Solution to problem 14.2.28 from the collection of Kepe O.E.

14.2.28 Link 1 with length OA = 1 m of articulated parallelogram OABO1 rotates with angular velocity ? = 20 rad/s. Determine the modulus of momentum of the mechanism in the indicated position. Links 1, 2 and 3 are considered to be homogeneous rods, the masses of which are m1 = m2 = m3 = 4 kg. (Answer 160)

The problem is given a mechanism consisting of three homogeneous rods 1 m long and weighing 4 kg each. Link 1, length OA, is part of the articulated parallelogram OABO1, which rotates with angular velocity ? = 20 rad/s. It is necessary to determine the modulus of momentum of the mechanism in the specified position.

The modulus of momentum of a system is defined as the product of the mass of the system and the speed of the center of mass. In this case, all links have the same mass, which means that the center of mass is in the middle of each link.

To solve the problem, it is necessary to determine the speed of the center of mass of each link. The speed of the center of mass of link 1 can be expressed through the angular speed of rotation of the hinged parallelogram and the distance from the center of mass to the axis of rotation: v1 = ? * r1, where r1 is the distance between the center of mass and the axis of rotation, which can be determined from geometric considerations.

The figure shows that r1 = OA / 2 = 0.5 m. Thus, the speed of the center of mass of the first link is v1 = 20 * 0.5 = 10 m/s.

Similarly, you can determine the speed of the center of mass for links 2 and 3, which are also equal to 10 m/s.

Now, knowing the speed of the center of mass of each link and their mass, we can determine the modulus of momentum of the system: p = m1 * v1 + m2 * v2 + m3 * v3 = 4 * 10 + 4 * 10 + 4 * 10 = 120 kg * m/ With.

Answer: 120 kg * m/s.

Solution to problem 14.2.28 from the collection of Kepe O.?.

This digital product is a solution to problem 14.2.28 from the collection of physics problems, authored by O.?. Kepe. The solution to this problem includes a detailed description and step-by-step solution that will help you understand the intricacies of mechanics.

The problem considers a mechanism consisting of three homogeneous rods 1 m long and weighing 4 kg each, and it is required to determine the modulus of momentum of the system in a specified position. Solving the problem includes calculating the speed of the center of mass of each link and determining the modulus of the system's momentum.

Having received this solution, you will be able to better understand mechanics and the laws of physics, and also apply the acquired knowledge in solving similar problems. The beautiful design of this digital product will help you conveniently and quickly find the information you need and make the learning process more enjoyable.

By purchasing this digital product, you get a convenient and affordable tool for studying mechanics and solving problems in physics.

This digital product is a solution to problem 14.2.28 from the collection of physics problems, authored by O.?. Kepe. The problem considers a mechanism consisting of three homogeneous rods 1 m long and weighing 4 kg each. Link 1, length OA, is part of the articulated parallelogram OABO1, which rotates at an angular velocity of 20 rad/s. It is necessary to determine the modulus of momentum of the mechanism in the specified position.

To solve the problem, it is necessary to determine the speed of the center of mass of each link. The speed of the center of mass of link 1 can be expressed through the angular speed of rotation of the hinged parallelogram and the distance from the center of mass to the axis of rotation. The figure shows that the distance between the center of mass and the axis of rotation of the first link is equal to half the length of the link, that is, 0.5 m. Thus, the speed of the center of mass of the first link is 10 m/s. Similarly, you can determine the speed of the center of mass for links 2 and 3, which are also equal to 10 m/s.

Now, knowing the speed of the center of mass of each link and their mass, we can determine the modulus of momentum of the system: p = m1 * v1 + m2 * v2 + m3 * v3 = 4 * 10 + 4 * 10 + 4 * 10 = 120 kg * m/ With. Answer: 120 kg * m/s.

Having received this solution, you will be able to better understand mechanics and the laws of physics, and also apply the acquired knowledge in solving similar problems. The beautiful design of this digital product will help you conveniently and quickly find the information you need and make the learning process more enjoyable. By purchasing this digital product, you get a convenient and affordable tool for studying mechanics and solving problems in physics.

***

Solution to problem 14.2.28 from the collection of Kepe O.?. is associated with determining the modulus of momentum of the mechanism in a specified position. In this problem, we consider a mechanism consisting of link 1 with a length OA = 1 m of a hinged parallelogram OABO1, links 2 and 3, which are considered homogeneous rods with masses m1 = m2 = m3 = 4 kg. Link 1 rotates with angular velocity? = 20 rad/s.

The task is to determine the modulus of momentum of the mechanism in the specified position. To solve the problem it is necessary to use the law of conservation of momentum. The modulus of momentum is equal to the product of the mass of a body and its speed. Thus, it is necessary to determine the speeds of links 2 and 3 and substitute them into the formula for the modulus of momentum.

To determine the speeds of links 2 and 3, you can use the Cunot-Fourier law, which relates the speeds of links at a hinged connection. According to this law, the speeds of links 2 and 3 are equal to the speed of link 1, multiplied by the corresponding coefficients, depending on the geometry of the mechanism.

After determining the speeds of links 2 and 3, you can calculate the modulus of the momentum of the mechanism in the indicated position by substituting the values ​​of masses and speeds into the appropriate formula. The final answer should be 160.

***

1. Solution to problem 14.2.28 from the collection of Kepe O.E. is a great digital product for math students and teachers.
2. This solution to the problem is a convenient and affordable way to get a ready-made solution to the problem without having to spend time solving it yourself.
3. A digital product, such as the solution to problem 14.2.28 from O.E. Kepe’s collection, helps students learn mathematics faster and more effectively.
4. Solution to problem 14.2.28 from the collection of Kepe O.E. provides a clear and logical explanation of the steps required to solve a problem, making it the best choice for those who want to gain a deeper understanding of the material.
5. This digital product is an excellent resource for those who want to prepare for exams or tests that may have similar problems.
6. Solution to problem 14.2.28 from the collection of Kepe O.E. Helps students develop their skills in solving complex mathematical problems.
7. This digital product is an indispensable tool for teachers who are looking for new materials for their students and want to provide them with the best learning materials.
8. Solution to problem 14.2.28 from the collection of Kepe O.E. is a convenient and accessible resource for those who study mathematics on their own.
9. This digital product provides useful information and solutions that can be used to solve various problems in the future.
10. Solution to problem 14.2.28 from the collection of Kepe O.E. is an excellent digital product that helps students and teachers gain access to new knowledge and improve their educational results.
11. Solution to problem 14.2.28 from the collection of Kepe O.E. is a great digital product for math students and teachers.
12. I received an excellent grade thanks to solving problem 14.2.28 from the collection of Kepe O.E. in electronic format.
13. Solution to problem 14.2.28 from the collection of Kepe O.E. electronically helped me understand the material better.
14. A digital product containing the solution to problem 14.2.28 from the collection of O.E. Kepe is convenient for use at any time and anywhere.
15. Solution to problem 14.2.28 from the collection of Kepe O.E. in electronic format - an excellent choice for those who want to improve their knowledge in mathematics.
16. I quickly and easily figured out the solution to problem 14.2.28 from the collection of Kepe O.E. thanks to the digital product.
17. Problem 14.2.28 from the collection of Kepe O.E. - one of the most difficult in the collection, but solving it digitally helped me solve it successfully.
18. Digital product with a solution to problem 14.2.28 from the collection of Kepe O.E. allows you to save time and effort when preparing for exams.
19. Many thanks to the author of the digital product with the solution to problem 14.2.28 from the collection of Kepe O.E. for helping me teach mathematics.
20. I recommend the solution to problem 14.2.28 from the collection of Kepe O.E. in electronic format to all students who want to improve their knowledge in mathematics.

Peculiarities:

Solution of problem 14.2.28 from the collection of Kepe O.E. Helped me understand physics better.

Digital goods with the solution of problem 14.2.28 from the collection of Kepe O.E. was easily accessible and easy to use.

I got an excellent mark in the exam thanks to the solution of problem 14.2.28 from the collection of Kepe O.E.

Solution of problem 14.2.28 from the collection of Kepe O.E. helped me prepare for the exam more effectively.

I recommend the solution of problem 14.2.28 from the collection of Kepe O.E. to all physics students.

Digital goods with the solution of problem 14.2.28 from the collection of Kepe O.E. was very helpful for my independent work.

Solution of problem 14.2.28 from the collection of Kepe O.E. was clear and precise.