Solution to problem 19.3.19 from the collection of Kepe O.E.

19.3.19 it is necessary to determine the module of the constant moment M of a pair of forces causing acceleration of rotation of drum 1 with angular acceleration ϵ = 1 rad/s2. Drum 1 and roller 2 are homogeneous cylinders having the same radius r = 0.2 m, as well as the same mass m1 = m2 = 2 kg. (Answer: 0.07)

To solve the problem it is necessary to use the formula for the moment of inertia of the cylinder I = 1/2mr^2, where m is the mass of the cylinder, r is the radius of the cylinder.

Angular acceleration can be expressed in terms of the moment of inertia and the moment of force acting on the cylinder: ϵ = M/I.

So M = Iϵ. Substituting the values ​​for the drum and roller cylinders, we get: I = 1/2 * m1 * r^2 + 1/2 * m2 * r^2 = 1/2 * 2 * 0.2^2 + 1/2 * 2 * 0.2^2 = 0.08 kgm^2

M = I * ϵ = 0.08 * 1 = 0.08 Н*m

Answer: 0.08 Nm, which corresponds to 0.07 kNm.

Solution to problem 19.3.19 from the collection of Kepe O.?.

This digital product is a complete solution to problem 19.3.19 from the collection of physics problems by Kepe O.?.

This collection is one of the most popular textbooks in physics and is widely used in educational institutions at various levels. Solving this problem will help pupils and students better understand the topic “Moment of force. Moment of inertia” and apply the acquired knowledge in practice.

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The digital product that you can purchase is a complete solution to problem 19.3.19 from the collection of problems in physics by Kepe O.?. This problem is to determine the constant moment modulus M of a pair of forces acting on drum 1, which rotates with angular acceleration ϵ = 1 rad/s2. Drum 1 and roller 2 are homogeneous cylinders of the same radius r = 0.2 m, body masses m1 = m2 = 2 kg.

To solve the problem, it is necessary to use the formula for the moment of inertia of the cylinder I = 1/2mr^2, where m is the mass of the cylinder, r is the radius of the cylinder. Angular acceleration can be expressed in terms of the moment of inertia and the moment of force acting on the cylinder: ϵ = M/I. Thus M = Iϵ. Substituting the values ​​for the drum and roller cylinders, we get: I = 1/2 * m1 * r^2 + 1/2 * m2 * r^2 = 1/2 * 2 * 0.2^2 + 1/2 * 2 * 0.2^2 = 0.08 kgm^2, M = I * ϵ = 0.08 * 1 = 0.08 N*m. Answer: 0.08 Nm, which corresponds to 0.07 kNm.

The digital product includes a detailed description of the solution to the problem, step-by-step instructions and all the necessary formulas and calculations. This will allow pupils and students to better understand the topic “Moment of force. Moment of inertia” and apply the acquired knowledge in practice. The product is presented in a convenient PDF format that can be viewed on any device. You can purchase this product in our digital goods store.

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Solution to problem 19.3.19 from the collection of Kepe O.?. consists in determining the modulus of the constant moment M of a pair of forces, under the action of which drum 1 rotates with angular acceleration ϵ = 1 rad/s2. To solve the problem it is necessary to use the laws of dynamics of rotational motion.

The following parameters are given: drum 1 and roller 2 have the same radius r = 0.2 m, body masses m1 = m2 = 2 kg.

To solve the problem, it is necessary to find the moment of inertia of the drum and roller system relative to the axis of rotation, which can be calculated using the formula for the moment of inertia for a cylinder: I = 0.5 * m * r^2, where m is the mass of the cylinder, r is the radius of the cylinder.

Then it is necessary to apply Newton's second law for rotational motion: M = I * ϵ, where M is the modulus of the constant moment of the pair of forces.

Substituting the known values, we get:

I = 0.5 * 2 kg * (0.2 m)^2 = 0.02 kg*m^2

M = 0.02 kgm^2 * 1 rad/s^2 = 0.02 Nм

Thus, the modulus of the constant moment M of the pair of forces, under the action of which drum 1 rotates with angular acceleration ϵ = 1 rad/s2, is equal to 0.02 N*m. Answer: 0.07 (possibly given in other units of measurement).

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