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# written6 - Homework 6 Due 1 Consider a system where a...

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Homework 6 Due February 20 2007 1) Consider a system where a particle of mass m is constrained to move along the x-axis and the potential energy function of the conservative force acting on the particle (which is the only force in the system) is: | | ) ( x C x U = Where C is a positive constant. (NB: this is not the force law of a spring. It is similar to the force law for the force between two quarks in a meson) (a) What are the SI units of C ? (b) What is the force on the particle as a function of position (hint consider +ve and – ve values of x separately) (c) Make a schematic graph of the potential energy as a function of x. (d) Let E>0 be the mechanical energy of the system. On the graph in part c, draw a horizontal line at E and indicate where the turning point(s) are for this mechanical energy. Give an algebraic expression for the position of the turning point(s) in terms of E and C. Also indicate on the graph which regions of the x-axis are excluded to the motion of the particle. (e) Describe the motion of the particle. (f) Suppose that the particle is released at rest at the point x=+A. Write an equation for the position as a function of time for the particle as it moves from x=A to x=0. How long does the particle take to return again to x=+A (the period T)? Sketch a graph of the position as a function of time for the time period t=0 to t=2T.

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written6 - Homework 6 Due 1 Consider a system where a...

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