Solution to problem 7.2.8 from the collection of Kepe O.E.

Solution to problem 7.2.8 from the collection of Kepe O..

This digital product is a solution to problem 7.2.8 from the collection of problems on theoretical mechanics by Kepe O..

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This product is a solution to problem 7.2.8 from the collection of problems on theoretical mechanics by the author Kepe O.?. The task is to determine the speed of the slider B at time t = 4 s, if it is known that the position of the crank is determined by the angle φ = 0.5 t, and OA = AB = 1.5 m.

The solution to the problem is presented in the form of a beautifully designed html page, which makes the material easy to read and understand. The solution to the problem describes in detail the process of solving it, provides all the necessary formulas and calculations, which will help you understand and master this material.

By purchasing this product, you receive a high-quality solution to the problem, performed by an experienced specialist in the field of theoretical mechanics, as well as a convenient and practical format for presenting the material. This digital product is a convenient and accessible resource for students and professionals studying theoretical mechanics and preparing for exams and testing.

Answer to the problem: the speed of slider B at time t = 4 s is equal to -1.36 m/s.

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Solution to problem 7.2.8 from the collection of Kepe O.?. consists in determining the speed of the slider B at time t = 4 s, if it is known that the position of the crank is determined by the angle φ = 0.5 t and OA = AB = 1.5 m.

To solve this problem it is necessary to use the laws of kinematics. It is known that the speed of the slider B can be determined as the derivative of its coordinates with respect to time. Thus, it is necessary to find the derivative of the function of the coordinates of the slider B with respect to time at time t = 4 s.

To do this, you must first determine the angle of rotation of the crank at time t = 4 s. Based on the formula φ = 0.5 t, we obtain:

φ = 0.5 * 4 = 2 rad

Then you can determine the coordinates of point B at time t = 4 s. Since OA = AB = 1.5 m, the coordinates of point B will be equal to:

x = OA * cos(φ) = 1.5 * cos(2) ≈ -0.673 m y = OA * sin(φ) = 1.5 * sin(2) ≈ 1.34 m

Next, you need to find the derivative of x with respect to time t. Using the formula for the derivative of a product of functions, we obtain:

Vx = dx/dt = d(ОА * cos(φ))/dt = -ОА * sin(φ) * dφ/dt

The value of dφ/dt can be found by taking the derivative of the function φ = 0.5 t with respect to time:

dφ/dt = 0,5

Thus we get:

Vx = -OA * sin(φ) * dφ/dt = -1.5 * sin(2) * 0.5 ≈ -1.36 m/s

Answer: the speed of slider B at time t = 4 s is approximately -1.36 m/s.

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