Question

Как относятся скорости точек плоской фигуры, если известно положение МЦС? Скорость точки А равна 5 м/с. Чему равна скорость точки В, которая ближе к МЦС в 2 раза?

Answer 1

Ответ: 2,5м/с

Объяснение:

Дано:

Va=5м/с

Rb=Ra/2

========

Vb-?

Vb=ω*Rb=Va/Ra*Rb=5*Ra/2Ra=5/2=2,5м/с

Answer 2

Understanding the Relationship Between Velocities of Points in a Plane Figure with Known Center of Mass Position

When the position of the center of mass (CM) of a plane figure is known, the relationship between the velocities of points within the figure can be determined.

Given: - Velocity of point A = 5 m/s

To find: - Velocity of point B, which is closer to the CM and is 2 times closer to it than point A

Solution:

The relationship between the velocities of points in a plane figure and the position of the center of mass can be determined using the principle of conservation of linear momentum. According to this principle, the total linear momentum of a system remains constant if no external forces act on it.

The velocity of a point in a plane figure is directly proportional to its distance from the center of mass. This relationship can be expressed as:

v = ω × r

Where: - v = velocity of the point - ω = angular velocity of the system - r = distance of the point from the center of mass

In this case, the velocity of point B can be calculated using the relationship between the velocities and distances from the center of mass.

Given that point B is 2 times closer to the center of mass than point A, the velocity of point B can be calculated as follows:

v_B = v_A × (r_A / r_B)

Where: - v_B = velocity of point B - v_A = velocity of point A - r_A = distance of point A from the center of mass - r_B = distance of point B from the center of mass

Calculation:

Given: - Velocity of point A (v_A) = 5 m/s - Distance of point B from the center of mass (r_B) = 2 * Distance of point A from the center of mass (r_A)

Using the formula: v_B = v_A × (r_A / r_B)

Substituting the given values: v_B = 5 m/s × (r_A / (2 * r_A))

Simplifying: v_B = 5 m/s × (1 / 2) = 2.5 m/s

Conclusion:

Therefore, the velocity of point B, which is closer to the center of mass and is 2 times closer to it than point A, is 2.5 m/s.