Solution to problem 17.2.2 from the collection of Kepe O.E.

17.2.2 At the initial moment, the articulated parallelogram OABO1 is at rest, while the 0.1 m long crank OA begins to rotate with a constant angular acceleration ϵ = 2 rad/s2. It is necessary to calculate the modulus of the resultant inertial forces of rod AB with a mass of 2 kg at the time t = 1 second. Answer: 0.894.

Solution to problem 17.2.2 from the collection of Kepe O.?.

This digital product is a solution to problem 17.2.2 from the collection of problems in physics by Kepe O.?. It contains a detailed description of the solution to the problem, allowing you to better understand the physical laws and apply them in practice.

The problem is to determine the modulus of the resultant forces of inertia of a rod AB with a mass of 2 kg at the moment of time t = 1 second, when the crank OA with a length of 0.1 m of the articulated parallelogram OABO1 begins to rotate from rest with a constant angular acceleration ϵ = 2 rad/s2. The solution to the problem is presented in an accessible and understandable format, using simple mathematical formulas.

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Problem 17.2.2 from the collection of Kepe O.?. is formulated as follows:

We consider a crank OA with a length of 0.1 m, which is part of the articulated parallelogram OABO1. The initial state of the crank is rest. From the moment the crank begins to move, its angular acceleration is constant and equal to ϵ = 2 rad/s^2. The mass of rod AB is 2 kg. It is necessary to find the modulus of the resultant inertial forces of the rod AB at the moment of time t = 1 s.

The answer to the problem is 0.894.

To solve this problem, it is necessary to use the law of change in the kinetic energy of a solid body, which is expressed by the following formula:

ΔK = K2 - K1 = A + L,

where ΔK is the change in the kinetic energy of the body over time Δt; K1 is the initial kinetic energy of the body; K2 is the final kinetic energy of the body; A - work of external forces during time Δt; L is the work of inertia forces during time Δt.

To find the modulus of the resultant inertial forces of the rod AB, it is necessary to find the work done by the inertial forces during the time t = 1 s.

The inertia force is determined by the formula:

Fin = ma,

where m is the mass of the body, a is the acceleration of the body.

The acceleration of the body is found from the equation of motion of the crank, which is expressed by the formula:

φ = ϵt^2 / 2,

where φ is the angle of rotation of the crank during time t.

Using these formulas and taking into account that the initial angular velocity of the crank is zero, we can find the modulus of the resultant forces of inertia of the rod AB at the time t = 1 s.

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