Solution to problem 19.2.3 from the collection of Kepe O.E.

19.2.3 Two weights, the masses of which m1 = m3 = 2 kg, are connected to each other by a thread thrown through block 2, the mass of which can be neglected. Determine the acceleration of the loads if the coefficient of sliding friction between load 1 and the plane f = 0.1. (Answer 4.41)

Solution to problem 19.2.3 from the collection of Kepe O.?. requires determining the acceleration of the loads, which are connected to each other by a thread thrown through block 2. The masses of the loads m1 and m3 are equal to 2 kg, and the mass of the block can be neglected.

To solve the problem it is necessary to apply Newton's laws. According to Newton's second law, the force acting on a body is equal to the product of the body's mass and its acceleration: F = m*a.

In this problem, the loads are connected to each other by a thread, so the accelerations of the loads will be equal. Also, the friction force between load 1 and the plane will be directed in the opposite direction of the movement of the load, and its value will be equal to f = 0.1 * m * g, where m is the mass of the load, g is the acceleration of gravity.

Thus, the sum of the forces acting on load 1 will be equal to F = m1 * a - f, and on load 3 - F = m3 * a.

Therefore, m1 * a - f = m3 * a, whence a = f / (m1 + m3) = 0.1 * 9.81 / (2 + 2) = 0.981 m/s^2.

The answer must be rounded to two decimal places: a = 0.98 m/s^2.

Thus, the acceleration of the loads in this problem is 0.98 m/s^2. However, the answer 4.41 provided in the description is not true.

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Problem 19.2.3 from the collection of Kepe O.?. refers to the field of mathematical statistics and is formulated as follows: it is required to test the hypothesis about the equality of two mathematical expectations using two independent samples. To solve the problem, it is necessary to carry out appropriate statistical calculations, determine the critical values ​​of the agreement criterion and compare the obtained values ​​with the level of significance. The solution to this problem can be used in various fields, for example, to compare the effectiveness of two treatment methods or evaluate the effectiveness of different strategies in business management.

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