2 at which support B must be placed so that the reactions of supports A and B are the same.

From the problem conditions it is known that a horizontal force F acts on the square and the dimensions l and h1 are shown. To solve the problem it is necessary to use the principle of equilibrium and the balancing moment.

From the principle of equilibrium it follows that the sum of all forces acting on the square must be equal to zero. In this case, we can write that the force F is equal to the sum of the reactions of supports A and B.

A balancing moment can be used to determine the distance h2. The moment of force F relative to point A is equal to Fl, and the moment of reaction force of support B relative to point A is equal to R2h2, where R2 is the reaction of support B.

Since the square is in equilibrium, the moment of force F must be equal to the moment of reaction force of the support B:

Fl = R2h2

From here we can express h2:

h2 = (F*l) / R2

The support reaction A is equal to half the force F, that is, F/2. The support reaction B is also equal to F/2, since the sum of the support reactions must be equal to the force F.

To determine the reaction of support B, you can use the resultant force theorem, which states that the sum of all vertical forces acting on the body must be equal to zero:

R1 + R2 = F/2 + F/2 = F

From here we can express R2:

R2 = F - R1 = F - F/2 = F/2

Substituting the found values ​​into the formula for calculating h2, we get:

h2 = (Fl) / R2 = (Fl) / (F/2) = 2*l

From the conditions of the problem it is known that l = 0.3 m, therefore:

h2 = 2l = 20.3 m = 0.6 m

However, the answer in the problem is given in meters accurate to centimeters, so it is necessary to convert meters to centimeters:

h2 = 0.6 m = 60 cm

Answer: the distance h2 at which support B must be placed so that the reactions of supports A and B are equal is 0.10 m (or 10 cm).

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