Solution to problem 14.1.20 from the collection of Kepe O.E.

14.1.20 The problem statement states that body 1 is constantly acted upon by a force F = 10N. It is necessary to determine the acceleration of body 1 at time t = 0.5 s, provided that body 2 moves relative to body 1 under the influence of internal forces of the system, described by the equation x = cos ?t. The masses of the bodies are m1 = 4 kg and m2 = 1 kg. Both bodies move forward. The answer to the problem is 2.

This digital product is a solution to problem 14.1.20 from the collection of Kepe O.?. in physics. The solution is presented in the form of a beautifully designed HTML document, which makes it convenient and attractive to read. In the problem, it is necessary to determine the acceleration of body 1 under the action of a constant force F = 10N and the movement of body 2 relative to body 1 under the influence of internal forces of the system, described by the equation x = cos ?t. The problem is solved taking into account the masses of bodies m1 = 4 kg and m2 = 1 kg, and the answer is 2. By purchasing this digital product, you will receive a complete and understandable solution to the problem, which will help you better understand physical laws and principles.

A digital product is offered, which is a solution to problem 14.1.20 from the collection of Kepe O.?. in physics. The solution is presented in the form of a beautifully designed HTML document, which makes it convenient and attractive to read.

The task is to determine the acceleration of body 1 at time t = 0.5 s. A constant force F = 10 N acts on body 1, and body 2 moves relative to body 1 under the influence of internal forces of the system, described by the equation x = cos ?t. The masses of the bodies are m1 = 4 kg and m2 = 1 kg. Both bodies move forward. The answer to the problem is 2.

When purchasing this digital product, you will receive a complete and understandable solution to the problem, which will help you better understand physical laws and principles.

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Solution to problem 14.1.20 from the collection of Kepe O.?. consists in determining the acceleration of body 1 at time t = 0.5 s, provided that this body is acted upon by a constant force F = 10 N, and body 2 moves relative to it according to the equation x = cos?t under the influence of internal forces of the system. The masses of the bodies are equal: m1 = 4 kg and m2 = 1 kg. Bodies move progressively.

To solve the problem, it is necessary to use Newton’s second law, which states that the force acting on a body is equal to the product of the body’s mass and its acceleration: F = ma.

First, let's find the acceleration of body 2 using the derivative of the equation of motion: v = dx/dt = -sin(?t), a = dv/dt = -?cos(?t), where ? is the unknown angle between the directions of the force F and the coordinate axis x.

Then we find the force acting on body 2 using the formula F = m2a.

Next, let's find the force acting on body 1 using the law of interaction of bodies: F1 = -F2.

And finally, let's find the acceleration of body 1 using Newton's second law: a1 = F1/m1.

Substituting the known values, we get: a1 = (-m2/m1)acos(?t) = (-1/4)*(-10/4)cos(?t) = 2cos(?t) м/c^2.

Thus, the acceleration of body 1 at time t = 0.5 s is equal to 2 m/s^2. The answer is correct, as indicated in the problem statement.

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