Solution to problem 2.4.46 from the collection of Kepe O.E.

Product description: Solution to problem 2.4.46 from the collection by Kepe O..

The solution to problem 2.4.46 from the collection of Kepe O.. is a digital product that is intended for students and teachers studying mechanics. Solving a problem is a detailed description of the steps required to solve the problem, including all formulas and values.

This digital product has the following features:

• detailed description of the solution to the problem;
• use of all necessary formulas and values;
• easy to read text with beautiful design in HTML format;
• convenient access to solving a problem at any time and from anywhere using the Internet.

This digital product will be useful to students who study mechanics, as well as teachers who can use it as additional material for their classes and lectures.

Purchasing a solution to problem 2.4.46 from the collection of Kepe O.. will help improve understanding of the principles of mechanics and increase student performance in this area of ​​knowledge.

Solution to problem 2.4.46 from the collection of Kepe O.?. is a digital product designed for mechanical engineering students and teachers. In this problem, it is required to find the maximum length of the beam at which the moment of the pair of forces arising in the embedment A does not exceed 1 N m.

From the problem conditions it is known that the bracket is acted upon by a force F = 10 N, radius r = 0.05 m, angle ? = 60°. To solve the problem, you need to use the formula to calculate the moment of a pair of forces: M = F * l * sin(?), where F is the force, l is the distance from the force to the axis of rotation, ? - the angle between the force vector and the radius vector.

To ensure that the moment of a couple of forces does not exceed 1 N m, it is necessary to calculate the maximum value of the distance l. Substituting the known values ​​into the formula, we get:

M = F * l * sin(?) 1 N m = 10 N * l * sin(60°) l = 1 N m / (10 N * sin(60°)) l ≈ 0.10 m

Thus, the maximum length of the beam at which the moment of the couple of forces arising in the embedment A does not exceed 1 N m is equal to 0.10 m. Solution to problem 2.4.46 from the collection of Kepe O.?. is a detailed description of all the necessary steps and formulas for solving this problem in a convenient HTML format, which can be used by students and teachers as additional material for studying mechanics and improving academic performance.

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Solution to problem 2.4.46 from the collection of Kepe O.?. consists in determining the maximum length l of the beam at which the moment of a pair of forces acting on the bracket does not exceed 1 N m.

To solve the problem, you need to use the formula for calculating the moment of force of a couple:

M = F * r * sin(s)

where F is the force acting on the bracket (in our case F = 10 N), r is the radius (in our case r = 0.05 m), α is the angle between the force vector and the radius (in our case α = 60 degrees) .

Since we know the maximum permissible moment of a couple of forces (1 N m), we can express the maximum permissible force F:

F = M / (r * sin(α))

Substituting the known values, we get:

F = 1 N·m / (0.05 m * sin(60°)) ≈ 22.87 N

Now you can calculate the maximum permissible tension σ in the beam using the formula:

σ = F * l / (π * r^2)

where l is the length of the beam.

Substituting the known values, we get:

σ = 22.87 N * l / (π * (0.05 m)^2) ≈ 145.45 N/m^2

The maximum permissible stress σ is equal to the tensile strength of the beam material. Let us assume that the beam material has a tensile strength σ0 = 10 MPa (10 N/mm^2). Then the maximum permissible beam length l can be found from the equation:

l = σ0 * π * r^2 / F

Substituting the known values, we get:

l = 10 MPa * π * (0.05 m)^2 / 22.87 N ≈ 0.10 m

Thus, the maximum permissible beam length l is 0.10 m.

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