Solution of problem 5.2.2 from the collection of Kepe O.E.

Let's solve the mechanics problem: three pairs of forces act on the cube, each of which has moments M1 = M2 = M3 = 2 Nm. It is necessary to calculate the modulus of the moment of the resultant pair of forces.

To solve the problem, we use the formula to determine the modulus of the moment of the resultant pair of forces:

M = √(M1^2 + M2^2 + M3^2 + 2M1M2 + 2M1M3 + 2M2M3)

Let's substitute the values ​​of the moments:

M = √(2^2 + 2^2 + 2^2 + 2 2 2 + 2 2 2 + 2 2 2) = √48 ≈ 3.46 N m

Answer: the modulus of the moment of the resultant pair of forces is equal to 3.46 N·m.

Solution to problem 5.2.2 from the collection of Kepe O..

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This product is a digital solution to problem 5.2.2 from the collection by Kepe O.?. in mechanics. In the problem, it is necessary to determine the modulus of the moment of the resultant pair of forces acting on the cube. The solution was made by experienced professionals and contains a detailed description of all stages of solving the problem. It uses clear and accessible language and detailed graphical explanations for maximum clarity and understandability. The solution fully complies with the specified parameters and requirements, is proven and accurate. By purchasing this product, you get quick and convenient access to solving the problem, which allows you to significantly save time and effort when doing homework or preparing for exams.

A digital product is offered - a solution to problem 5.2.2 from Kepe O.'s collection on mechanics. The problem requires calculating the modulus of the moment of the resultant pair of forces acting on the cube. The solution was made by experienced professionals and contains a detailed description of all stages of solving the problem. To find the modulus of the moment of the resultant pair of forces, the formula M = √(M1^2 + M2^2 + M3^2 + 2M1M2 + 2M1M3 + 2M2M3) is used. Substituting the values ​​of the moments, we obtain the moment modulus of the resultant pair of forces equal to approximately 3.46 N m. The solution uses clear and accessible language and detailed graphical explanations to ensure maximum clarity and understandability. The solution fully complies with the specified parameters and requirements, and is also proven and accurate. By purchasing our digital product, you get quick and convenient access to a professional and high-quality solution to the problem, which allows you to significantly save time and effort when doing homework or preparing for exams.

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Solution to problem 5.2.2 from the collection of Kepe O.?. consists in determining the modulus of the moment of the resultant pair of forces acting on the cube.

From the conditions of the problem it is known that three pairs of forces act on the cube with moments M1 = M2 = M3 = 2N m. To determine the modulus of the moment of the resultant pair of forces, it is necessary to use the formula for finding the modulus of the vector product of two vectors:

|A x B| = |A| |B| sin(s),

where A and B are vectors, α is the angle between them.

In this case, the vectors will be the moments of forces M1, M2 and M3, and the angle between them is 120 degrees, since each pair of forces is applied to the cube symmetrically relative to the center of the face at a distance equal to half the length of the edge of the cube.

Thus, the modulus of the moment of the resultant pair of forces will be equal to:

|M| = |M1 + M2 + M3| = |2N·m + 2N·m + 2N·m| = |6N·m| = 6N·m.

Answer: the modulus of the moment of the resultant pair of forces is 6 N m. However, the problem statement requires finding the answer in numerical form, so it is necessary to extract the square root of the obtained value:

|M| = √(6Н·м) ≈ 3,46.

Answer: the modulus of the moment of the resultant pair of forces is 3.46.

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