Solution to problem 20.2.1 from the collection of Kepe O.E.

20.2.1 Potential energy of a mechanical system P = 15?2, where y is in rad.

It is necessary to find the generalized force corresponding to the generalized coordinate ? at the moment in time when the angle ? = 90o.

Answer: -47.1

The potential energy of the mechanical system is given P = 15?2, where y is in rad. It is necessary to find the generalized force corresponding to the generalized coordinate ? at the moment in time when the angle ? = 90o. Answer: -47.1.

Solution to problem 20.2.1 from the collection of Kepe O.?.

This digital product is a solution to problem 20.2.1 from the collection of Kepe O.?. in mechanics. The solution was completed at a high level by an expert in the field and is guaranteed to help students and teachers in studying the theory and practice of mechanics.

This digital product is a solution to problem 20.2.1 from the collection of Kepe O.?. in mechanics. The problem gives the potential energy of the mechanical system P = 15?2, where y is in rad, and it is required to find the generalized force corresponding to the generalized coordinate ? at the moment in time when the angle ? = 90o. The solution is made by an expert in the field and is guaranteed to help students and teachers in studying the theory and practice of mechanics. Answer to the problem: -47.1.

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Problem 20.2.1 from the collection of Kepe O.?. is formulated as follows: an expression is given for the potential energy of the mechanical system P = 15?2, where y is in rad. It is required to determine the generalized force corresponding to the generalized coordinate ? at the moment of time when the angle ? = 90°.

To solve the problem, it is necessary to calculate the derivative of potential energy with respect to the generalized coordinate ? and substitute the value ? = 90°. Thus, the generalized force will be defined as F = -dП/d?, where d/d? denotes differentiation with respect to the generalized coordinate ?.

Let's calculate the derivative of potential energy with respect to the generalized coordinate ?:

dП/d? = d/d? (15?2) = 30?

Substituting the value? = 90°:

F = -dП/d? = -30° × (π/180°) = -0.5236 rad/s × 15 = -7.8548 Nm

The answer is rounded to one decimal place:

F = -7.9 Nm

So, the generalized force corresponding to the generalized coordinate ? at the moment in time when the angle ? = 90°, equal to -7.9 Nm.

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