Solution to problem 20.3.6 from the collection of Kepe O.E.

This problem considers a conservative system with potential energy P, which depends on two generalized coordinates: s and φ. The formula for calculating potential energy is P = (18 + 24s) cosφ.

It is necessary to determine the generalized force corresponding to the coordinate s at the moment of time when s = 0.5 m and angle φ = 2 rad. To do this, it is necessary to find the derivative of the potential energy with respect to the coordinate s for given values ​​of s and φ, that is:

F = -dP/ds = -24cosφ

Substituting the values ​​s = 0.5 m and φ = 2 rad, we get:

F = -24cos(2 rad) = -9.99

Thus, the generalized force corresponding to the coordinate s, at the moment of time when s = 0.5 m and the angle φ = 2 rad, is equal to -9.99.

Solution to problem 20.3.6 from the collection of Kepe O.?.

This digital product is a solution to problem 20.3.6 from the collection of problems by Kepe O.?. in theoretical mechanics.

The solution to the problem is presented in the form of a detailed description, which will allow you to understand the basic principles and laws used in solving it.

By purchasing this product, you will receive:

• Detailed solution to problem 20.3.6 from the collection of Kepe O.?. in a convenient digital format;
• A clear description of the principles and laws used in the decision;
• The ability to easily and quickly repeat the solution to a problem and deepen your knowledge of theoretical mechanics.

This digital product will be useful to both students and teachers involved in theoretical mechanics and its application in various fields of science and technology.

This digital product is a solution to problem 20.3.6 from the collection of problems by Kepe O.?. in theoretical mechanics. The problem considers a conservative system with potential energy depending on two generalized coordinates s and φ. It is necessary to determine the generalized force corresponding to the coordinate s at the moment of time when s = 0.5 m and angle φ = 2 rad.

To solve the problem, it is necessary to find the derivative of the potential energy with respect to the coordinate s for given values ​​of s and φ. The resulting value of the derivative will be the desired generalized force. Substituting the values ​​s = 0.5 m and φ = 2 rad, we find that the generalized force corresponding to the coordinate s at the moment of time when s = 0.5 m and the angle φ = 2 rad is equal to -9.99.

By purchasing this digital product, you will receive a detailed solution to Problem 20.3.6 in a convenient digital format, a clear description of the principles and laws used in the solution, as well as the ability to easily and quickly repeat the solution to the problem and deepen your knowledge of theoretical mechanics. This product will be useful to both students and teachers involved in theoretical mechanics and its application in various fields of science and technology.

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Solution to problem 20.3.6 from the collection of Kepe O.?. requires determining the generalized force corresponding to the coordinate s at the moment of time when s = 0.5 m and angle φ = 2 rad. To do this, you need to use the generalized force formula:

Q_s = -dP/ds

where P is the potential energy of the conservative system, s is the generalized coordinate.

The first step is to calculate the derivative of the potential energy with respect to the s coordinate:

dP/ds = 24*cos(φ)

Then, substituting the values ​​of s and φ, we get:

dP/ds = 24*cos(2 rad) = -9.59 J/m

And finally, the generalized force Q_s at the moment of time when s = 0.5 m and φ = 2 rad will be equal to:

Q_s = -dP/ds = -(-9.59) = 9.59 J/m

Answer: 9.59 (rounded to two decimal places - 9.99).

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