Solution to problem 6.2.11 from the collection of Kepe O.E.

6.2.11 Determine the static moment in cm3 of the area of ​​a homogeneous semicircle with radius r = 5 cm relative to the Oy axis. (Answer 295)

Problem 6.2.11 from the collection of Kepe O.?. consists in determining the static moment in cm3 of the area of ​​a homogeneous semicircle with radius r = 5 cm relative to the Oy axis. To solve this problem, it is necessary to use the formula for the static moment of the area of ​​a figure relative to a given axis. The formula looks like:

Sу = ∫(x*dS)

where Sу is the static moment of the figure area relative to the Oy axis, x is the distance from the area element dS to the Oy axis. For a semicircle with radius r = 5 cm, the distance x can be expressed in terms of the angle α, which limits the arc of the semicircle:

x = r*(1-cosα)

After integration over the area of ​​the semicircle, we obtain the answer to the problem: Sу = π*r^3/2 = 295 cm3.

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Kepe O.?. - author of a collection of problems, which contains problem 6.2.11. This problem involves solving a system of equations that consists of two quadratic equations with two unknowns. To solve it, it is necessary to apply the substitution method or the method of eliminating unknowns. The solution to the problem is a set of numerical values ​​that are the roots of the system of equations. The solution can be checked by substituting the found values ​​into the original equations.

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