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Unformatted text preview: Physics 325, Fall 2010 Homework Assignment #4 Due Thursday 23 September at 11:15 am Note that this homework is not due until a couple of days after the quiz will be given in Discussion Sessions. However, these three problems are all constitute review for the quiz. See the last page for the formula sheet so that you know what you will be provided with the quiz. 1) (15 points) A particle of mass m is subjected to the force ~ F ( x, y, z ) = 9 x 2 y 2 z- 2 xyz 3 x + 6 x 3 yz- x 2 z 3 y + 3 x 3 y 2- 3 x 2 z 2 y z a) Show that the curl of this force field vanishes everywhere which means it is a conser- vative force. b) Obtain an expression for the potential energy of this force U ( x, y, z ) with the property that U (0 , , 0) = 0 by computing the work done by the force ~ F when the particle travels from the origin to ( x, y, z ) along a suitable path. c) A bead of mass m slides on a frictionless, straight wire which runs from the origin (0 , , 0) to the point ( d, d, d ) where d > 0. The force vector field described above acts on it. The beads initial speed is v . How fast is the bead traveling when it reaches the end....
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