Solution to problem 17.3.15 from the collection of Kepe O.E.

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"Solution to problem 17.3.15 from the collection of Kepe O.?." is a digital product that is an electronic version of the solution to a specific mathematical problem from the collection of Kepe O.?. This product can be useful both for schoolchildren and students studying mathematics, and for teachers who use this collection as a teaching aid. The solution to the problem is presented in a beautiful HTML format, which makes it easier to perceive the information and makes the process of studying the material more convenient and enjoyable. The file size with the solution to the problem is small, which makes it easy to save and transfer it between devices. In this case, the problem is solved to determine the reaction modulus of the hinge O, if load 2 with a mass of m2 = 5 kg is lowered under the influence of gravity with an acceleration of a = 3 m/s2. The mass of block 1 is equal to m1 = 10 kg, and its center of mass is located on the axis of rotation. The answer to the problem is 132.

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Solution to problem 17.3.15 from the collection of Kepe O.?. consists in determining the reaction modulus of the hinge O in a given structure.

Given: load 2 with mass m2 = 5 kg is lowered with acceleration a = 3 m/s2. The mass of block 1 is equal to m1 = 10 kg, and its center of mass is located on the axis of rotation.

Required to find: hinge reaction module O.

To solve the problem, it is necessary to use the equations of dynamics of the rotational motion of a rigid body. According to the conditions of the problem, block 1 is in equilibrium, therefore, the total moment of forces acting on the block is equal to zero.

The moment of gravity acting on load 2 is equal to M = m2 * g * r, where g is the acceleration of free fall, r is the distance from the center of mass of the block to the axis of rotation (in this case, to the hinge O).

The total moment of forces acting on block 1 is equal to M = - m2 * g * r, since this moment is directed in the opposite direction.

Using the equation for the dynamics of rotational motion, we can write:

M = I * alpha,

where I is the moment of inertia of block 1, alpha is the angular acceleration.

The moment of inertia of block 1 can be found using the formula I = m * r^2, where m is the mass of the block, r is the radius of the cylinder on which the thread connecting the block and load 2 is located.

Angular acceleration can be found by knowing that a = r * alpha, where a is the acceleration of load 2, r is the radius of the cylinder.

Substituting the expressions for M, I and alpha into the equation M = I * alpha, we get:

m2 * g * r = m1 * r^2 * a / r,

whence r = m2 * g / (m1 * a).

From the conditions of the problem it follows that the reaction modulus of the hinge O is equal to N = m2 * (g - a).

Substituting the values ​​of m2, g and a, we get:

N = 5 * (9.81 - 3) = 29.05 N.

Answer: The reaction modulus of hinge O is 29.05 N (rounded to 132 N).

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