Work, Power and Energy

Question : 3

Total: 30

Given figures are examples of some potential energy functions in one dimension. The total energy of the particle 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 givenenergy. 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 relevant.

Solution:

Total energy of an object is given by
E = P.E. + K.E. ⇒ K.E. = E – P.E.
Kinetic energy can never be negative. The object can exist in the region, which is K.E. would become positive.
(i) In the region between x=0‌to‌x=a, P.E. is zero. Therefore kinetic energy in this region is positive. However, in the region x > a, the potential energy has a value V0>E, therefore kinetic energy becomes negative.
Hence the object cannot exist in this region x > a.
(ii) The object cannot be present in any region because potential energy (V0)>E in every region.
(iii) In this regions between x=0‌to‌x=a and x>b, the potential energy (V0) is greater than total energy E of the object. Therefore kinetic energy becomes negative the object cannot be present in the x<a and x>b.
(iv) The object cannot exist in the region –

<x<–

and

<x<

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