Solution to problem 11.2.15 from the collection of Kepe O.E.

11.2.15 Consider a square plate with a side of 6 m, rotating around axis 001 with angular velocity ? = 3 rad/s. On one of the sides of the plate there is a point M, which moves at a constant speed vr = 4 m/s. It is necessary to determine the absolute speed of point M in the position indicated in the figure.

Let's move on to solving this problem. Let us express the absolute speed of point M in terms of the relative speed and the speed of motion of the plate. The relative velocity vector of point M relative to the plate is directed tangentially to the side of the square and is equal to vr. The speed of movement of the plate can be expressed as the vector product of the angular velocity of the plate and the radius vector of point M relative to the axis of rotation of the plate. The radius vector is directed along the side of the square and is equal to half its length. Thus, the speed of plate movement is (6/2) * ? = 9 m/s.

Let us depict the velocity vectors of point M relative to the plate and the motion of the plate in the figure. Let's add these vectors and find the modulus of the resulting vector sum. We get: |V| = √(vr² + vpl² + 2 * vr * vpl * cos α), where α is the angle between the velocity vectors. After substituting the known values, we obtain |V| = 17.5 m/s.

Thus, the absolute speed of point M in the position indicated in the figure is 17.5 m/s.

Solution to problem 11.2.15 from the collection of Kepe O.?.

We present to your attention the solution to problem 11.2.15 from the collection of Kepe O.?. - a digital product that will help you successfully complete a physics task.

In this solution, we considered a square plate with a side of 6 m, rotating around axis 001 with an angular velocity ? = 3 rad/s, and point M moving along one of the sides of the plate at a constant speed of 4 m/s. We outlined in detail the method for finding the absolute speed of point M, provided the necessary formulas and calculated the value of the speed. As a result, we received the answer: the absolute speed of point M in the position indicated in the figure is 17.5 m/s.

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We offer a digital product “Solution to problem 11.2.15 from the collection of Kepe O.?”, which will help you successfully cope with the problem in physics. This solution describes a square plate with a side of 6 m, rotating around axis 001 with an angular velocity ? = 3 rad/s, and point M moving along one of the sides of the plate at a constant speed of 4 m/s. The solution contains a detailed method for finding the absolute speed of point M, the necessary formulas and the calculated speed value, which is 17.5 m/s. The product is presented in a beautiful html design, which makes it attractive and easy to use. By purchasing this product, you can improve your knowledge of physics and successfully cope with this task.

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The product is the solution to problem 11.2.15 from the collection of Kepe O.?. The task is to determine the absolute speed of point M on a square plate, which rotates around axis 001 with angular speed ? = 3 rad/s, when point M moves along the side of the plate at a speed vr = 4 m/s. To solve the problem, it is necessary to use a formula to determine the absolute speed of a point moving relative to a rotating coordinate system.

To solve the problem, the formula V = V0 + w x r is used, where V is the absolute speed of the point, V0 is the speed of the point in a fixed coordinate system, w is the angular velocity of rotation of the coordinate system, r is the radius vector of the point relative to the center of rotation of the coordinate system.

To solve the problem, you need to determine the radius vector of point M relative to the center of rotation of the coordinate system. Since the sides of the square are equal to 6 m, the radius vector of point M is equal to 3 m. It is also known from the problem conditions that the angular velocity of rotation of the coordinate system is equal to 3 rad/s, and the speed of point M in a fixed coordinate system is equal to 4 m/s.

Substituting the known values ​​into the formula, we get: V = 4 + 3 x 3 = 13 m/s.

Answer: the absolute speed of point M in the position indicated in the figure is 13 m/s.

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