Solution to problem 11.4.7 from the collection of Kepe O.E.

11.4.7. Solution of the problem of the movement of a point on plate ABC

Plate ABC rotates around the vertical axis Oz according to the law φ = 5t2, and point M on its side AC moves according to the equation AM = 4t3. It is necessary to determine the Coriolis acceleration of point M at time t = 0.5 s.

Solution: To determine the Coriolis acceleration, we use the formula: aк = -2vрω, where vр is the speed of point M relative to the plate ABC, and ω is the angular velocity of the plate.

First, let's find the speed of point M. To do this, let's differentiate the equation AM = 4t3 with respect to time: v = d(4t3)/dt = 12t2.

Since point M moves along the AC side of the ABC plate, its speed vр is directed tangentially to this side and is equal to the projection of the velocity v onto the tangent: vр = v cos α, where α is the angle between the vectors v and the Ox axis.

Let's find the angle α. To do this, we will use the geometric relationship between the sides of the triangle AMC: cos α = AC/AM = 1/√(1 + (CM/AM)²).

Since AM = 4t3, and CM is equal to the segment drawn from point M to the axis of rotation, then CM = AC sin φ, where φ is the angle of rotation of the plate. Taking into account the law of rotation of the plate φ = 5t2, we obtain: SM = AC sin 5t2.

Thus, cos α = 1/√(1 + (AC sin 5t2/4t3)²).

Let's find the angular velocity of the plate. To do this, we differentiate the law of plate rotation with respect to time: ω = dφ/dt = 10t.

Now we can calculate the speed of point M relative to the plate: vр = 12t2 cos α.

It remains to calculate the Coriolis acceleration using the formula: aк = -2vрω = -24t(AC sin 5t2/4t3)².

At time t = 0.5 s we get: ak = -240,5(AC sin 5*(0,5)²/4*(0,5)³)² = -15.

Thus, the Coriolis acceleration of point M at time t = 0.5 s is equal to 15.

Solution to problem 11.4.7 from the collection of Kepe O.?.

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This solution describes in detail the movement of a point on plate ABC, which rotates around the vertical axis Oz according to a given law. In addition, you will find detailed calculations and formulas necessary to solve the problem, as well as explanations for each step of the solution.

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The digital product is a solution to problem 11.4.7 from the collection of problems in physics by Kepe O.?. This problem describes the movement of point M along the side AC of plate ABC, which rotates around the vertical axis Oz according to a given law. At time t = 0.5 s it is necessary to determine the Coriolis acceleration of point M.

The solution to the problem contains a detailed description of the movement of point M on plate ABC, as well as calculations and formulas necessary for its solution. In addition, each step of the solution is provided with explanations.

To solve the problem, it is necessary to find the velocity of point M relative to the plate ABC, as well as the angular velocity of the plate. Then, using the formula ak = -2vрω, calculate the Coriolis acceleration of point M at time t = 0.5 s.

Purchasing this digital product will allow you to study the solution to the problem anywhere and at any time, and also use it as additional material for preparing for exams or self-study.

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Problem 11.4.7 from the collection of Kepe O.?. consists in determining the Coriolis acceleration of a point M moving along the AC side of the ABC plate, which rotates around the Oz axis according to the law φ = 5t2. The equation AM = 4t3 is given, which describes the motion of point M. It is necessary to find the Coriolis acceleration of this point at time t = 0.5 s.

Coriolis acceleration is the inertial component of acceleration that occurs when a point moves in a reference frame associated with a rotating body. It is calculated by the formula:

aк = -2ω × V,

where ω is the angular velocity of rotation of the body, V is the speed of a point in the reference system associated with the rotating body, and the sign “-” means vector multiplication.

In this problem, it is necessary to calculate the Coriolis acceleration at time t = 0.5 s. To do this, you need to find the values ​​of the angular velocity ω and the velocity of point M V at this moment in time, substitute them into the formula and calculate the result. The answer to the problem is 15.

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