Find the tension in the string at time t

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Reference no: EM131383430

A particle P is connected to one end of a light inextensible string which passes through a small hole O in a smooth horizontal table and extends below the table in a vertical straight line. P slides on the upper surface of the table while the string is pulled downwards from below in a prescribed manner. (Suppose that the length of the horizontal part of the string is R(t) at time t.)

Take θ, the angle between O P and some fixed reference line in the table, as generalised coordinate and obtain Lagrange's equation.

Show that θ is a cyclic coordinate and find (and identify) the corresponding conserved momentum p_θ. Why is the kinetic energy not conserved? If the constant value of p_θ is m L, find the tension in the string at time t.

Reference no: EM131383430

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