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8 2a lkx 2 cx415cm 3 i36 knm 015 could be

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Unformatted text preview: , in the form of kinetiC energy imparted toa mass, for example, it is referred to as stored energy. 4(220 Njm)(0.15 mJ2 + m)4 = 2.93 J. Since this energy Problem 16. The force on a particle is given by F=Aljx2, where A is a positive constant. (a) Find the potential energy difference between two points and X2, where Xl >X2. (b) Show that the potential energy difference remains finite ,even when Xl -+ 00. Xl -! = Solution (a) U(X2) - U(XI) = A --. X2 (1 1) Xl l x2 Xl (b) For Xl -+ 00, U(X2) - U(oo) A/X2. In tpis case, it makes sense to define the zero of potential energy at infinity, U(oo) = 0, so U(x) = A/x. '. = A 8 Problemi8 Solution. Problem 17. A particle moves along the :z;-axisunder the influence of a force F ax2 + b, where a and bare constants. Find its potential energy as a function of position, taking U = 0 at X = O. = Problem 19. The force exerted by a rubber band is given approximately by Solution Equation 8-2a, with U(O) = 0, gives U(x) = -l x Fx dx' = -l x (ax,2 + b)dx' i+ X i2] [T- (i+X)2 F=Fo ' = -~ax3 Problem - bx. where i is the unstretched length, and Fo is a constant. Find the potential energy of the rubber band as a function o...
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