Solution to problem 15.5.6 from the collection of Kepe O.E.

In this problem there is a crank 1 of a hinged parallelogram with a length OA = 0.4 m, which rotates uniformly around the axis O with an angular velocity co1 = 10 rad/s. The moments of inertia of cranks 1 and 3 relative to their axes of rotation are equal to 0.1 kg•m2, and the mass of the connecting rod 2 m2 = 5 kg. It is necessary to find the kinetic energy of the mechanism.

To solve this problem, we use the formula for the kinetic energy of a mechanical system: E = 1/2 * I * ω^2 + 1/2 * m * v^2, where I is the moment of inertia, ω is the angular velocity, m is the mass, v - linear speed.

First, let's find the angular speed of rotation of crank 1: ω1 = со1 / l1, where l1 is the length of the crank. Substituting the known values, we get: ω1 = 10 / 0.4 = 25 rad/s.

Now you can find the moment of inertia of crank 3 relative to its axis of rotation: I3 = I1 + m2 * l2^2, where I1 is the moment of inertia of crank 1 relative to its axis of rotation, l2 is the length of the connecting rod. Substituting the known values, we get: I3 = 0.1 + 5 * 0.4^2 = 1.3 kg•m2.

Next, we find the linear speed of point A of crank 1: v = l1 * ω1. Substituting the known values, we get: v = 0.4 * 25 = 10 m/s.

Finally, we substitute all known values ​​into the formula for kinetic energy: E = 1/2 * (0.1 + 1.3) * 25^2 + 1/2 * 5 * 10^2 = 50 J.

Thus, the kinetic energy of the mechanism is 50 J.

Solution to problem 15.5.6 from the collection of Kepe O.?.

We present to your attention the solution to problem 15.5.6 from the collection of problems by Kepe O.?. This digital product is an excellent assistant in preparing for exams and tests in the Theoretical Mechanics course.

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Product description:

We present to your attention the solution to problem 15.5.6 from the collection of problems on theoretical mechanics by the author Kepe O.?. In this digital product you will find a complete solution to the problem with a step-by-step description of each step.

The problem is to determine the kinetic energy of a mechanism in which there is a crank 1 of a hinged parallelogram with a length OA = 0.4 m, which rotates uniformly around the axis O with an angular velocity co1 = 10 rad/s. The moments of inertia of cranks 1 and 3 relative to their axes of rotation are equal to 0.1 kg•m2, and the mass of the connecting rod 2 m2 = 5 kg.

The problem is solved using the formula for the kinetic energy of a mechanical system: E = 1/2 * I * ω^2 + 1/2 * m * v^2, where I is the moment of inertia, ω is the angular velocity, m is the mass, v - linear speed.

First, the angular velocity of rotation of crank 1 is calculated: ω1 = со1 / l1, where l1 is the length of the crank. Substituting the known values, we get: ω1 = 10 / 0.4 = 25 rad/s.

Then we find the moment of inertia of crank 3 relative to its axis of rotation: I3 = I1 + m2 * l2^2, where I1 is the moment of inertia of crank 1 relative to its axis of rotation, l2 is the length of the connecting rod. Substituting the known values, we get: I3 = 0.1 + 5 * 0.4^2 = 1.3 kg•m2.

Next, we find the linear speed of point A of crank 1: v = l1 * ω1. Substituting the known values, we get: v = 0.4 * 25 = 10 m/s.

Finally, we substitute all known values ​​into the formula for kinetic energy: E = 1/2 * (0.1 + 1.3) * 25^2 + 1/2 * 5 * 10^2 = 50 J.

Thus, the kinetic energy of the mechanism is 50 J. Our digital product is an excellent assistant in preparing for exams and tests in the Theoretical Mechanics course. The solution is carried out by a qualified specialist in the field of theoretical mechanics and guarantees the correctness of the results.

Our digital product is available for download in a convenient format, making it easy and quick to get the information you need. In addition, we provide a money-back guarantee if you are not satisfied with the product. Buy our digital product right now and get a reliable and high-quality source of knowledge on theoretical mechanics.

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This product is a solution to problem 15.5.6 from the collection of problems in physics "Kepe O.?".

The problem considers crank 1 of a hinged parallelogram with a length OA = 0.4 m, which rotates uniformly around the axis O with an angular velocity co1 = 10 rad/s. The moments of inertia of cranks 1 and 3 relative to their axes of rotation are equal to 0.1 kg•m^2, the mass of the connecting rod is 2 m2 = 5 kg. It is necessary to find the kinetic energy of the mechanism.

After solving the problem, the answer was received - the kinetic energy of the mechanism is 50.

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