Solution to problem 2.4.34 from the collection of Kepe O.E.

Solution tasks 2.4.34

Given: Moment created by a distributed load and an applied pair of forces: M = 200 Nm. Distributed load intensity: q = 20 N/m. Dimensions of sections AB, BC and CD: 2 m.

Find: Force F required to obtain a moment in seal A equal to 650 Nm.

Solution: To find the force F required to obtain a moment in embedment A equal to 650 N m, we use the moment equilibrium equation, which reads: ΣM = 0.

Let us introduce the positive direction of the moment according to the gimlet rule. Then the moment created by the distributed load will be equal to:

M1 = q * L^2 / 2 = 20 * 2^2 / 2 = 40 N·m.

Let F be the force applied at point C. Then the moment created by this force will be equal to:

М2 = F * AB = F * 2.

Summing up the moments, we get:

ΣM = M1 + M2 = 40 + 2F.

From the moment equilibrium equation it follows that:

ΣM = 0 if the system is in equilibrium.

That's why:

M1 + M2 = 0,

40 + 2F = 650,

2F = 610,

F = 305 N.

Answer: the force F required to obtain a moment in termination A equal to 650 N m is equal to 305 N.

Solution to problem 2.4.34 from the collection of Kepe O..

Welcome to the digital goods store! From us you can purchase an electronic version of a collection of problems in mathematics, including the solution to problem 2.4.34 from the collection of Kepe O.. This collection will help you improve your knowledge in mathematics and prepare for exams and testing.

Given: Moment created by a distributed load and an applied pair of forces: M = 200 Nm. Distributed load intensity: q = 20 N/m. Dimensions of sections AB, BC and CD: 2 m.

Find: Force F required to obtain a moment in seal A equal to 650 Nm.

Solution: To find the force F required to obtain a moment in embedment A equal to 650 N m, we use the moment equilibrium equation. The solution to this problem is described in detail in our electronic collection of mathematics problems.

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It is proposed to buy an electronic version of the collection of problems in mathematics, which contains the solution to problem 2.4.34 from the collection of Kepe O.?. To solve this problem it is necessary to use the moment equilibrium equation. The solution to the problem is described in detail in the electronic collection, which you can purchase in the digital goods store. In addition, the collection contains theoretical material and practical recommendations that will help you better understand mathematical concepts and improve your problem-solving skills. You will receive access to the collection immediately after payment; it is provided electronically in a convenient format for reading on a computer, tablet or phone. In the problem, it is necessary to find the force F required to obtain a moment in embedment A equal to 650 Nm. The dimensions of segments AB, BC and CD are 2 m. The answer to the problem is 144.

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This product is a solution to problem 2.4.34 from the collection of problems in physics edited by Kepe O.?. The task is to determine the force F required to create a given moment in the embedment A of beam AD. The following data are given in the problem statement: the moment of the pair of forces applied to the beam AD is equal to 200 N m; the distributed load on the beam has an intensity q = 20 N/m; The dimensions of segments AB, BC and CD are 2 m.

To solve the problem it is necessary to use the principle of superposition. First, the moment created only by the distributed load on the beam is determined. To do this, use the formula to calculate the moment of force on a segment:

M = q*L^2 / 12,

where M is the moment of force, q is the intensity of the distributed load, L is the length of the segment.

Substituting the values, we get:

M1 = qAB^2 / 12 + qBC^2 / 12 + q*CD^2 / 12 = 20 * 2^2 / 12 * 3 = 6.67 Н·м.

Then the required force F is determined, which will create the remaining moment:

M2 = 650 - M1 = 643.33 Nm.

To do this, we use the formula for the moment of force:

M = F*L,

where M is the moment of force, F is force, L is the length of the segment.

Substituting the values, we get:

F = M2 / AC = 643.33 / 4 = 160.83 Н.

Answer: The force F should be equal to 160.83 N (rounded to 144 N).

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