Solution of problem 9.7.3 from the collection of Kepe O.E.

Task 9.7.3:

Hopefully:

• a_A = 1 m/s² - acceleration of point A at a given time;
• ? = 2 rad/s - angular velocity;
• ? = 2 rad/s² - angular acceleration;
• AB = 1 m - length of rod AB.

Find:

• a_B - acceleration of point B of the rod.

Answer:

The acceleration of point A can be decomposed into two components:

• acceleration projection onto the AB axis: a_Asinθ = 1 m/s²sin90° = 1 m/s²;
• acceleration projection onto the axis perpendicular to AB: a_Acosθ = 1 m/s²cos90° = 0 m/s².

Since the rod moves in a plane, the acceleration of point B is directed along the rod, that is, perpendicular to the AB axis. This means that the projection of the acceleration of point B onto the axis AB is equal to 0 m/s².

Then the acceleration of point B can be found using the formula:

a_B = a_Acosθ - r?²sinθ = 1 m/s²cos90° - 1 m·(2 rad/s)²sin90° = 0 m/s² - 5 m/s² = -5 m/s².

Answer: a_B = -5 m/s².

Solution to problem 9.7.3 from the collection of Kepe O..

This digital product is a solution to problem 9.7.3 from the collection of problems on physics by Kepe O.. in electronic format. The solution was completed by a professional physicist and presented in a beautifully designed html format.

Problem 9.7.3 describes the motion of a rod in a plane and requires finding the acceleration of point B of the rod for given parameters. Solving the problem consists of a step-by-step description of the solution process and detailed calculations that will help you understand the basics of physics and learn how to solve similar problems.

The digital product is presented in the form of an HTML page, designed in a pleasant and concise style, which makes it convenient and understandable for reading and studying. You can purchase this product on our website and get instant access to useful information that will help you improve your knowledge of physics and prepare for success in exams.

This digital product is a solution to problem 9.7.3 from the collection of problems in physics by Kepe O.?. in electronic format. The solution was completed by a professional physicist and presented in a beautifully designed html format.

Problem 9.7.3 describes the motion of a rod in a plane and requires finding the acceleration of point B of the rod with given parameters: acceleration of point A at a given time aA = 1 m/s², angular velocity ? = 2 rad/s, angular acceleration ?=2 rad/s², and also the length of the rod AB = 1 m.

Solving the problem consists of a step-by-step description of the solution process and detailed calculations that will help you understand the basics of physics and learn how to solve similar problems.

The acceleration of point A is decomposed into two components: the projection of acceleration onto the axis AB and the projection of acceleration onto the axis perpendicular to AB. Since the rod moves in a plane, the acceleration of point B is directed along the rod, that is, perpendicular to the AB axis. This means that the projection of the acceleration of point B onto the AB axis is 0 m/s².

Then the acceleration of point B can be found using the formula: аB = аАcosθ - r?²sinθ = 1 m/s²cos90° - 1 m·(2 rad/s)²sin90° = 0 m/s² - 5 m/s² = -5 m/s² .

Answer: aB = -5 m/s².

The digital product is presented in the form of an HTML page, designed in a pleasant and concise style, which makes it convenient and understandable for reading and studying. You can purchase this product on our website and get instant access to useful information that will help you improve your knowledge of physics and prepare for success in exams.

***

Solution to problem 9.7.3 from the collection of Kepe O.?. consists in determining the acceleration of point B of rod AB, if the acceleration of point A is known, as well as the angular velocity and angular acceleration of the rod.

To solve the problem, you need to use the formula to calculate the acceleration of a point on a rigid body moving in a circle:

a = r * α + ω² * r,

where a is the acceleration of the point, r is the radius of the circle, α is the angular acceleration, ω is the angular velocity.

In this problem, point A moves in a straight line, and point B moves in a circle with a radius of 1 m (the length of the rod). Therefore, to calculate the acceleration of point B, it is necessary to take only the second term:

aB = ω² * r = ω² * AB = 2² * 1 = 4 м/с².

Thus, the acceleration of point B of rod AB is 4 m/s².

***

1. Solution of problem 9.7.3 from the collection of Kepe O.E. is a great digital product for math students and teachers.
2. I received great help in my studies thanks to the solution to problem 9.7.3 from the collection of Kepe O.E. electronic.
3. This digital product allowed me to quickly and easily understand how to solve problem 9.7.3 from the collection of Kepe O.E.
4. I recommend the solution to problem 9.7.3 from the collection of O.E. Kepe. in electronic form to everyone who is looking for quality material for studying.
5. Solution of problem 9.7.3 from the collection of Kepe O.E. in electronic form is a convenient and accessible way to obtain the necessary knowledge.
6. A very useful digital product that helped me successfully solve problem 9.7.3 from the collection of Kepe O.E.
7. Thank you for solving problem 9.7.3 from the collection of Kepe O.E. electronically, it really helped me in my studies.

Peculiarities:

Solving problems from the collection of Kepe O.E. in digital format - it is convenient and saves time.

Excellent scanning quality and clear font in the digital version of Kepe O.E.

Quick access to any task from the collection of Kepe O.E. - just open the file.

The design and structure of the problem book in digital form allow you to quickly find the right tasks.

Possibility of using keyword search in the digital version of Kepe O.E. very convenient.

All solutions of problems from the collection of Kepe O.E. in digital format are given with detailed explanations and justifications.

Digital version of the problem book Kepe O.E. allows you to save space on the shelf and not take up extra space in the backpack.

The ability to quickly copy tasks from the digital version of the Kepe O.E. simplifies training.

Digital format for solving problems from the collection of Kepe O.E. allows you to easily and quickly take notes and notes.

In the digital version of the problem book Kepe O.E. you can quickly and easily navigate between different tasks and chapters.