Solution to problem 11.2.17 from the collection of Kepe O.E.

11.2.17. Rotating cone

We consider a cone that rotates around the Oz axis with an angular velocity ω = 3 rad/s. In this case, its generatrix moves with a constant speed vᵣ = 4 m/s from point A to point B. It is necessary to determine the absolute velocity modulus of point M in the position where the distance AM = 2 m and the angle α = 30°.

Answer:

Let O be the vertex of the cone, AB its generator, and M a point on the generator. Point M moves together with the generatrix, so its speed is equal to the speed of the generatrix:

vᵣ = 4 m/s.

The angle α between OM and Ox is 30°, then

IF = 2 м * sin(30°) = 1 м.

The trajectory of point M is a circle of radius OM.

The absolute speed of point M consists of two components: the speed due to the rotation of the cone around the Oz axis, and the speed due to the movement of point M along the generatrix AB.

The speed due to the rotation of the cone is directed tangentially to the circle, i.e. perpendicular to the vector OM. Its module is equal

v₁ = ω * OM = 3 rad/s * 1 m = 3 m/s.

The speed caused by the movement of point M along the generatrix AB is directed in the direction of the generatrix. Its module is equal

v₂ = vᵣ = 4 м/с.

The modulus of the absolute velocity of point M is equal to

v = √(v₁² + v₂²) = √(3² + 4²) ≈ 5 м/с.

Answer: 5 m/s.

Solution to problem 11.2.17 from the collection of Kepe O.?.

We present to your attention the solution to problem 11.2.17 from the collection of problems in physics by Kepe O.?. This digital product is an excellent assistant for students and schoolchildren who study mechanics. The solution was completed by a professional teacher and contains a detailed analysis and step-by-step solution to the problem.

This solution is a digital product, which allows you to save time searching for a similar solution in paper textbooks. You can also easily print the solution or save it to your computer.

By purchasing this digital product, you receive a ready-made solution to the problem that will help you better understand the theory and consolidate the material in practice.

This product is a solution to problem 11.2.17 from the collection of problems in physics by Kepe O.?. The solution was completed by a professional teacher and contains a detailed analysis and step-by-step solution to the problem.

The task is to determine the magnitude of the absolute velocity of point M on a rotating cone, when the distance from point A to point M is 2 m, and the angle between the vectors OM and Ox is 30°. To solve it, it is necessary to calculate the speed due to the rotation of the cone around the Oz axis, and the speed due to the movement of the point M along the generatrix AB. Then you need to find the absolute velocity modulus of point M, which is equal to the square root of the sum of the squares of these velocities.

By purchasing this digital product, you receive a ready-made solution to the problem that will help you better understand the theory and consolidate the material in practice. This will also save time searching for a similar solution in paper textbooks. The solution can be easily printed or saved on your computer.

***

Product description: Solution to problem 11.2.17 from the collection of Kepe O.?.

Given a cone-shaped figure that rotates around the Oz axis with an angular velocity ? = 3 rad/s. The generatrix of the cone moves at a constant speed vr = 4 m/s in the direction from point A to point B. It is known that the distance from point A to point M is 2 m, and the angle between the Oz axis and the line connecting points M and B is equal 30 degrees.

It is required to find the absolute velocity of point M at the moment when the distance AM is 2 m.

Answer: 5.

***

1. Solution to problem 11.2.17 from the collection of Kepe O.E. is a great digital product for those preparing for math exams.
2. With the help of this digital product, I easily understood the assignment and got an excellent grade in the exam.
3. A very convenient and understandable format for solving the problem, which helps you quickly master the material.
4. Solution to problem 11.2.17 from the collection of Kepe O.E. - an indispensable assistant for students and schoolchildren.
5. Quick access to this digital product reduces the time spent preparing for the exam.
6. Solution to problem 11.2.17 from the collection of Kepe O.E. - an excellent choice for those who want to improve their knowledge in mathematics.
7. Many thanks to the author for such a useful and convenient digital product!

Peculiarities:

An excellent solution for students who want to improve their knowledge in mathematics.

A very convenient digital product that allows you to solve the problem anytime and anywhere.

Thanks to this digital product, I was able / was able to better understand the material and successfully complete the task.

Solution of the problem from the collection of Kepe O.E. is a reliable and proven material that will help you understand the difficult questions of mathematics.

I really liked this digital product, it was useful and informative.

Thanks to the author for a clear and understandable explanation of the solution to the problem. The digital format is convenient and saves time.

With the help of this solution, I easily coped with the task, which seemed to me very difficult.

I recommend this digital product to anyone who wants to improve their math skills and pass their exams.

I really liked that the solution of the problem is accompanied by detailed comments and explanations.

Thank you for a great digital product that helped me figure out a difficult math problem.