Solution to problem 2.3.23 from the collection of Kepe O.E.

2.3.23 At what intensity of the distributed load q is the moment of the couple arising in the seal. MA = 200 Nm. if the distance l = 1 m? (Answer 400)

Problem 2.3.23 from the collection of Kepe O.?. consists in determining the intensity of the distributed load q, at which a couple moment in the seal occurs equal to 200 N m at a distance l = 1 m.

To solve this problem, it is necessary to use the formula for calculating the moment of a couple: M = q*l^2/2, where M is the moment of the couple, q is the intensity of the distributed load, l is the distance from the embedment to the point of application of the load.

Substituting the known values, we get the equation 200 = q*1^2/2, from which q = 400.

Therefore, the answer to the problem is 400, which means that the distributed load intensity must be 400 N/m to produce a couple moment of 200 N·m at a distance of 1 m from the embedment.

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Problem 2.3.23 from the collection of Kepe O.?. refers to the topic of mathematical analysis and is formulated as follows:

Given a function f(x), defined on the interval [a,b]. It is necessary to prove that if f(x) is continuous on the interval [a,b] and has at least two distinct zeros on this interval, then between these zeros there is at least one more zero of the function f(x).

To solve this problem, you can use the intermediate function theorem, which states that if the function f(x) is continuous on the interval [a,b], then it takes on all values ​​between f(a) and f(b) on this interval.

Consequently, if the function f(x) has at least two distinct zeros on the interval [a,b], then it takes on both positive and negative values ​​on this interval, and therefore, according to the theorem on the intermediate value of the function, between these zeros there is at least one more zero of the function f(x).

Thus, problem 2.3.23 from the collection of Kepe O.?. reduces to using the theorem on the intermediate value of a function to prove the existence of an additional zero between two known zeros of the function f(x), provided that it is continuous on the interval [a,b].

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