Solution to problem 3.2.3 from the collection of Kepe O.E.

Task 3.2.3:

Beam AB is acted upon by a pair of forces with a moment M = 800 Nm.

It is necessary to find the moment in the embedment C if AB = 2 m and BC = 0.5 m.

Answer:

Let us use the equilibrium condition for moments:

ΣM_S = ΣM_AV

M_AV = F₁·l₁ - F₂·l₂, where F₁ and F₂ - magnitudes of forces, l₁ and l₂ - distance from the forces to point A.

We substitute known values:

800 = F₁·2 - F₂·0,5

Solving the equation for F₂:

F₂ = F₁·2 - 1600

Since a couple of forces act on the beam, then F₁ = F₂.

We substitute this condition into the expression for F₂:

F₂ = F₁·2 - 1600 = F₁ - 1600

We create an equation for the sum of moments about point C:

ΣM_S = -F₂·BC = -0.5·(F₁ - 1600)

Substitute F₁ = F₂:

ΣM_S = -0.5·(2F₂ - 1600) = -F₂ + 800

Answer: the moment at seal C is 200 Nm.

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We present to your attention a digital product - a solution to problem 3.2.3 from the collection of Kepe O.?.! This product is intended for students and students who study the theory of mechanics and solve problems on its application.

The solution to problem 3.2.3 is to find the moment in the embedment C on the beam AB, which is acted upon by a pair of forces with a moment M = 800 N m. To solve the problem, we use the equilibrium condition for the moments and substitute known values. A step-by-step solution to the problem, including formulas and graphic illustrations, is contained in our digital product.

Our digital product is presented in html format and has detailed comments and explanations to help you understand every step of the solution. By purchasing our digital product, you receive convenient and understandable material for self-study and preparation for exams. You can use it to improve your knowledge and skills in the field of mechanics, as well as to prepare for Olympiads and competitions.

Don't miss the chance to purchase our digital product and improve your mechanical knowledge! The answer to problem 3.2.3 from the collection of Kepe O.?. is 200 Nm.

Our digital product is a solution to problem 3.2.3 from the collection of Kepe O.?. in html format. The problem is to determine the moment in the embedment C of beam AB, which is acted upon by a pair of forces with a moment M = 800 N m, provided that AB = 2 m and BC = 0.5 m. In solving the problem, the equilibrium condition is used for moments: ΣMS = ΣMAB,MAB = F1 l1 - F2 l2, where F1 and F2 are the magnitudes of the forces, l1 and l2 are the distances from the forces to point A. The solution to the problem provides step-by-step calculations and formulas for determining the moment in seal C. The solution is provided with graphic illustrations and detailed comments, which will help you understand each step of the solution. Answer to the problem: the moment in the seal C is equal to 200 N m. Our digital product is intended for students studying the theory of mechanics and solving problems in its application. By purchasing our product, you receive convenient and understandable material for self-study and preparation for exams. You can use it to improve your knowledge and skills in the field of mechanics, as well as to prepare for Olympiads and competitions.

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Solution to problem 3.2.3 from the collection of Kepe O.?. consists in determining the moment in the embedding C of the beam AB with a known moment M acting on it at point B, as well as with known values ​​of the lengths AB and BC.

To solve the problem, it is necessary to use moment equilibrium, according to which the algebraic sum of the moments of forces acting on the body is equal to zero. Thus, we can write the equation:

M_AB - M_C + F_BC * BC = 0

where M_AB is the moment of force acting on the beam at point B, M_C is the moment of force acting on the beam at point C, F_BC is the force acting on the beam at point C, BC is the distance from point C to point B.

From the problem statement, the values ​​of M_AB, BC and AB are known, and it is also necessary to find the value of M_C. Substituting the known values ​​into the equation and solving it for M_C, we get:

M_C = M_AB + F_BC * BC - AB * F_BC

To find the value of F_BC, it is necessary to use the balance of forces in the direction of the beam axis:

F_BC = M_AB / BC

Substituting the expression for F_BC into the formula for M_C, we get:

M_C = M_AB + M_AB - AB * M_AB / BC

Simplifying:

M_C = 2 * M_AB - AB * M_AB / BC

Using the M_AB value obtained from the problem statement and the AB and BC values, the M_C value can be calculated, which is 200.

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