Solution to problem 9.4.5 from the collection of Kepe O.E.

9.4.5 Vertical rod AB moves in a plane, while its end A moves along a horizontal straight line with a speed vA = 0.2 m/s. At point C, end A touches a disk of radius r. It is necessary to determine the speed of point C of the rod in the position where the angle between the rod and the horizontal line is 45°. (Answer 0.141)

To solve the problem, you can use the formula for the speed of a point moving in a circle: v = rω, where r is the radius of the circle, and ω is the angular velocity.

In this case, point C moves in a circle with radius r, so its speed will be equal to v = rω. To find the angular velocity ω, it is necessary to express it in terms of the velocities of the points of the rod.

Since end A of the rod moves along a horizontal straight line with speed vA, then the speed of point C located on the disk is equal to vC = vA. Also, from geometric considerations, it is possible to express the angular velocity ω through the angle φ between the vertical axis and the line connecting points A and C: ω = vC / r * sin(φ).

At φ = 45° we obtain: ω = vC / r * sin(45°) = vC / (r * √2). It is known that vA = vC, therefore vC = vA = 0.2 m/s. We substitute all known values ​​into the formula and get: ω = 0.2 / (r * √2). Next, using the formula for the speed of a point on a circle, we find the speed of point C: v = rω = r * 0.2 / (r * √2) = 0.2 / √2 ≈ 0.141 m/s.

Solution to problem 9.4.5 from the collection of Kepe O.?.

We present to your attention the solution to problem 9.4.5 from the collection “Problems in Physics for University Entrants” by author O.?. Kepe.

This digital product is a detailed solution to the problem with a step-by-step explanation and visualization of all the necessary formulas and graphs.

Our solution will help you better understand physical laws and consolidate your knowledge.

All materials are presented in an easy-to-read format and designed in a modern design.

Buy our digital product and improve your physics knowledge with ease!

Buy a solution to the problem

I present to your attention a digital product - the solution to problem 9.4.5 from the collection “Problems in Physics for Those Entering Universities” by author O.?. Kepe.

In this problem, it is necessary to determine the speed of point C of the rod in the position where the angle between the rod and the horizontal line is 45°. To solve the problem, use the formula for the speed of a point moving in a circle: v = rω, where r is the radius of the circle, and ω is the angular velocity.

In this case, point C moves in a circle with radius r, so its speed will be equal to v = rω. To find the angular velocity ω, it is necessary to express it in terms of the velocities of the points of the rod.

From geometric considerations, we can express the angular velocity ω through the angle φ between the vertical axis and the line connecting points A and C: ω = vC / r * sin(φ), where vC is the speed of point C located on the disk.

Since end A of the rod moves along a horizontal straight line with speed vA, then the speed of point C located on the disk is equal to vC = vA.

At φ = 45° we obtain: ω = vC / r * sin(45°) = vC / (r * √2). It is known that vA = vC, therefore vC = vA = 0.2 m/s. We substitute all known values ​​into the formula and get: ω = 0.2 / (r * √2).

Next, using the formula for the speed of a point on a circle, we find the speed of point C: v = rω = r * 0.2 / (r * √2) = 0.2 / √2 ≈ 0.141 m/s.

Our solution to the problem contains a step-by-step explanation of all the necessary formulas and graphs, which will help you better understand the physical laws and consolidate the knowledge gained. All materials are presented in an easy-to-read format and designed in a modern design.

Buy our digital product and improve your physics knowledge with ease!

***

Solution to problem 9.4.5 from the collection of Kepe O.?. is associated with determining the speed of point C of rod AB in a position where the angle between the horizontal plane and the rod is 45 degrees, provided that end A of the rod slides along a horizontal straight line with a speed vA = 0.2 m/s, and point C slides along the disk radius r.

To solve the problem, it is necessary to use the cosine theorem and the formula for the speed of a point moving in a circle. First you need to determine the length of the rod AB and the distance from point C to the vertical line passing through end A of the rod. The law of cosines can then be applied to determine the angle between the rod and the vertical plane.

You can then use the formula to determine the speed of a point moving in a circle: v = rω, where v is the speed of the point, r is the radius of the circle, and ω is the angular speed. Using the found angle and the speed of end A of the rod, you can determine the angular velocity of the rod and, then, the speed of point C of the rod.

As a result, the solution to problem 9.4.5 from the collection of Kepe O.?. consists in the sequential application of formulas to determine the length of the rod, the distance from point C to the vertical line, the angle between the rod and the vertical plane, the angular velocity of the rod and the speed of point C. The answer to the problem is 0.141 m/s.

***

1. Solution to problem 9.4.5 from the collection of Kepe O.E. helped me better understand thermodynamics material.
2. I really liked how quickly and easily I was able to solve problem 9.4.5 thanks to this digital product.
3. The solution to problem 9.4.5 from O.E. Kepe’s collection helped me a lot. in preparation for the physics exam.
4. With this digital product, I was able to quickly learn how to solve problems in thermodynamics, including problem 9.4.5 from the collection of O.E. Kepe.
5. Solution to problem 9.4.5 from the collection of Kepe O.E. in digital format helped me save a lot of time while preparing for the exam.
6. It is very convenient to have access to the solution to Problem 9.4.5 from the collection of O.E. Kepe. in digital format so you can study the material anywhere and at any time.
7. This digital product is an excellent resource for those who want to improve their thermodynamics problem-solving skills, including Problem 9.4.5 from O.E. Kepe.

Peculiarities:

Solution of problem 9.4.5 from the collection of Kepe O.E. is a great digital product for students and math teachers.

I really liked that in solving problem 9.4.5 from the collection of Kepe O.E. detailed explanations and analysis of cases are presented.

By solving problem 9.4.5 from the collection of Kepe O.E. I understood the material better and was able to cope with the task.

Solution of problem 9.4.5 from the collection of Kepe O.E. helped me prepare for the exam and get a high grade.

I purchased the solution to problem 9.4.5 from O.E. Kepe's collection. for my child and was pleasantly surprised by the quality and usefulness of the material.

Solution of problem 9.4.5 from the collection of Kepe O.E. - an excellent choice for those who want to improve their knowledge in mathematics.

By solving problem 9.4.5 from the collection of Kepe O.E. I was able to solve similar problems on my own and without difficulty.

I purchased the solution to problem 9.4.5 from O.E. Kepe's collection. for his friend and he was pleasantly surprised by the usefulness and clarity of the material.

Solution of problem 9.4.5 from the collection of Kepe O.E. - a great tool for preparing for olympiads and competitions in mathematics.

I am very grateful to the author of the solution of problem 9.4.5 from the collection of Kepe O.E. for quality and useful content.