Exam01 - PHYS 3113 – Analytical Mechanics Fall...

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Unformatted text preview: PHYS 3113 – Analytical Mechanics Fall 2011 Exam 1 Problem 1.1 The position vector of a particle is given by: ˆ ˆ r ( t ) = i b cos(ωt ) + ˆc sin(ωt ) + kv 0 t j where b, c, and v0 are constants. a) Compute the velocity and acceleration vectors for this particle. b) Compute the magnitude of the acceleration. € c) Is the acceleration constant? d) Describe the motion of this particle. Problem 1.2 What are the two conditions that must be satisfied for a force to be conservative? Problem 1.3 2 32 Consider the potential function: V ( x ) = x 3 − 8 x + 3 3 a) Compute the location of the local minimum, xmin, and the local € maximum, xmax, of this potential. b) What condition must the kinetic energy of a particle (of mass m) at xmin satisfy so that the particle oscillates about xmin (it is confined to the local potential well?) c) Find the velocity as a function of position for a particle of mass m with initial velocity v0 at x = 0. d) If a particle of mass m was released from x = 0 with zero initial velocity, compute its other turning point. ...
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