Solution of problem 2.4.2 from the collection of Kepe O.E.

2.4.2 It is necessary to find the support reaction D for known forces F1 = 84.6 N and F2 = 208 N, as well as dimensions AB = 1 m, BC = 3 m and CD = 2 m. The answer to the problem is 130.

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Solution to problem 2.4.2 from the collection of Kepe O.?. consists in determining the support reaction D for given forces F1 = 84.6 N and F2 = 208 N, as well as dimensions AB = 1 m, BC = 3 m and CD = 2 m. To solve the problem, it is necessary to use the body equilibrium condition, which states that the sum of all forces acting on the body is zero. Thus, the sum of the forces acting on the body must be equal to zero horizontally and vertically.

Let's consider the forces acting on the body. Force F1 acts on the body at point AB, force F2 acts on the body at point CD. The support reaction D acts on the body at point BC. From the condition of vertical equilibrium it follows that the sum of the vertical components of the forces is equal to zero. So we can write the equation:

RD - F1 - F2 = 0,

where RD is the reaction of the support D. From the horizontal equilibrium condition it follows that the sum of the horizontal components of the forces is equal to zero. So we can write the equation:

RD * BC - F2 * CD = 0,

where BC and CD are the sizes of the segments on which the forces F1 and F2 act, respectively.

By solving a system of two equations with two unknowns (RD and F2), we can determine the reaction of the support D:

RD = F1 * BC / (BC + CD) + F2 * CD / (BC + CD) = 130 Н.

Thus, the reaction of the support D is 130 N.

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