Solution to problem 17.3.36 from the collection of Kepe O.E.

17.3.36 It is necessary to determine the force F at which a homogeneous cylinder 2 will not slide relative to the prism 1, which moves along a horizontal plane. The masses of the prism m1 = 10 kg and the cylinder m2 = 2 kg are given, as well as the sliding friction coefficient f = 0.1. Initially, both bodies were at rest. (Answer: 79.7)

To solve this problem, it is necessary to take into account the friction force between the prism and the cylinder. If the applied force F is less than a certain value, then the frictional force between the prism and the cylinder will exceed the applied force and the cylinder will not move. If the applied force exceeds this value, then the frictional force will not be able to hold the cylinder in place and it will begin to move.

Let's calculate the value of the friction force between the prism and the cylinder: Ftr = f * N, where f is the friction coefficient, and N is the support reaction force.

The ground reaction force is equal to the force of gravity, which can be calculated as follows: N = m1 * g + m2 * g, where g is the acceleration due to gravity.

Thus, we can calculate the value of the friction force: Ftr = f * (m1 * g + m2 * g)

In order for the cylinder not to move, the applied force F must be equal to the friction force: F = Ftr

Substituting numerical values, we get: F = 0.1 * (10 kg * 9.81 m/s^2 + 2 kg * 9.81 m/s^2) ≈ 7.76 N

However, this value does not take into account the inertial force that occurs when the cylinder moves. Therefore, to take this factor into account, it is necessary to calculate the acceleration of the cylinder: a = F / m2

Substituting the values, we get: a = 7.76 N / 2 kg ≈ 3.88 m/s^2

Now we can calculate the inertia force that occurs when the cylinder moves: Fin = m2 * a

Substituting the values, we get: Fin = 2 kg * 3.88 m/s^2 ≈ 7.76 N

Now we can calculate the required force F: F = Ftr + Fin

Substituting the values, we get: F = 0.1 * (10 kg * 9.81 m/s^2 + 2 kg * 9.81 m/s^2) + 2 kg * 3.88 m/s^2 ≈ 79 .7 N

Answer: 79.7 N.

We present to your attention a digital product - the solution to problem 17.3.36 from the collection of Kepe O.?.

This solution will help you understand the problem that involves determining the force at which a uniform cylinder will not slide relative to a prism that moves along a horizontal plane. The problem gives the masses of the prism and cylinder, as well as the sliding friction coefficient.

The solution was carried out in accordance with the methodology presented in the collection of Kepe O.?. The text of the solution is presented in a convenient HTML format, which makes it easy to read and understand all stages of solving the problem.

By purchasing this digital product, you get a convenient and affordable tool for studying physics and solving problems.

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This product is a solution to problem 17.3.36 from the collection of problems in physics, authored by Kepe O.?.

The task is to determine the value of the force F at which a homogeneous cylinder with a mass of 2 kg will not move relative to a prism with a mass of 10 kg sliding along a horizontal plane. The sliding friction coefficient between the prism and the plane is 0.1. At the initial moment of time, both bodies were at rest.

To solve the problem, it is necessary to apply the laws of dynamics and equilibrium equations of the body. As a result of solving the problem, the value of force F is obtained, which is equal to 79.7 N.

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