Solution to problem 15.4.8 from the collection of Kepe O.E.

15.4.8 In this problem, it is necessary to find the kinetic energy of a homogeneous rod AB with a length of 2 m and a mass of m = 6 kg at the moment of time when the angle between the rod and the horizon is 45 degrees and the speed of point A is 1 m/s. The rod moves by sliding ends A and B along horizontal and vertical planes.

To solve the problem, it is necessary to use the formula for the kinetic energy of rotational motion: K = Iω²/2, where I is the moment of inertia relative to the axis of rotation, and ω is the angular velocity of rotation.

Rod AB can be divided into two parts: horizontal and vertical. For each of them, it is necessary to find the moment of inertia about the axis of rotation passing through the center of mass.

The moment of inertia of the horizontal part of the rod relative to the axis passing through the center of mass is equal to Ig = (1/12) * m * l², where l is the length of the horizontal part of the rod (l = 2/√2 m).

The moment of inertia of the vertical part of the rod relative to the same axis is equal to Iв = m * (l/2)².

The total moment of inertia of the rod relative to the axis passing through the center of mass is equal to the sum of the moments of inertia of its parts: I = Ig + Iv.

Knowing the moment of inertia, we can find the angular velocity of rotation ω, which is equal to ω = vA / (l/2) = 1 / (2/√2) rad/s.

Now, knowing the moment of inertia and angular velocity of rotation, you can find the kinetic energy of the rod: K = Iω²/2 = ((1/12) * m * l² + m * (l/2)²) * (1 / (2/√ 2))² / 2 = 2 mJ.

Thus, at the time when the angle between the rod and the horizon is 45 degrees and the speed of point A is 1 m/s, the kinetic energy of rod AB is 2 mJ.

Solution to problem 15.4.8 from the collection of Kepe O.?.

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Product characteristics:

• Format: PDF;
• Number of pages: 2;
• Russian language;
• File size: 0.5 MB.

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The offered product is a solution to problem 15.4.8 from the collection of Kepe O.?. in physics. The problem is to determine the kinetic energy of a homogeneous rod AB with a length of 2 m and a mass of 6 kg at a time when the angle between the rod and the horizon is 45 degrees and the speed of point A is 1 m/s. The rod moves by sliding ends A and B along horizontal and vertical planes. The solution to the problem is based on the formula for the kinetic energy of rotational motion and the calculation of the moment of inertia about the axis of rotation passing through the center of mass. The solution was carried out by an experienced physics teacher, each step of the solution is explained in detail and is accompanied by the necessary formulas and explanations. The product is presented in PDF format, contains 2 pages in Russian and has a file size of 0.5 MB. By purchasing this product, you are guaranteed to receive the correct answer to problem 15.4.8 from the collection of Kepe O.?. in physics, and also improve your knowledge in the field of rotational motion of a rigid body and learn to apply it in practice. We also guarantee complete confidentiality and security when paying and downloading the solution.

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