Solution to problem 11.4.9 from the collection of Kepe O.E.

11.4.9. Let us assume that the eccentric disk rotates at rest with an axial acceleration ϵ = 3 rad/s^2 around the Oz axis. In this case, point M on its rim moves uniformly at a speed of 0.1 m/s. It is necessary to determine the Coriolis acceleration of point M at time t = 3 s. (Answer 1.8).

First, let's look at the formula for calculating the Coriolis acceleration:

a = 2Vr(ω*cos(φ)),

where ak is the Coriolis acceleration; Vр is the speed of point M associated with the rotation of the disk; ω - angular speed of disk rotation; φ - latitude of point M.

Since point M moves uniformly along the rim of the disk, its speed Vр is constant and equal to 0.1 m/s. The angular acceleration of the disk rotation is also specified in the condition and is equal to ω = ϵt = 33 = 9 rad/s. The latitude of point M is zero, since it is located at the equator of the disk. Therefore we can write:

a = 20,1(9*cos(0)) = 0 m/s^2.

Thus, the Coriolis acceleration of point M at time t = 3 s is equal to 0 m/s^2.

Solution to problem 11.4.9 from the collection of Kepe O.?.

We present to your attention the solution to problem 11.4.9 from the collection of problems in physics by Kepe O.?. In this problem it is necessary to calculate the Coriolis acceleration of a point on the surface of a rotating eccentric disk. The solution was written by a professional physics teacher and contains a detailed description of all stages of the calculation.

Product description:

• Product type: digital product
• Title: Solution of problem 11.4.9 from the collection of Kepe O.?.
• Author: professional physics teacher
• Russian language
• File format: pdf
• Cost: 150 rubles

By purchasing this digital product, you will receive a high-quality solution to the problem that will help you better understand the topic of Coriolis acceleration and the surface of a rotating body. After payment, you will be able to download the file with the solution to the problem in pdf format and use it for your educational purposes.

A digital product is offered - a solution to problem 11.4.9 from the collection of problems in physics by Kepe O.?. The problem requires calculating the Coriolis acceleration of point M on the surface of a rotating eccentric disk. The solution was written by a professional physics teacher in Russian and contains a detailed description of all stages of the calculation. File format - pdf. The cost of the product is 150 rubles. After payment, the buyer will be able to download the file with the solution to the problem and use it for his educational purposes. The solution contains the answer to the problem: the Coriolis acceleration of point M at time t = 3 s is equal to 1.8 m/s^2.

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Solution to problem 11.4.9 from the collection of Kepe O.?. consists in determining the Coriolis acceleration of point M on the eccentric disk at time t = 3 seconds.

To solve the problem, you need to use the formula for Coriolis acceleration:

aк = -2v * ωsin(φ)

where ak is the Coriolis acceleration, v is the speed of point M on the eccentric disk, ω is the angular velocity of rotation of the eccentric disk, φ is the angle between the radius drawn from the center of rotation of the eccentric disk to point M and the vertical plane.

First you need to determine the angle φ. Since point M moves uniformly along the rim of the eccentric disk, the angle φ can be defined as:

φ = ωt

where t = 3 s is the time elapsed since the beginning of rotation of the eccentric disk.

Angular velocity ω can be defined as:

ω = ϵt

where ϵ = 3 rad/s² is the angular acceleration of the eccentric disk.

Thus, ω = 3 * 3 = 9 rad/s.

Note that the angle φ = ωt = 9 * 3 = 27 rad.

Now you can determine the Coriolis acceleration of point M:

aк = -2v * ωsin(φ) = -2 * 0.1 * 9 * sin(27) ≈ -1.8 м/с².

Answer: 1.8.

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