Solution to problem 20.2.4 from the collection of Kepe O.E.

20.2.4 A brake pad is pressed against a cylinder, which rotates under the action of a pair of forces with a moment M = 20 N • m, with a force F = 100 N. Determine the generalized force corresponding to the generalized coordinate ? if the sliding friction coefficient between the block and the cylinder is f = 0.4, a R = 0.4 m. (Answer 4)

Let's say we have a cylinder that rotates under the action of a pair of forces with a moment M = 20 N • m. A brake pad is pressed against the cylinder with a force F = 100 N. We need to determine the generalized force corresponding to the generalized coordinate ? if the sliding friction coefficient between the block and the cylinder is f = 0.4, and R = 0.4 m. Answer: 4.

Solution to problem 20.2.4 from the collection of Kepe O.?.

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This product is a solution to problem 20.2.4 from the collection of Kepe O.?. in physics. The problem is to determine the generalized force corresponding to the generalized coordinate when a pair of forces acts on a rotating cylinder, to which the brake pad is pressed with a force of 100 N. To solve the problem, it is necessary to take into account the coefficient of sliding friction between the pad and the cylinder, which is equal to 0.4, and the radius of the cylinder , which is equal to 0.4 m.

Solving a problem includes a detailed description of the problem statement, solution steps, analytical calculations and the final answer to the problem. This product is presented in digital format and is available for download in the digital goods store.

By purchasing this digital product, the buyer receives a high-quality and detailed solution to problem 20.2.4 from the collection of Kepe O.?. in physics in a convenient digital format, designed in a beautiful html format, which ensures ease of reading and understanding of the material.

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The proposed solution to problem 20.2.4 from the collection of Kepe O.?. consists in determining the generalized force corresponding to the generalized coordinate when a brake pad is pressed against a cylinder rotating under the action of a pair of forces with a moment M = 20 N • m with a force F = 100 N. To solve the problem, it is necessary to take into account the coefficient of sliding friction between the pad and the cylinder f = 0.4, and also the radius of the cylinder R = 0.4 m.

First you need to calculate the moment of friction force acting on the cylinder. It is equal to the difference between the moment of force causing rotation of the cylinder and the moment of force created by the brake pad:

Mтр = M - FR

where M is the moment of force causing rotation of the cylinder, F is the force with which the brake pad is pressed against the cylinder, R is the radius of the cylinder.

Substituting the known values, we get:

Mtr = 20 N • m - 100 N • 0.4 m = 20 N • m - 40 N • m = -20 N • m

A negative sign means that the frictional moment is directed against the direction of rotation of the cylinder.

Next, it is necessary to express the generalized force through the moment of the friction force and the generalized coordinate. The generalized force is the derivative of the potential energy with respect to the generalized coordinate:

Q = dU/d?

Since there is no potential energy in this problem, the generalized force is equal to the mechanical work performed by the moment of friction when rotating the cylinder through an angle ?:

Q = ΔA = Mтр • Δ?

where is Δ? - angle of rotation of the cylinder.

Substituting the known values, we get:

Q = -20 Н • м • Δ?

Thus, the generalized force corresponding to the generalized coordinate ? is equal to -20 N • m. Answer: 4.

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