Solution to problem 17.1.13 from the collection of Kepe O.E.

17.1.13. It is necessary to find the minimum speed v of a material point M moving along the inner surface of a cylinder of radius r = 9.81 m in the vertical plane, at which the point will not come off the cylinder in this position. The answer is 9.81.

To solve this problem, you should use the condition of no separation of the point from the cylinder, which can be expressed in terms of the friction force and centripetal acceleration. When the minimum required speed is reached, the friction force will be equal to the weight of point M, and the point will not come off the cylinder.

Thus, we can write the equation: mg = N = mv²/r, where m is the mass of the point, g is the acceleration of gravity, N is the support reaction force, v is the speed of the point, r is the radius of the cylinder.

Solving the equation for v, we get: v = √(gr).

Substituting numerical values, we get: v = √(9.81 m/s² × 9.81 m) ≈ 9.81 m/s.

Thus, the minimum speed of point M at which it will not break away from a cylinder of radius 9.81 m is 9.81 m/s.

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This digital product is a detailed solution to problem 17.1.13 from the collection of Kepe O.?. in physics. The problem is to determine the minimum speed of a material point M moving along the inner surface of a cylinder of radius 9.81 m in a vertical plane, at which the point will not come off the cylinder in this position.

In this product you will find a detailed solution to this problem with step-by-step explanations of each step and formulas. The solution is written in accessible language, understandable to everyone who is familiar with physics at the school level.

The minimum speed of point M, at which it will not break away from a cylinder of radius 9.81 m, is 9.81 m/s, which is confirmed in this solution. The product is available in HTML format, which makes it easy to read and study the solution on any device. The beautiful design of the product and user-friendly interface make it easy to navigate in solving the problem.

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Solution to problem 17.1.13 from the collection of Kepe O.?. consists in determining the minimum speed of a material point M moving along the inner surface of a cylinder of radius r = 9.81 meters in a vertical plane, at which the point will not come off the surface of the cylinder in the specified position.

To solve the problem, it is necessary to use the laws of dynamics of a material point and the law of conservation of energy. The minimum speed at which a material point does not break away from the surface of the cylinder is equal to the acceleration of gravity g, which on Earth is 9.81 m/s².

Therefore, the answer to the problem is 9.81 m/s.

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