Given in figure are examples of some potential energy functions in 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 which the particle cannot be found for the given energy .Also , indicate the minimum total energy the particle must have in each case . Think of simple physical contexts for which these potential energy shapes are relvant .

Explanation

We know that total energy ,
`E = K+V `where V = potential energy ,
K = kinetic energy
` :. K = E - V `
and kinetic energy (K) can never be negative If 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 , kinetic energy is positive .In the region `x gt a ` the potential energy has a value greater than 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 energy that the particle can have in 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 potential energy is more than total energy , so kinetic energy is negative . the particle cannot exist in these portions .
(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 .