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Given in figure are examples of some potential energy functionsin one dimension. The total energy of the aprticle is indicated by a cross on the ordinate axis . In each case , specify the regions ,if any , in whichthe particlecannotbe foundfor the given energy .Also , indicatethe minimum totalenergythe particle must havein each case . Thinkof simple physical contexts for which these potential energyshapes are relvant . |
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Answer» Solution :We knowthat total energy , `E = K+V `where V = potential energy , K = kinetic energy ` :. K = E - V ` and kinetic energy (K) can never be negativeIf K is negative, the object cannot exist in the region . (a) In the region between x = 0 and x = a potential energy is ZERO . So , kineticenergy is positive .In the region `x gt a ` the potentialenergy has a valuegreaterthan E . So, kinetic energy has a value greater than E . So kinetic energy will be negative in this region . THUS , the particle cannot be present in the region`x gt a ` .the minimum total energythat the particlecan havein this case is zero . (b) In graph (b) potentail energy `gt` the total energy and HENCE kinetic energy` [ K = E-V]`WOULD be negative . Thus , object cannot be present in any region of the graph . (c ) Here x = 0 to x = 0 and `x gt b ` the potentialenergy is more than total energy, so kineticenergyis negative. the particle cannot existin theseportions . (d) The object cannot exist in the region between `x = - b/2 to x = - a/2 and x = - a/2" to " x = -b/2 ` .Because in this region potential energy `gt ` total energy . |
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