Solution to problem 20.6.1 from the collection of Kepe O.E.

Task: from the differential equation of motion of the system corresponding to the generalized coordinate x2, find the acceleration x2 at the moment of time when the acceleration x1 is 5 m/s2 and the generalized force Qx2 is 2.5 N. The kinetic energy of the system is determined by the formula T = 0.25x12 + 0.25(x12 + x1x2 + x22).

Answer:

The differential equation of motion of the system in generalized coordinates has the form:

d/dt (∂T/∂x˙i) - (∂T/∂xi) = Qi, where i = 1, 2.

Let us calculate the partial derivatives of the kinetic energy of the system:

∂T/∂x˙1 = 0,5x1 ∂T/∂x˙2 = 0,5(x1 + x2)

∂T/∂x1 = 0,5x1 ∂T/∂x2 = 0,5x2 ∂T/∂x1˙∂x2 = ∂T/∂x2˙∂x1 = 0,25

Let us substitute the obtained values ​​into the differential equation of motion of the system:

d/dt (0,5x1) - 0,5x1 = 0 d/dt (0,5(x1 + x2)) - 0,5x1 = 2,5

Considering that the acceleration x1 is 5 m/s2, we get:

0,5x1¨ - 0,5x1 = 0 0,5(x1¨ + x2¨) - 0,5x1 = 2,5

Let us express x1¨ from the first equation and substitute it into the second equation:

x1¨ = x1/2 0.5(x1/2 + x2¨) - 0.5x1 = 2.5 x2¨ = 2.5 - x1/2 = 2.5 - 5/2 = 2.5

Answer: the acceleration x2 at the moment of time when the acceleration x1 is 5 m/s2 and the generalized force Qx2 is 2.5 N is equal to 2.5 m/s2.

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This digital product is a solution to problem 20.6.1 from a collection of problems in physics, authored by Kepe O.?. The problem requires finding the acceleration x2 at the time when the acceleration x1 is 5 m/s2 and the generalized force Qx2 is 2.5 N.

The solution to the problem is presented in the form of a beautifully designed html document, which allows you to conveniently and quickly familiarize yourself with the problem conditions and the resulting solution. All information is presented in an accessible and understandable manner, which makes this product an ideal choice for those who want to quickly and efficiently prepare for exams or improve their knowledge in the field of physics.

The solution to the problem is based on the differential equation of motion of the system in generalized coordinates and the calculation of partial derivatives of the kinetic energy of the system. After substituting the known values ​​into the differential equation, the acceleration x2 was found, which is equal to 2.5 m/s2.

By purchasing this digital product, you not only get a solution to a specific problem, but also the opportunity to better understand the principles of physics and improve your problem-solving skills. In addition, beautiful html design makes using the product more convenient and enjoyable!

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The product is the solution to problem 20.6.1 from the collection of Kepe O.?. The problem is to determine the acceleration x2 of the system at the moment of time when the acceleration x1 is equal to 5 m/s2, and the generalized force Qx2 is equal to 2.5 N. To solve the problem, it is necessary to use the differential equation of motion of the system corresponding to the generalized coordinate x2, as well as an expression for the kinetic energy of the system. As a result, we get the answer 2.5.

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