Solution to problem 18.3.5 from the collection of Kepe O.E.

18.3.5 A pair of forces with a moment M1 = 40 N • m is applied to gear 1. Determine the moment M of the pair of forces that must be applied to the crank OA in order for the mechanism to be in equilibrium if the radii are r1 = r2. (Answer 80)

Solution to problem 18.3.5 from the collection of Kepe O.?. consists in determining the moment M of a pair of forces that must be applied to the crank OA so that the mechanism is in equilibrium. It is known that a pair of forces with a moment M1 = 40 N • m is applied to gear 1, and the radii are r1 = r2.

To solve the problem, you need to use the equilibrium condition of the mechanism, which states that the sum of the moments of all forces acting on the mechanism is equal to zero. Thus, in order for a mechanism to be in equilibrium, the moment created by a pair of forces must be compensated by the moment created by another pair of forces.

From the problem conditions it is known that the radii of gear 1 and crank OA are equal, so we can conclude that to compensate for the moment M1 of a pair of forces, it is necessary to apply the same pair of forces to point A with a moment M2 = 40 N • m. Consequently, the total moment , necessary for the equilibrium of the mechanism, will be equal to the sum of the moments M1 and M2, that is, M = M1 + M2 = 40 + 40 = 80 N • m.

Thus, in order for the mechanism to be in equilibrium, it is necessary to apply a couple of forces to point A with a moment of 80 N • m.

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Problem 18.3.5 from the collection of Kepe O.?. refers to the section "Thermodynamics and molecular physics" and has the following wording:

"The isothermal process of compression of gas molecules is carried out under conditions where the average kinetic energy remains constant. Find the work of compression if the initial volume of the gas is V1, and the final volume is V2."

To solve this problem, it is necessary to use the formula for the work of gas compression:

A = -P∆V,

where P is the gas pressure, ∆V is the change in gas volume.

Under the conditions of the problem, the gas temperature remains constant, so the pressure can be expressed through the Boyle-Mariotte law:

P1V1 = P2V2,

where P1 and P2 are the initial and final gas pressure, respectively.

Substituting the expression for P into the work formula, we get:

A = -P1(V1 - V2).

Therefore, to solve the problem it is necessary to know the initial volume of gas V1, the final volume of gas V2 and the initial gas pressure P1. By substituting these values ​​into the formula, we can calculate the work of compression of the gas A.

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