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HW3_prob1_particleonfiber - Particle Suspended on a Sti...

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Particle Suspended on a Sti ff Fiber next to an Attractive Wall Because the motion of the mass point is con fi ned to a plane and the fi ber has constant length L , the system has only one degree of freedom. In plane polar coordinates a suitable generalized coordinate is the polar angle θ , which will be measured from a y axis that points downwards. I’ll imagine that the charged wall is to the left of the particle, so that the constant force F acts in the negative x direction (to the left), and θ will be positive when the mass point is displaced to the left from its rest position. Note that x = 0 corresponds to the particle hanging vertically ( θ = 0 ). The kinetic energy of the mass point is then T = m 2 ( · x 2 + · y 2 ) . (1) In the polar coordinate system we have x = L sin θ , y = L cos θ . (2) The minus sign is needed because θ is positive for displacements in the negative x direction. From this it follows that · x = L · θ cos θ , · y = L · θ sin θ , (3) and Eq.(1) can then be written as T = 1 2 mL 2 · θ
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