Solution to problem 17.3.39 from the collection of Kepe O.E.

There is a problem on the page that describes the rotation of a gear under the influence of angular acceleration. Carrier 1 rotates in a horizontal plane and transmits angular acceleration ϵ = 400 rad/s to gear 2. The wheel can be considered a homogeneous cylinder of radius r = 0.1 m and mass 1 kg. It is necessary to determine the modulus of the force in the engagement acting along the engagement line L. The answer to the problem is 21.3.

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This digital product is a solution to problem 17.3.39 from the collection of Kepe O.?. The problem describes the rotation of a gear wheel under the influence of angular acceleration, where carrier 1 rotates in a horizontal plane and transmits angular acceleration ϵ = 400 rad/s to gear 2. The wheel can be considered a homogeneous cylinder of radius r = 0.1 m and mass 1 kg.

In this digital product you will find a description of the problem, an analysis of the conditions, a solution algorithm, calculations and an answer. The solution to the problem is presented in a beautiful HTML format, which makes its use more convenient and enjoyable.

By purchasing this digital product, you will gain access to a high-quality solution to the problem that will help you better understand the material and successfully complete the task. The answer to the problem is 21.3. This product is intended for students and teachers who study physics and mathematics. Don't miss the opportunity to purchase this digital product and improve your knowledge in physics and mathematics!

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Solution to problem 17.3.39 from the collection of Kepe O.?.

Given a system consisting of a carrier 1, a gear 2 and a force acting at the engagement point L. The carrier rotates in a horizontal plane with angular acceleration ϵ = 400 rad/s. Gear 2 can be considered a homogeneous cylinder of radius r = 0.1 m and mass 1 kg. It is required to determine the modulus of the force in the engagement acting along the engagement line L.

To solve the problem, it is necessary to use the laws of dynamics of the rotational motion of a rigid body. According to Newton's second law for rotational motion, the moment of force is equal to the product of the moment of inertia of the body and its angular acceleration. The moment of inertia of gear 2 can be calculated using the formula I = (1/2)mr^2, where m is the mass of the body, r is the radius of the body.

Thus, we find the moment of inertia of gear 2:

I = (1/2)mr^2 = (1/2) * 1 kg * (0.1 m)^2 = 0.005 kg*m^2

Then, using Newton's second law for rotational motion, we find the magnitude of the force in the mesh:

M = IL = ϵI

where L is the radius vector of the force application point. Since the force acts along the meshing line, then L = r, where r is the radius of the gear.

Thus,

M = ϵI = 400 rad/s * 0.005 kgm^2 = 2 Nm

The force modulus in the clutch is M/r = 2 N*m / 0.1 m = 20 N.

Answer: the modulus of the force in the engagement acting along the engagement line L is equal to 20 N.

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